                                    US-EPA
Approach to Assessing Non-cancer Health Effects from Formaldehyde and Benefits from Reducing Non-cancer Health Effects as a Result of Implementing Formaldehyde Emission Limits for Composite Wood Products



                               Table of Contents
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Title							          	                		      Page
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Section 1: Background and Scope 						4

1.0 Background										4
1.1 Scope of the Document									5

Section 2: Non-cancer Health Effects -- 
Derivation of Concentration-Response Functions 		         6

2.0 Background on the Identification of Non-Cancer Health Effects		            6
2.1 Sensory Irritation								            7
2.1.1 Sensory Irritation: Background						                        7
2.1.2 Sensory Irritation: Relevant Studies					          	            7
2.1.3 Sensory Irritation:
       Derivation of Concentration-Response Relationship for Eye Irritation                    8
2.1.4 Sensory Irritation: Discussion of Uncertainties			                       14
2. 2 Asthma 										           16
2.2.1 Asthma: Background							                       16
2.2.2 Asthma: Relevant Studies						                       16
2.2.3 Asthma: Derivation of Concentration-Response Relationship		                       17
2.2.4 Asthma: Discussion of Uncertainties					                       19
2.3 Female Reproductive Toxicity							           21
2.3.1 Female Reproductive Toxicity: Background				                       21
2.3.2 Female Reproductive Toxicity: Relevant Studies			                       21
2.3.3 Female Reproductive Toxicity:	
	Derivation of Concentration-Response Relationship		                                   22
2.3.4 Female Reproductive Toxicity: Discussion of Uncertainties		                       25
2.4 References									           30

Section 3: Benefits Assessment Approach				        33
3.1 Introduction/Background							           33
	3.1.1 General Model								           33
	3.1.2 Simplified Model							           34
3.2 Sensory Irritation 								           37
	3.2.1 Monetization								           37
	3.2.2 Annual approach							           39
	3.2.3 Example calculation						                       40
	3.2.4 Discussion of uncertainties						           46
3.3 Asthma incidence								           47
	3.3.1 Monetization								           47
	3.3.2 Annual approach							           52
	3.3.3 Example calculation						                       58
	3.3.4 Discussion of uncertainties						           62
3.4 Reduced Fertility									           62	
	3.4.1 Monetization								           62
	3.4.2 Annual Approach							           66
	3.4.3 Example Calculation							           68
	3.4.4 Discussion of uncertainties						           71
3.5 References 									           74






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Section 1: Background and Scope 

1.0 Background

In March 2008, the Sierra Club and other organizations and individuals petitioned EPA under Section 21 of the Toxic Substances Control Act (TSCA).  The petitioners requested that EPA use TSCA Section 6 to adopt a newly-promulgated California Air Resources Board (CARB) Airborne Toxic Control Measure (ATCM) as a national standard for formaldehyde emissions from hardwood plywood, particleboard, and medium-density fiberboard products.  The petitioners expressed particular concern over the levels of formaldehyde found in emergency housing provided for Hurricane Katrina survivors, but noted that there are no federal regulations on formaldehyde emissions from composite wood products other than those applicable to manufactured housing regulated by the U.S. Department of Housing and Urban Development.  In response to the petition, EPA announced in the Federal Register on June 27, 2008 (73 FR 36504) that EPA would initiate a proceeding to investigate whether and what type of regulatory or other action might be appropriate to protect against risks that may be posed by formaldehyde emitted from composite wood products.  In December 2008, EPA published an Advance Notice of Proposed Rulemaking (ANPR) to publicly initiate the investigation and obtain stakeholder input (73 FR 73620).   

On July 7, 2010, the Formaldehyde Standards for Composite Wood Products Act (FSCWPA) was signed into law.  This statute, which adds a Title VI to TSCA, establishes formaldehyde emission standards for hardwood plywood, particleboard, and medium-density fiberboard that are identical to the CARB ATCM Phase II standards.   TSCA Title VI directs EPA to promulgate implementing regulations by January 1, 2013 that address: sell-through dates for products; stockpiling; third-party testing and certification; auditing and reporting of third-party certifiers; recordkeeping; chain of custody; labeling; enforcement; products made with no-added formaldehyde (NAF) and ultra-low emitting formaldehyde (ULEF) resins; laminated products; finished goods; hardboard; and products containing de minimis amounts of composite wood products.  

In support of the implementing regulations, as with other rulemakings that are determined to be "significant regulatory action[s]" under Executive Order 12866 -- Regulatory Planning and Review, EPA is required to conduct an economic analysis of the costs and benefits associated with the rulemaking.  On June 2, 2010, EPA released a draft document titled Toxicological Review of Formaldehyde-Inhalation Assessment: In Support of Summary Information on the Integrated Risk Information System (IRIS). This draft IRIS assessment, which recently underwent independent scientific peer review by the National Academy of Sciences (NAS), addresses both non-cancer and cancer human health effects that may result from chronic inhalation exposure to formaldehyde.  However, this draft IRIS assessment does not include concentration-response functions for non-cancer health effects, which are needed for the benefits assessment.  Therefore, this draft report titled Approach to Assessing Non-cancer Health Effects from Formaldehyde and Benefits from Reducing Non-cancer Health Effects as a Result of Implementing Formaldehyde Emission Limits for Composite Wood Products (referred to hereafter as draft Approach Document) was developed, which provides discussion of several non-cancer endpoints as well as a discussion of the derivation of concentration-response functions, uncertainties, and EPA's proposed approach for using the concentration-response functions in the benefits assessment.  

0.1 Scope of the Document

The economic analysis to support EPA's implementing regulations under the TSCA Title VI will weigh the costs of complying with the regulations against the benefits to society.  Benefits from both reduced cancer cases and non-cancer health effects will be assessed; however, this draft Approach Document does not include a discussion of EPA's approach to assessing benefits from reduced cancer cases.                                                                                                                  	

As part of the economic analysis, EPA is also assessing inhalation exposure to formaldehyde.  EPA has developed an indoor air model, which has already been peer reviewed, to assess exposure to formaldehyde in different types of homes.  EPA has also assessed occupational exposure to formaldehyde during resin manufacture, composite wood product manufacture, and manufacture of products made with composite wood (e.g., furniture), as well as exposure from wholesale and retail of composite wood products and products made with composite wood, and exposure to formaldehyde in office buildings.  Using the indoor air model and the occupational exposure assessment, EPA is estimating formaldehyde inhalation exposure to the general population at baseline (prior to implementing the rule) and the change in exposure as a result of the rule.  The occupational and general population exposure assessments are discussed in detail in other documents, which will be publicly available at www.regulations.gov when the proposed rule is published.  This draft Approach Document uses preliminary estimates from the exposure assessment as examples, but it does not describe how they were derived, as the derivation is covered in a separate document.

The purpose of this draft Approach Document is to describe how EPA derived concentration-response functions for formaldehyde effects on sensory irritation, asthma, and female reproductive toxicity as well as the approach EPA will take to use these concentration-response functions to estimate benefits from the contribution of reduced non-cancer effects as a result of the rule.  This document describes in detail how the concentration-response functions were derived as well as uncertainties.  This document also briefly describes the epidemiological studies that were used to derive the concentration-response functions; however, a detailed analysis of these studies (as well as others) is included in the draft IRIS assessment for formaldehyde, which was already peer reviewed by the NAS, and therefore is not provided here.  This draft Approach Document also describes how EPA plans to use the concentration-response functions to estimate benefits.  It provides sample calculations but not the actual benefits assessment.  The full benefits assessment will be provided in the economic analysis that will be publicly available (at www.regulations.gov) when the proposed rule is published.

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Section 2: Non-cancer Health Effects --  
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Derivation of Concentration-Response Functions 

2.0 Background on the Identification of Non-Cancer Health Effects			         
In 2010, EPA released a draft IRIS assessment of adverse cancer and non-cancer health effects from inhalation of formaldehyde (U.S. EPA, 2010).  This draft identified non-cancer health effects for which quantitative concentration-response relationships were sought for the purpose of deriving a reference concentration (RfC), which represents an exposure level expected to be without an appreciable risk of deleterious effects in human, including susceptible populations, with little uncertainty (within an order of magnitude).  The draft IRIS assessment has since been externally peer-reviewed by the National Academy of Sciences (NAS, 2011).
This section is largely a recapitulation of portions of the text from EPA's draft IRIS assessment specific to the identified non-cancer health effects, taking the external peer-review comments into consideration.  The aim of the current effort is to describe the quantitative inhalation concentration-response relationship (i.e., the concentration-response function) for each of the identified non-cancer health effects, where possible, to inform the economic benefits assessment of potential economic welfare gains which could reasonably be expected to be attributable to decrements in formaldehyde exposures resulting from the proposed implementing regulations under FSCWPA.
The following subsections describe the studies of non-cancer health outcomes which were judged in the draft IRIS assessment to be the most informative for candidate RfC derivation within health effect categories.  These studies were judged to have been adequately conducted, and all were published in the peer-reviewed literature.  The relative merits and limitations of these studies were evaluated with respect to the characteristics of the study population, the quality and frequency of exposure measurements, and the exposure levels at which effects were observed.  The studies identified in the draft IRIS assessment as the best available for candidate RfC derivation also represent the best available studies from which to quantitatively estimate the concentration-response relationship between inhalation exposures and non-cancer health effects for the purposes of the economic benefits assessment.  Additional details on specific studies discussed here may be found in the draft IRIS assessment (Chapters 4 and 5 of U.S. EPA, 2010).
Only the studies reviewed in the draft IRIS assessment were further evaluated for use in the concentration-response modeling in support of the economic benefits assessment.  It should be noted that one of the comments in the NAS report was that it was not always clear how EPA selected and advanced studies for further consideration in RfC development.  In two specific instances, the NAS peer-review report recommended not using particular studies for the derivation of candidate RfCs and, consequently, those studies were not used here to estimate quantitative concentration-response relationships.    
  The draft IRIS assessment identified seven categories of health outcomes for potential RfC derivation including: 1) Sensory Irritation; 2) Upper Respiratory Tract Pathology; 3) Pulmonary Function Effects; 4) Asthma and Allergic Sensitization (Atopy); 5) Immune Function Effects; 6) Neurological and Behavioral Toxicity; 7) Developmental and Reproductive Toxicity.  From those categories, the draft IRIS assessment proposed RfCs based on four effects: sensory irritation, pulmonary function effects, asthma and allergic sensitization (atopy), and reproductive toxicity.  The NAS supported the derivation of candidate RfCs for each of these four endpoints based on human epidemiologic data.  For some non-cancer endpoints, it was possible to derive a candidate RfC for a particular health outcome based on a no-observed-adverse-effect level (NOAEL) or a lowest-observed-adverse- effect level (LOAEL), but those same data may not have supported a more fully characterized concentration-response function.  At this time, only three of the health effect categories were judged to have sufficient data for quantitative concentration-response modeling in support of the economic benefits assessment: sensory irritation, asthma, and female reproductive toxicity.  The available data on pulmonary function effects showing an association between increased formaldehyde concentrations and decreased peak expiratory flow rates could not be advanced in this Approach document because it was not possible to link specific decrements in pulmonary function with specific economic costs.

2.1 Sensory Irritation
2.1.1 Sensory Irritation: Background						             
Formaldehyde, a chemical irritant, binds to protein receptors of the trigeminal nerve, triggering a burning and painful sensation in humans.  This process is distinct from taste and smell (Nielsen 1991; Cometto-Muniz and Cain, 1992).  Stimulation of the trigeminal nerve may also result in reflex responses including lacrimation, coughing, and sneezing.  Both the reflex responses and sensations such as burning, pain, and itching of the eyes, nose, and throat are considered adverse.
Formaldehyde-induced eye, nose, and throat irritation has been well documented in a wide range of epidemiologic and other human studies.  Common effects of chemically induced sensory irritation include lacrimation, burning of the eyes and nose, rhinitis, burning of the throat, and cough (Feron et al., 2001).  Studies examining these endpoints were either controlled chamber studies with a defined population (e.g., healthy volunteers or sensitive individuals), worker/student studies, or general population studies (e.g., residential).  Chamber studies, by design, are acute studies, although some researchers have investigated the outcomes after repeated exposures.  Occupational, student, and residential exposures are generally of longer duration, although there is variability in exposure level and duration among subjects.  The endpoints for assessing irritation include self-reporting of symptoms (e.g., pain, burning, itching) and objective measures of irritation (e.g., eye-blink counts, lacrimation).

2.1.2 Sensory Irritation: Relevant Studies
Eye irritation is the most sensitive of reported effects in human studies.  Two different short-term chamber studies provide similar benchmark concentrations for 10% extra risk of eye irritation of 560 ppb and 240 ppb for 3 and 5 hour exposures, respectively (Kulle, 1993; Andersen and Molhave, 1983, modeled by Arts et al., 2006b).  Various occupational studies have noted increased eye irritation for average exposures ranging from 180 ppb to 690 ppb (e.g., Horvath et al., 1988, Alexandersson and Hedenstiera, 1988; Holmstrom and Wilhelmsson, 1988).  The results of residential studies of the general population, where in-home formaldehyde levels are used as the exposure metric, indicate eye irritation may increase with increasing exposure from less than 100 ppb to more than 500 ppb for these chronic exposure scenarios (Ritchie and Lehnen, 1987, Hanrahan et al., 1984; Liu et al., 1991.)
Details of the human studies reporting associations between formaldehyde inhalation exposures and sensory irritation and a review of their findings are presented in Chapter 4 of the draft IRIS assessment of formaldehyde (U.S. EPA, 2010) along with experimental animal evidence supporting the plausibility of these epidemiologic findings.  A synthesis of the most relevant findings and conclusions is also presented in Chapter 4 (U.S. EPA, 2010).  Although exposure concentrations are well-defined in the chamber studies, the chamber studies are not appropriate for estimating the effects of chronic exposures because they are acute studies.  The participants in the chamber studies also typically represent healthier individuals (although some studies do include asthmatics) and do not include either young or old people.  The occupational studies also typically represent healthier individuals and do not include either young or old people, and both chamber and occupational studies involve higher exposure levels than occur in most residential settings, which are the focus of the formaldehyde rule.  Additionally, occupational exposures often include short-term "peak" exposures of higher concentrations.  Thus, the human epidemiology studies of lower, chronic residential exposures are more relevant and convey less uncertainty than the acute chamber studies or the occupational studies and are preferred for the purposes of application in the economic analysis.
Of the various independent sensory irritation effects for which one may wish to estimate economic benefits ensuing from the formaldehyde rule, only eye irritation had adequate quantitative data from residential studies for the derivation of a concentration-response function.

2.1.3 Sensory Irritation: Derivation of Concentration-Response Relationship for Eye Irritation
There are three studies that report sensory irritation in humans from chronic exposures in a residential environment and provide sufficient exposure data to support quantitative assessment (Ritchie and Lehnen, 1987; Hanrahan et al., 1984; Liu et al., 1991).  Each study reports site-specific exposure measurements and presents some metric of individual exposure.  These studies employ in-home measurements for each study participant, either as average exposure level in the home (Ritchie and Lehnen, 1987; Hanrahan et al., 1984) or as calculated cumulative exposure based on the time in the home (Liu et al., 1991).  Eye irritation is the most sensitive endpoint representing sensory irritation and is reported at similar levels of residential formaldehyde exposure in the three studies (U.S. EPA, 2010, Figures 5-8 and 5-9).  Each study provides an estimated concentration-response relationship for prevalence of eye irritation in relation to in-home formaldehyde exposure based on individual-level data, including levels of exposure below 100 ppb.  Liu et al. (1991) additionally evaluated responses by season (summer and winter).  These studies generally assume a constant concentration-response over time which may have been attenuated due to acclimatization to relatively constant formaldehyde exposure levels in residential environments.  It has been shown that short-term responses to formaldehyde exposures including reductions in pulmonary function, and irritation of the eyes, nose and throat can diminish over time with repeated episodic exposure (Kriebel et al., 1993; 2001).  The detailed exposure information and chronic nature of the exposures support the selection of these residential epidemiology studies for concentration-response modeling.
While the concentration-response relation reported in Ritchie and Lehnen (1987) was consistent with those reported in the two other studies, it is possible that the Ritchie and Lehnen results were impacted by potential selection bias − owing to the need for a doctor's note to be able to participate; thus, these results may not accurately describe the concentration-response in the general public and are not considered further here.
The two remaining studies report eye irritation in humans from chronic exposures in a residential environment and provide sufficient exposure data to support quantitative assessment (Liu et al., 1991; Hanrahan et al., 1984).  The Liu et al. (1991) residential study is a random-sample study of over 1,000 mobile home residents across the State of California (1,394 in the summer; 1,096 in the winter) that included both young children (< 4 years) and the elderly (> 65 years).  Cumulative weekly exposures were based on in-home formaldehyde sampling and a participant survey of time spent at home.  Air sampling was conducted for a 7-day period using 2 passive samplers in each home (for both summer and winter).  One passive sampler was placed in the kitchen and one in the master bedroom; however, there was no significant difference in exposure levels between the two locations, so the two values were averaged to reflect the household concentration.  The resulting estimates of cumulative exposure assumed no formaldehyde exposure outside of the home.  The authors based their measure of exposure on the product of the measured concentration of formaldehyde in the home and the number of hours per week the individual spent in the home.  Liu et al. (1991) reported that this measure of cumulative formaldehyde exposure was a significant predictor of numerous irritant symptoms in a multivariate linear logistic regression, including "burning eyes" (p < 0.05).  The highest prevalence rates were reported for those aged 20−64 years and the prevalence of eye irritation increased with increasing cumulative exposure in a categorical analysis of participants in this age group for both summer and winter exposure estimates, as shown in Figure 1 below (U.S. EPA, 2010, Figure 5-9).							        
Liu et al. (1991) presented results for three categorical levels of cumulative exposure.  The lowest exposure group extended from 0 to 7.0 ppmxhours/week and did not constitute a `non-exposed' reference group but rather a comparative lower exposure level.  The mid-level exposure group encompassed exposure from 7.0 to 12.0 ppmxhours/week and the high exposure group covered exposure greater than 12.0 ppmxhours/week.  Liu et al. reported that the average concentration of formaldehyde in the homes was 88 ppb in the summer and 89 ppb in the winter.  The range of cumulative exposures extended from 0 to 53.4 ppmxhours in the summer and 0 to 40.9 ppmxhours in the winter, with respective average cumulative exposures of 9.8 ppmxhours and 9.9 ppmxhours.  Dividing the average 7-day cumulative exposures reported by Liu et al. (1991) by the average concentrations, the average time spent in the homes can be estimated as approximately 111 hours (about 16 hours per day).  The prevalence of eye irritation was above 10% in the lowest exposure group (0 - 7.0 ppmxhours/week) and increased to 17.1% in the mid-exposure group (7.0−12.0 ppmxhours/week) and to 21.4 % in the high-exposure group (12.0 ppmxhours/week) in the summer survey time; winter rates were slightly lower but showed a similar increase with increasing cumulative exposure.

Figure 1.  See Figure 5-9 U.S. EPA (2010).  Positive concentration-response relationships reported for in-home formaldehyde exposures and sensory irritation (burning eyes).  Cumulative formaldehyde exposure was estimated for each participant from measured in-home formaldehyde levels (7-day passive air samples) and reported hours spent in the home.  Prevalence rates are given for the 20-64 year-old age group for both summer (n = 739) and winter (n = 587) survey periods.  Adapted from Liu et al. (1991).
While these data are not well suited to developing continuous concentration-response relationships because there are only three categories of exposure and the distributions of exposures and times spent indoors within each category are unknown, this study does provide the most specific information on the relative timing of exposure to formaldehyde and the occurrence of sensory irritation symptoms, which is important for the economic benefits assessment.  The described methodology states that the symptoms were reported for a two-week period that included the week preceding and the week of exposure monitoring.  Knowledge of the timing of exposure is an important aspect for the application of a concentration-response function to inform the economic benefits assessment, and the data from the paper by Liu et al. (1991) provide supportive information on the shape of the concentration-response function as well as an estimate of the general prevalence of sensory irritation in a highly relevant population.
Hanrahan et al. (1984) reported a concentration-response relationship for burning eyes in a study of 61 teenage and adult residents of mobile homes in Wisconsin.  Note that ocular discomfort was recorded in two related ways as `eye irritation' and as `burning eyes'; however, only the concentration-response relationship for `burning eyes' was reported and this endpoint was used by EPA to represent eye irritation more broadly.   In-home formaldehyde measurements were obtained for all participants, and measured formaldehyde levels (average of two approximately 1-hour air samples  -  one from the kitchen or living room and one from a bedroom) were used to characterize average in-home exposures.  Measured residential formaldehyde concentrations ranged from less than 100 ppb to 800 ppb.  The median (geometric mean) was reported as 160 ppb.  No information was provided on the arithmetic mean or standard deviation of the indoor measurements.  However, the standard deviation of the outdoor measurements was reported as 30 ppb and effectively serves as a lower bound on the standard deviation of the indoor concentrations because indoor levels are generally considerably higher and more variable than outdoor levels.  Given the information provided by Hanrahan et al. (1984) on the indoor geometric mean and a lower bound estimate on the indoor arithmetic standard deviation, the percentages of indoor formaldehyde measurements below 100 ppb and below 50 ppb can be estimated.  Using an estimated expected value (arithmetic mean) of 163 ppb based on an arithmetic standard deviation of 30 ppb [for log-normally distributed concentrations, the arithmetic mean is a function of the geometric mean and the standard deviation], and an assumption that the measured concentrations were log-normally distributed, 44% of actual residential measurements are estimated to have been below 100 ppb with 36% below 50 ppb.  If the actual, but unreported, standard deviation of the indoor measurements was greater than 30 ppb, then these percentages would be expected to increase.  This information is important, as it shows that the underlying residential exposure data which inform the concentration-response relationship are relevant to concentrations modeled in the exposure assessment for use in the economic analysis.  Different distributional assumptions would produce different estimates of the proportion of measured samples which were below 50 ppb, but, under the assumption of a log-normal distribution, which is common for exposure estimates, at least one third of the measurements informing the concentration-response function were in the range that is most applicable to the economic analysis.
Hanrahan et al. (1984) reported that eye irritation was associated with in-home formaldehyde exposures (p < 0.05) (both as "burning eyes" and "eye irritation"), and the authors provided a graphical representation of the best-fitting logistic regression model results of predicted prevalence of "burning eyes" for exposures from 100 to 800 ppb.  From inspection of this graph (shown here as Figure 2), EPA determined the prevalence of eye irritation predicted at 100 ppb is approximately 4%.  Although, as discussed above, a large percentage (44%) of the indoor formaldehyde measurements were estimated to have been below 100 ppb, the predicted model results were simply not shown below 100 ppb.  At the time of publication, the World Health Organization standard was 300 ppb and the central conclusion of Hanrahan et al. (1984) was that indoor formaldehyde levels below 100 ppb would lower the risk of sensory irritation for most residents.  Nonetheless, it is possible to approximate the functional form of the concentration-response relationship below 100 ppb from the graphical results provided in the plot from Hanrahan et al. (1984) presented below in Figure 2 because a single functional form was used to plot the results shown and reconstruction of that form can show the results of the Hanrahan et al. (1984) model where they were omitted below 100 ppb.










Figure 2.  See Figure 5-8 U.S. EPA (2010).  Regression of prevalence of "burning eyes" versus indoor formaldehyde concentration (ppm) in mobile homes (approximately 1-hour air samples).  Dashed lines show upper and lower 95th percentile confidence intervals on model results.  Model based on reported eye irritation from individuals in 42 mobile homes.  Adapted from Hanrahan et al. (1984).
In this figure, the dependent variable is displayed as predicted % prevalence of eye irritation.  However, the method used by Hanrahan et al. (1984) to model prevalence was logistic regression, which predicts the log odds of prevalence, which the authors then transformed to prevalence for graphing.  In order to describe the underlying functional form of the results displayed, EPA converted the prevalence data back to prevalence odds.  Table 1 shows the prevalence values which EPA visually estimated from the plot as well as the associated prevalence odds, which EPA calculated as estimated prevalence divided by the complement of estimated prevalence, that is p/(1-p).  Figure 3a plots the estimated prevalence of eye irritation against the residential concentration of formaldehyde.  Figure 3b plots the estimated prevalence odds against the residential concentration of formaldehyde.
Table 1. Concentration-response information extracted from Hanrahan et al. (1984).
Residential Formaldehyde
Concentration (ppb)
Prevalence
(p)
Prevalence Odds
(p/[1-p])
100
0.0375
0.039
200
0.175
0.212
300
0.35
0.538
400
0.52
1.08
500
0.66
1.86
600
0.725
2.64
700
0.8
4
800
0.85
5.67

Figure 3a & b. Plot of residential concentration-response information from Table 1.
Using MS Excel(R), the EPA fit a simple trend line to the discrete prevalence odds data in Figure 3b and not the continuous raw data and found that a power function could be fit which yielded an R[2] value of 0.9997.  This indicates nearly a perfect fit.  A similar fit would not have been achieved from analysis of the raw data (unavailable), but the objective here was to recreate the functional form of the modeled data presented by Hanrahan et al. (1984).  Note that this power function will asymptotically approach zero for a zero formaldehyde exposure concentration.    The following describes the functional form for the prevalence odds:

                     p1-p=7*10-7*(exposure)2.3743				(2-1)
                                       
Solving for prevalence (p) itself:

         p= 7*10-7*(exposure)2.37431+7*10-7*(exposure)2.3743					(2-2)

Figure 4a shows the predicted prevalence odds from the functional form above overlaid on the prevalence odds estimates extracted from Hanrahan et al. (1984).  This concentration-response function is clearly consistent with the reported model results and provides an estimate of the concentration-response relationship below 100 ppb residential exposure, in the region of exposures of interest for the economic benefits analysis.  Figure 4b shows the same plot with greater focus on the lower range of the concentration-response relationship. 



Figure 4a. Relationship between residential formaldehyde exposures and the predicted prevalence of sensory irritation (burning eyes) as report by Hanrahan et al. (1984) [red squares] and the continuous concentration-response relationship as estimated by EPA.



Figure 4b. Relationship between residential formaldehyde exposures and the predicted prevalence of sensory irritation (burning eyes) as report by Hanrahan et al. (1984) [red square] and the continuous concentration-response relationship as estimated by EPA for formaldehyde concentration below 150 ppb.
2.1.4 Sensory Irritation: Discussion of Uncertainties
Both studies (Liu et al., 1991; Hanrahan et al., 1984) have the strength of having individual in-home exposure measurements, and each demonstrates a positive concentration-response relationship for eye irritation within a range of residential formaldehyde exposures (for both conventional and mobile homes).  The assessment of formaldehyde concentrations in these studies were by two different methods.  Liu et al. (1991) measured formaldehyde concentration using passive monitors over seven days.  Hanrahan et al. (1984) based their exposure assessment on short-term samples taken over approximately one hour.  Short-term sampling is a less precise methodology and the resulting measures can be reasonably expected to include a greater degree of exposure measurement error than those from week-long passive monitoring.  The short-term nature of the exposure sampling in Hanrahan et al. (1984) is a limitation; however, the results in Liu et a. (1991) based on the stronger exposure assessment methodology (although still prone to some measurement error) are well aligned and strengthen the validity of the Hanrahan et al. (1984) results.  
One weakness of these studies was that the assessment of sensory irritation was conducted by surveys and not objectively assessed by trained observers of physiological measurements.  While it was considered a common strength that these studies did have in-home measurement of formaldehyde exposures in temporal proximity to the assessment of irritation, those measurements were of relatively short sampling duration and they do not reflect daily fluctuations which may include relative peak exposures.  Both studies were based on randomly selected people representative of the general population, although the study size in Hanrahan et al. (1984) was small with just 61 participants.
Both studies did control for major potential confounders but did not measure and control for all the factors that could potentially be confounders.  Liu et al. (1991) controlled for the potentially confounding effects of age, gender and smoking as well as controlling for chronic respiratory and allergy problems.  The analysis by Hanrahan et al. (1984) controlled for age, gender and smoking, and the authors reported that the presence of either smokers or gas appliances was not associated with indoor concentrations of formaldehyde, making those factors unlikely confounders.  Nonetheless, there is always the potential for other possible confounders, such as molds or other volatile organic compounds, to have played a role in the observed concentration-response relations described by Liu et al. (1991) and Hanrahan et al. (1984).  No data on these potential confounders were noted in these papers, but the reported concentration-response relationships are strong evidence of a formaldehyde effect and, for these reported relationships to have been the spurious product of confounding, those unmeasured confounding factors would need to have been strongly associated with both eye irritation and the concentrations of formaldehyde.
Both studies support a finding of increased eye irritation with increasing exposures to formaldehyde at concentrations starting below 100 ppb.  Liu et al. (1991) reported an average concentration of 88 ppb, with measured concentrations from 10 ppb (the limit of detection) to 460 ppb.  Hanrahan et al. (1984) reported exposures ranging from less than 100 ppb to 800 ppb, with a median of 160 ppb.  While it is not clear from the published report what the distribution of exposures below 100 ppb was, if it can reasonably be assumed that the formaldehyde concentrations were log-normally distributed with median of 160 ppb and a standard deviation of 30 ppb (based on the reported standard deviation from the outdoor measurements), then it would be expected that about 44% of the measured indoor samples were below 100 ppb, with 36% below 50 ppb.  Given that the measured indoor levels were likely to have been more variable than the reported outdoor levels, the true indoor standard deviation would likely have been higher than 30 ppb and, consequently, the percentages below 100 ppb and below 50 ppb would have been greater.
The results as graphed in Hanrahan et al. (1984) did not show the shape of the concentration-response curve below 100 ppb even though the study had exposure data at these exposure levels.  EPA was able to derive a concentration-response function that closely approximated the results from Hanrahan et al. (1984) and, from this functional form, to infer the shape of the published concentration-response function below 100 ppb  -  a range EPA considers to encompass at least 44% of the indoor measurements.   Thus, while there is clearly uncertainty in estimating effects below 100 ppb residential exposure, these effects can be estimated from the published concentration-response curve.  Re-modeling of the reported results from Hanrahan et al. (1984) provided the best available estimate of the adverse response below 100 ppb, and this concentration-response function can be used in the economic benefits assessment.
These studies provided a reasonable basis for quantitative concentration-response modeling, with Liu et al. (1991) supporting the modeling based on Hanrahan et al. (1984).  Additionally, the study populations have been drawn from the general population, including children and the elderly, and have not been limited to those healthy enough for full-time employment (as is often the case in occupational cohorts). The results in these studies are further supported by the consistent findings of an extended concentration-response relationship reported in some non-residential studies at higher levels of exposure.  For example, Kriebel et al. (2001) reported that increasing formaldehyde exposures were positively associated with symptoms of eye irritation (p<0.001) among anatomy students with measured exposure concentrations having a geometric mean of 700 ppb but with 25% of exposures below 300 ppb.  

2. 2 Asthma
2.2.1 Asthma: Background
Asthma is a chronic respiratory disease characterized by inflammation of the airways.  Sensitization to inhalational chemical exposure may manifest as an allergic or asthmatic response that is characterized by bronchial constriction or bronchial hyper-responsiveness.  This may be a result of immune involvement, as in the case of hypersensitivity, or a neurogenic sensitization, where a chemical may directly stimulate inflammation.  In the United States, the prevalence of asthma is common.  The Centers for Disease Control and Prevention estimated that in 2005 approximately 9% of children had asthma (6.5 million children) and that the prevalence rate of asthma in children had more than doubled from 1980 to the mid-1990s and has remained at historically high levels (Akinbami, 2006).  In 2009, it was estimated that nearly 10% of children had asthma (CDC, 2009).  

2.2.2 Asthma: Relevant Studies
Multiple epidemiologic studies have reported associations between formaldehyde inhalation exposures and childhood asthma.  Details of these epidemiologic studies and a review of their findings are presented in Chapter 4 of the draft IRIS assessment of formaldehyde (U.S. EPA, 2010) along with experimental animal evidence supporting the plausibility of these epidemiologic findings.   A synthesis of the most relevant findings and conclusions is presented also in Chapter 4 (U.S. EPA, 2010).
The study that is most relevant for developing a concentration-response function for use in the economic benefits assessment is the meta-analysis of formaldehyde-associated asthma conducted by McGwin et al. (2010) based on seven peer-reviewed studies providing quantitative concentration-response results for children.  All of the studies were observational in nature and were predominantly cross-sectional or case-control in design.  The mean ages of the children in the seven studies ranged from 1.9 years up to 14.3 years.  Details of the individual studies were provided by the authors in their Table 1 reproduced below (see Table 2 of this document).  For the meta-analysis, odds ratios (ORs) and confidence intervals (CIs) were abstracted from the studies, and effect estimates were standardized to OR per 10 ug/m[3] increase in formaldehyde concentration.  Funnel plots were used to assess publication bias and did not show such a bias (McGwin et al., 2010).  Fixed- and random-effects models were used to calculate pooled ORs and 95% CIs following a test of heterogeneity.  A fixed-effect model assumes that all the individual studies provided estimates of the same effect or slope, while the random-effects model allows for different effects or slopes in the source studies that may reflect differences in baseline risk factors within the study populations.  McGwin et al. (2010) preferred the fixed-effect model when heterogeneity was low and the random-effects model when the data were more heterogeneous.  Both models were presented, as the degree of heterogeneity, measured by the Q-test and the I[2] statistic, indicated the presence of low to moderate heterogeneity, depending on the analysis.  The referenced Q-test is also known as Cochran's Q and is a classical measure of heterogeneity calculated as the sum of the weighted squared differences between the individual study effects and the pooled effect across studies, where the weights are those used in the pooling method.  The I[2] statistic described the percentage of variation across studies that is due to heterogeneity rather than chance and is computed as 100%*(Q  -  degrees of freedom)/Q.
Table 2.  Reproduction of McGwin et al. (2010) Table 1: Summary of studies selected for inclusion in meta-analysis.
  

2.2.3 Asthma: Derivation of Concentration-Response Relationship
Of the seven studies that were included in the McGwin et al. meta-analysis, six reported increased risks of asthma associated with exposure to formaldehyde.  The results of the random-effects model showed an overall effect estimate of OR = 1.17 per 10 ug/m[3] formaldehyde (95% CI: 1.01-1.36) (see U.S. EPA, 2010: Figure 4-2).  The three studies with the highest statistical weights based on the inverse of the variance of the study ORs were the studies by Rumchev et al. (2002), Garrett et al. (1999) and Krzyzanowski et al. (1990).  Higher weights reflect the narrower confidence intervals in these studies, which implied that the studies were able to yield more precise effects estimates, warranting greater weight in the meta-analysis.  Note that the two results from the Zhao et al. (2008) study, including the school results, which showed a health protective effect of formaldehyde, had such large confidence intervals that their weights in the meta-analysis were virtually zero.
Source: McGwin et al. (2010), Fig. 2.
McGwin et al. (2010) noted that the study by Rumchev et al. (2002) may have had `undue influence on the study data' and recomputed the fixed- and random-effects model results without that study.  They also suggested that one aspect of Rumchev et al. (2002) which was unique among the seven studies was the focus on very young children.  According to the National Heart Lung and Blood Institute, a diagnosis of asthma is most reliable when it is based on a physical exam, a medical history and a test of pulmonary function.  However, conducting lung function tests on young children is difficult and doctors may rely on signs and symptoms rather than spirometry in making diagnostic decisions (U.S. HHS, 2007).  In the peer-review report of the draft IRIS formaldehyde assessment (U.S. EPA, 2010), the NAS (2011) noted that many of the studies of childhood asthma in the epidemiologic literature were decades old and that the understanding of asthma was not characterized as well then as it is now.  The NAS report (2011) noted that while Rumchev and coauthors (2002) interpreted the health outcome in their study as a diagnosis of asthma, study participants of such young ages are now thought to have been more likely to have actually had lower respiratory illnesses with wheezing of an infectious etiology, a diagnosis which could often have been mislabeled as asthma.  For these reasons, the results from the Rumchev et al. (2002) study are not included in the approach proposed here to estimate the concentration-response relationship for asthma-related formaldehyde exposures.
Excluding Rumchev et al. (2002) from the meta-analysis, McGwin et al. (2010) reported the summary measure of the concentration-response relationship based on the random-effects model as OR = 1.24 per 10 ug/m[3] formaldehyde (95% CI: 1.07-1.45) with a p-value of 0.0026, while for the fixed-effect model they reported an OR = 1.24 (95% CI: 1.09-1.42) with a p-value of 0.0013.  Without including Rumchev et al. (2002), the heterogeneity statistics, Q and I[2], were 6.76 and 11.3, respectively, which indicate low heterogeneity.  Consistent with the low heterogeneity, both models estimated a similar magnitude of effect (the same OR estimate in this instance) but with the fixed-effect estimate having a narrower confidence interval.  
This concentration-response relationship (OR = 1.24 per 10 ug/m[3]) is recommended for application in the economic benefits assessment for the formaldehyde rule.  The units of this concentration-response relationship can be converted to show the effects per part per billion (ppb) of formaldehyde.  Converting from ug/m[3] to ppb depends on the molecular weight of formaldehyde, which is 30.03 g/mol.  The formula to convert concentrations in air (at 25°C) from ug/m[3] to ppb is:  ppb = (ug/m[3]) x (24.45 L) / (gram molecular weight of the compound).  The number 24.45 in the equations above is the volume (liters) of a mole (gram molecular weight) of a gas or vapor when the pressure is at 1 atmosphere (760 torr or 760 mm Hg) and at 25°C.  For formaldehyde, 1 ug/m3 = 0.814 ppb.  Therefore, the effect estimate from McGwin et al. (2010) of OR = 1.24 per 10 ug/m[3] is equivalent to OR = 1.24 per 8.14 ppb.  This odds ratio represents the exponentiated linear slope (beta) derived from the fixed-effect regression model.  In order to rescale this effect to one ppb, the slope (beta) should be rescaled to represent the change in response per unit increase in exposure.  The natural log of 1.24 is 0.215 and this represents the slope for each 8.14 ppb increase in exposure.  Dividing by 8.14 yields a slope (beta) per one ppb increase in exposure of 0.0264.  Exponentiating back to the odds ratio scale, the rescaled OR = 1.027 per one ppb increase in formaldehyde exposure.  The variance of the rescaled OR based on the random-effects model and the associated 95% CI can also be scaled by the same methods.  This OR = 1.027 per one ppb increase in formaldehyde exposure has a 95% CI: 1.008-1.047.  The p-value for the rescaled OR remains unchanged (p=0.0026).  Note that this function is in terms of residential or (in-school) exposure levels. 

2.2.4 Asthma: Discussion of Uncertainties
As noted by the NAS (2011), the health endpoints described as asthma constitute a broad range of respiratory effects that differ in cause, and the definition of asthma has changed over time, as the asthma phenotype has become better characterized.  The meta-analysis included studies from a wide geographic range, and there are some inconsistencies in the studies included in the meta-analysis, including different effect sizes across different exposure ranges.  The studies that contributed to the McGwin et al. (2010) meta-analysis span a time period from 1990 to 2008 and include both self-reported and physician-diagnosed asthma.  Due to this heterogeneity of location, effect size, exposure range, calendar time and diagnostic criteria, there is some uncertainty in summarizing all these findings in a single summary concentration-response measure as representative of the effect on asthma.  However, once the study by Rumchev et al. (2002) was excluded from the meta-analysis, McGwin et al. (2010) did not observe that the various findings were heterogeneous in the magnitude of the effect estimates.  This observation might mitigate some potential uncertainty regarding the different ways in which the related health endpoints may have been defined.  This appears to have been further substantiated by additional random-effects models which were fit by McGwin et al. (2010) based on diagnostic criteria  --  studies in which the ORs were for self-reported asthma yielded a summary OR = 1.26 (95% CI: 0.97−1.64), which was very similar to the overall summary OR = 1.24. 
In addition to differences in the calendar year of each source study in the meta-analysis, there were also differences in the exposure settings and in the range of exposure values.  Some studies were based on measured residential exposures, while others were based on exposures measured in schools.  Both exposure settings appear to be relevant for the economic benefits assessment approach proposed here.  It also appears that the range of exposures in the studies on which the concentration-response function for formaldehyde-associated asthma was based is appropriate for use in the economic analysis described in this document.  Exposure concentrations in the source studies for the meta-analysis ranged from 1 ug/m[3] up to more than 87.5 ug/m[3] (1 ppb to 70+ ppb).  
Another difference among the studies was the differing levels of adjustment for potential confounders.  McGwin et al. (2010) noted that some of the source stud - ies provided adjusted estimates but others did not. Thus, they stated that their pooled results may be subject to residual confounding.  This is a weakness that reflects the limitations of the data available for the meta-analysis.  However, a strength of the McGwin analysis is that it incorporated different studies from different investigators in different countries over different time frames.  Such diversity can be considered a strength since if there were any operative biases in the study design, such as confounding, they would be less likely to be replicated throughout all the studies in the same fashion.  
Finally, these data describe the effects in children but do not provide information on potential effects among adults.  As the onset and diagnosis of asthma is more common before a person reaches the age of 18 years, many fewer persons would be expected to develop asthma and be diagnosed in adulthood.  While the identified concentration-response relationship discussed here is limited to children, any potential adult-onset asthma incidence that is associated with formaldehyde exposure is considered to be relatively small.  Excluding the study by Rumchev et al. (2002), the range of the mean ages of the participants in the included studies was from 8.1 to 14.3 years and is considered to be appropriate for application to all but the youngest children in the economic analysis.
In summary, the meta-analysis results in McGwin et al. (2010) estimated an increased risk of asthma among exposed children for incremental increases in formaldehyde inhalation concentration.  While the effect estimates from the fixed-effect modeling and the random-effects modeling were equivalent and the lack of appreciable heterogeneity led McGwin et al. to select the fixed-effect result, the observation of some heterogeneity and the remaining uncertainties in the individual studies support the selection of the random-effects result, with its wider confidence interval.  The magnitude of this effect was reported by McGwin et al. (2010) as an odds ratio of 1.24 per 10 ug/m[3] increase in formaldehyde concentration (95% CI 1.09  -  1.42) with a p-value of 0.0026 for the random-effects analysis.  Scaling this finding to parts per billion, the odds ratio is 1.027 per ppb increase in formaldehyde concentration (95% CI: 1.008-1.047) with p-value of 0.0026.

2.3 Female Reproductive Toxicity
2.3.1 Female Reproductive Toxicity: Background
Although the available database for assessment of the effects of formaldehyde exposure on the female reproductive system was limited, epidemiologic studies suggest an association between occupational exposure to formaldehyde and adverse reproductive outcomes in women.  Several of these studies examined the risks of spontaneous abortion following maternal occupational formaldehyde exposure with increased relative risk estimates for those exposed versus those unexposed in the range of 1.7 to more than 3.0  (Taskinen et al., 1999, 1994; John et al., 1994; Seitz and Baron, 1990; Hemminki et al., 1985, 1982; Axelsson et al., 1984).  However, other studies (Hemminki et al., 1985, 1982) did not identify an association between occupational formaldehyde exposure and spontaneous abortion.  A general weakness of these studies is the lack of rigorous exposure assessment, which could diminish the power to detect a true association and also limit the ability of the studies to appropriately control for any potential confounders.  Nonetheless, these studies of formaldehyde exposure are generally consistent in their reporting of adverse reproductive effects, an association similar to other air pollutants such as particulate matter (Glinianaia et al., 2004a; Glinianaia et al., 2004b) and reactive gaseous air pollutants such as nitrogen oxides, sulfur dioxide, carbon monoxide (Lacasana et al., 2005;  Maisonet et al. 2004; Sram et al., 2005).
Details of the epidemiologic studies reporting associations between formaldehyde inhalation exposures and reproductive and developmental outcomes and a review of their findings are presented in Chapter 4 of the draft IRIS assessment of formaldehyde (U.S. EPA, 2010) along with supportive experimental animal evidence of these epidemiologic findings.  A synthesis of the most relevant findings and conclusions is also presented in Chapter 4 (U.S. EPA, 2010).

2.3.2 Female Reproductive Toxicity: Relevant Studies
On review of the developmental and reproductive toxicity studies in humans and laboratory animals in the draft IRIS assessment (U.S. EPA, 2010), the Taskinen et al. (1999) Finnish retrospective cohort study was considered to represent the best available study evidence of female reproductive toxicity for the purpose of deriving a concentration-response relationship for use in the economic benefits assessment.  The subjects, recruited from a woodworkers' union and other businesses involving wood processing, were linked to a national register of births.  Women were included if they were born between 1946 and 1975, had a live birth at age 20−40 years during 1985−1995, had worked in the wood processing industry for at least 1 month, and had first employment in the wood processing industry beginning at least 6 months before the index pregnancy.  The first pregnancy that fulfilled the above criteria was the index pregnancy.  There were 1,094 women with these criteria.  Information about personal characteristics, pregnancies, and exposures were collected from mailed questionnaires for which the response rate was 64%.  After other exclusions (primarily infertility history, unknown time to pregnancy, and contraceptive failure), the final sample included 602 women.
Estimates of mean daily exposure to formaldehyde were based on measurements taken at the women's factories of employment during the early 1990s.  Where measurements were unavailable, measurements from equivalent industries were used.  An exposure index representing a time-weighted average exposure (TWA) was established for every person in the study based on the concentration of their workplace formaldehyde multiplied by the proportion of the workday exposed to formaldehyde.  The investigators categorized the time-weighted average formaldehyde exposure into categories of low (mean of 18 ppb), medium (mean of 76 ppb), and high (mean of 219 ppb) exposure.  Personal protection equipment included gloves and respirators.  Taskinen et al. (1999) reported that 40% of the women noted that they always wore gloves, with 19% wearing them occasionally, and that respirators were rarely used (4-6%).
Time-to-pregnancy data were analyzed by a discrete proportional hazards regression procedure with a fecundability density ratio (FDR) as the outcome.  In this method, a time scale (typically age or calendar time) is divided into discrete units to allow for the comparison of exposures and events within narrow time periods thereby effectively controlling for time.  Taskinen et al. (1999) do not state explicitly that age was used as the timescale in the proportional hazards regression analyses but this is standard practice and would effectively control for age by design.  The FDR compares the average incidence density of pregnancies for exposed women with that of the employed, unexposed women.  As explained by Taskinen et al. (1999), an FDR significantly below unity suggests that conception was delayed  -  and indicates reduced fertility.  The employment-, smoking-, alcohol consumption-, number of children-, and menstrual irregularity-adjusted FDR was 0.64 (95% CI: 0.43−0.92) for women exposed to high formaldehyde levels compared with the unexposed controls, indicating that there was a substantial, and statistically significant, delay in time to conception in this group of women.  At the medium exposure, there was a smaller adverse effect on fecundity that appeared to be concentration-dependent. 
The investigators further conducted an analysis of the risk of spontaneous abortion, which also showed a trend towards increased risk associated with increased air concentrations of formaldehyde.  The risk of spontaneous abortion was reported to be elevated with formaldehyde exposure in the low exposure group (OR = 2.4 [95% CI: 1.2−4.8]), in the medium exposure group (OR = 1.8 [95% CI: 0.8−4.0]), and in the high exposure group (OR = 3.2 [95% CI: 1.2−8.3]).  Endometriosis was also associated with the highest formaldehyde level (OR = 4.5 [95% CI: 1.0−20.0]).

2.3.3 Female Reproductive Toxicity: Derivation of Concentration-Response Relationship
The available evidence that formaldehyde exposure could be associated with spontaneous abortion and reduced fertility (subfertility) is a serious concern.  Given this association of formaldehyde with a reduction in fertility, based on the statistically significant reduced fecundity density ratio, one method to estimate the monetary cost of infertility potentially attributable to exposure to formaldehyde is to define the concentration-response relationship for the inability to conceive within 12 months.  An inability to conceive within 12 months is the generally accepted definition of infertility; however, since the Taskinen et al. study is only of women who did at some point conceive and give birth to a live child, this study is measuring subfertility but not all forms of infertility.  Table 5 in Taskinen et al. (1999) provides data on the number of women whose time to pregnancy exceeded 12 months at four occupational levels of exposure to formaldehyde: `non-exposed' (0 ppb), `low exposure' (mean of ~18 ppb), `medium exposure' (mean of ~76 ppb), and `high' exposure (mean of ~219 ppb).  Typically, exposures from occupational studies are adjusted to account for the daily breathing volume appropriate to an environmental (versus occupational) setting and for continuous exposure across the total exposure period (U.S. EPA, 1993).  However, with formaldehyde, there is potential for exposure outside of work from in-home and environmental sources of formaldehyde. A contemporaneous study of formaldehyde exposures in Finland reports an average exposure level of 21.4 ppb (measured over 48 hours with a personal monitor) (Jurvelin et al., 2001).  It should be noted that both the mean exposure (18 ppb 8hr TWA) and lowest reported exposure (10 ppb 8hr TWA) of the `low exposed' category in the Taskinen et al. (1999) study are below the reported average exposure level for Finland (21.4 ppb).  The investigators in Taskinen et al. (1999) appear to have assumed that while the women were away from their "exposed" work areas their exposure to formaldehyde was zero.  Thus, the reported occupational exposure levels did not account for levels of formaldehyde outside the workplace or away from "exposed" work stations within the workplace.  This would explain why both the mean exposure and the lower end of work shift exposures for women in the low exposure group were reported at and below expected average exposure levels.  The draft IRIS assessment (Table 5-5 of U.S. EPA, 2010) provides details of the exposure adjustments needed to convert the reported exposure levels from Taskinen et al. (1999) to 8-hour TWA exposure levels taking estimated background (i.e., "non-exposed" work area) exposure levels in the workplace into account.  Jurvelin et al. (2001) reported average formaldehyde exposures of 21.4 ppb among 15 randomly selected residents of Helsinki, Finland in 1997 based on 48-hour measurements with personal monitors.  While major metropolitan formaldehyde concentrations likely exceed those of other locations in the country where the study subjects lived and worked and the 1997 sampling date occurred after the study period (1985-1995), 21.4 ppb serves as a reasonable estimate of the non-work-station exposure experienced by the study subjects. Factoring in the average non-work-station exposure concentration of 21.4 ppb (Jurvelin et al., 2001) for all times when the study subjects were not working in "exposed" workplace areas, the 8-hr TWA exposure levels are `non-exposed' (21 ppb), `low exposure' (mean of 34 ppb), `medium exposure' (mean of 86 ppb), and `high' exposure (mean of ~226 ppb).  The same approach can be used to derive 24-hour TWAs, with the average exposure level of 21.4 ppb from Jurvelin et al. (2001) serving as an estimate of background exposure levels outside of work.  The adjusted 24-hour TWA exposure levels are `non-exposed' (21 ppb), `low exposure' (mean of 26 ppb), `medium exposure' (mean of 43 ppb), and `high' exposure (mean of 89 ppb).  These data are summarized in Table 2 below.  



Table 2.  Concentration-response data on time to pregnancy from Taskinen et al. (1999) Table 5 with reported and adjusted exposure concentrations.
                                       
                                  < 1 year
                                  >= 1 year
                                     Total
                    Risk of Not Conceiving within 12 months
                                      RR
                    Formaldehyde conc w/o background (ppb)
            8-hour TWA exposure conc adjusted for background (ppb)
            24-hour TWA exposure conc adjusted for background (ppb)
                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                       
                                   Unexposed
                                      261
                                      27
                                      288
                                     0.094
                                     1.00
                                       0
                                      21
                                      21
Low
                                      107
                                      12
                                      119
                                     0.101
                                     1.08
                                      18
                                      34
                                      26
Medium
                                      68
                                       9
                                      77
                                     0.117
                                     1.25
                                      76
                                      86
                                      43
High
                                      31
                                       8
                                      39
                                     0.205
                                     2.19
                                      219
                                      226
                                      89

Regression equations for linear and exponential fits to the adjusted 24-hour TWA data in Table 2 are provided below.  The estimated concentration-response functions are shown in Figure 6.


Figure 6.  Linear and exponential concentration-response relationships between formaldehyde exposure and subfertility (24-hour TWA exposure with adjustment for background exposure concentration) based on data from Table 5 of Taskinen et al. (1999).	      The linear function of subfertility risk based on estimated 24-hour TWA exposure concentrations adjusted for background exposures yielded a measure of fit of R[2]=0.987 indicating a good fit to these data.  The linear function can be expressed as:
                     Risk=0.056+0.0016(exposure)				(2-3)

Here the estimated background risk of subfertility is 5.6% (in the hypothetical absence of any ambient formaldehyde), which is somewhat lower than reported rates for the general United States population.  Stephen and Chandra (1998) cite data from the National Survey of Family Growth showing the infertility rates in the United States range from 4-6% among females age 15-24 years, from 10-11% among those aged 25-34 years and from 11-13% among those aged 35-44 years.
The exponential function of risk (which is equivalent to the linear function of ln(risk)) yielded a measure of fit of R[2]=0.997, also indicating a good fit to these data.  The exponential function can be expressed as:
                     Risk=0.074*e0.011(exposure)				(2-4)

Here the background risk of subfertility is 7.4%, which is closer to the reported rates cited above.
The results based on the estimated 24-hour TWA exposures adjusted for background are considered the most applicable for use in the economic benefits assessment.  Both the linear and exponential models appear to slightly underestimate background rates for subfertility for a hypothetical zero exposure concentration for formaldehyde; however, exposure scenarios for the benefits analysis are more in the range of the data (i.e., 24-hour ADCs near or > 20 ppb), and both models fit well in that range.  Thus, the linear function is preferred (see Equation 2-3) because of its ease of applicability in the benefits analysis.  Note that this function is based on formaldehyde concentration in terms of a 24-hour average exposure; this is in contrast to the functions provided for sensory irritation and asthma above, where the formaldehyde concentrations are in terms of residential (and some in-school for asthma) concentration levels.
2.3.4 Female Reproductive Toxicity: Discussion of Uncertainties
Systemic effects of formaldehyde beyond the portal of entry are unlikely to arise from the systemic delivery of formaldehyde; however, it was noted by the NAS (2011) that it is important to differentiate between systemic delivery and systemic effects and that the delivery of formaldehyde to distal sites was not a prerequisite for systemic effects.  As mentioned previously, adverse reproductive effects of other air pollutants, including other reactive gases, have been reported in the literature.
The study by Taskinen et al. (1999) was a well-designed population-based study that appears to have been well executed and analyzed using appropriate methods.  The study population of Finnish women appears well defined and adequately selected so as to allow for meaningful comparisons of health effects between individuals with different levels of exposure to formaldehyde, with qualifications discussed below.  The participation rate was 64%, which is low enough to raise a concern about the potential for selection bias.  However, the authors noted that selection bias has not influenced the results of other reproductive epidemiology studies reporting results on smoking, irregular menstruation, and earlier miscarriages, which are known to lengthen the time to pregnancy (Bolumar et al., 1996; Sallmén et al., 1995; Baird and Wilcox, 1985).  Furthermore, there is no evidence to support the conjecture that an individual's decision to participate in this study would be differential with respect to their workplace formaldehyde exposures while being nondifferential with respect to the other exposures examined in the study, including organic solvents, wood dust, and phenols.  Similarly, since the women who chose to participate in this study were not likely to be aware of the specific hypotheses under investigation, they could not have known their formaldehyde exposures, which were independently estimated by an industrial hygienist.  Thus, selection bias is not a likely explanation for the findings of adversity.  The findings by Taskinen et al. (1999) of reduced fertility and increased risk of spontaneous abortion are internally consistent and coherent with other reports of increased risk of pregnancy loss associated with exposure to formaldehyde (John et al., 1994; Taskinen et al., 1994; Seitz and Baron, 1990; Axelsson et al., 1984).  
Other strengths include the linking of workers with the national database of birth outcomes and the exposure assessment by workplace measurement and an industrial hygienist.  It is possible, however, that the women in the study may have inaccurately recalled their workplace histories.  Weaknesses include the collection by questionnaire of data on pregnancy history, including spontaneous abortions and time to pregnancy.  However, spontaneous abortion is the most common adverse outcome of pregnancy (Kline et al., 1989), and retrospective self-report of spontaneous abortion has been found to match well with prospectively collected reproductive histories (Wilcox and Horney, 1984).  Many spontaneous abortions, however, are missed with self-reporting, with the magnitude likely exceeding 25%, but only rarely do women self-report false positive events (Wilcox and Horney, 1984).  The effect of such an undercount is to cause a bias towards the null when the likelihood of undercounting is unrelated to exposure.  The implication is that the observed association of increased risk of spontaneous abortion associated with occupational exposure to formaldehyde may be an underestimation of the true risk.  Taskinen et al. (1999) state that only a few women could not report the length of time to pregnancy, so it is unlikely that there could have been differential accuracy in this outcome variable by difference in formaldehyde exposures, and, therefore, any systematic bias is also unlikely.  Non-differential errors in reporting of outcomes is generally understood to obscure any true associations making them more difficult to detect statistically.
There is a possibility of exposure measurement error in the computation of mean daily exposure concentrations.  The exposure assessment was based on a detailed questionnaire on workplace, occupation, and work tasks, which were matched to industrial hygiene measurements from the same factory, when available, or from other work places of the same industrial activity.  Differential recall of workplaces, occupations and work tasks as an explanation for the reported findings is a realistic concern in general.  However, it is unclear why recall would have been differential for formaldehyde in such a way as to create bias for that exposure but not for exposures to phenols or dusts which were also evaluated as potential exposures of concern.  Had there been differential recall, such a phenomenon would likely have been across all exposures.  As the industrial hygiene exposure estimates of all exposures were done without knowledge of the pregnancy history, any measurement error would likely have been non-differential.  It is well known that non-differential (random) measurement error tends to create a bias towards the null.  In this case, the implication would be that the true effect of the formaldehyde exposures may have been an even lower FDR, which was attenuated towards the null value of 1 (unity).  It is difficult to estimate the magnitude of such exposure measurement bias.  Recent methodological work which imposed substantial measurement error on simulated exposure values showed that attenuation was as high as 50% (Bateson and Wright, 2010), with more modest error resulting in a 20% attenuation.  For the concentration-response function derived here, the true slope may be somewhat steeper than estimated due to potential exposure measurement error.  There is also uncertainty in the adjustment for non-work-station exposures, which was based on the average exposure concentration from 48-hour sampling of 15 individuals (who were not part of the Taskinen et al. study).
In addition, there is uncertainty regarding the extent to which the effect of formaldehyde on FDR involves inhalation and/or dermal exposure.  While there did appear to be a trend towards greater reductions in fertility associated with greater air concentrations of formaldehyde, only the most highly exposed group showed a statistically significant effect, with a FDR of 0.64 [95% CI: 0.43-0.92].  Taskinen et al. (1999) noted that of the 39 women with the highest exposures, 22 wore gloves.  The FDR for the 17 women who did not wear gloves was 0.51 [95% CI: 0.28−0.92].  The FDR for women who did wear gloves was 0.79 [95% CI: 0.47−1.23].  Results stratified by respirator use were not presented.  
The FDR estimates stratified by glove use can be interpreted in at least three ways.  First, these results may indicate that there was some protective effect of glove use since when the highly exposed group was separated based on glove use, the FDR for women who did wear gloves appeared higher and was not significantly different from one (FDR=0.79 [95% CI: 0.47−1.23]).  If the route of exposure were dermal rather than by inhalation, then the use of protective gloves may have a beneficial effect on the time to pregnancy.
Second, while only the results for all highly exposed women (FDR = 0.64; 95% CI: 0.43-0.92) and those who did not wear gloves are statistically significantly different from 1, which may suggest a role for dermal contact in the observed subfertility associated with formaldehyde exposure, all 3 results are below 1 and the confidence intervals have substantial overlap with each other.  The substantial overlap of the confidence intervals suggests that there is not a statistically significant difference between the results with and without gloves.  Thus, the difference in adverse effect estimates based on glove usage may simply be the result of random variability in subdividing the 39 highly exposed women into smaller groups of 17 and 22.  
Third, it is well understood that workplace safety protocols will result in the correlation of use of protective equipment.  Therefore, it is plausible that women who were more likely to wear gloves were also more likely to wear respirators and that the difference in FDR estimates between those who used gloves and those who did not may be partially explained by the joint usage of gloves and respirators.
EPA used a general form of a Wald statistic to test the homogeneity hypothesis that the FDR of 0.64 reported for all highly exposed women was uniform across both strata of glove use.  The Wald statistic is the sum of the squared differences between the stratum-specific effect estimates and the hypothesized common value of the effect estimate divided by the variance of the stratum-specific effect estimate (Rothman and Greenland, 1998).  For ratio measures such as the FDR, the natural logarithm should be taken.  The variances of the stratum-specific ln(FDR) were calculated by extracting the standard errors from the confidence intervals.  The Wald statistic was computed as follows:
       χWald2= [ln0.51-ln0.64]20.303+ [ln0.79-ln0.64]20.245=1.30		(2-5)

The Wald statistic has one less degree of freedom than the number of strata.  Here the p-value is 0.25, so the hypothesis of homogeneity of effect across strata of reported glove use is not rejected.

This assessment relied on the facts that the a priori null hypothesis that air concentrations of formaldehyde were not associated with reduced fertility was statistically rejected based on the FDR for all highly exposed women and that, in a sub-group analysis of glove use, a statistical test of the homogeneity of effect across levels of glove use did not show that the effect was modified by glove use.  Therefore, this assessment developed a concentration-response function assuming that the reduced fertility effects as measured by the increased time to pregnancy are attributable to inhalation exposure, recognizing that there are potentially important uncertainties which remain. 
 
Lastly, although Taskinen et al. (1999) controlled for several possible confounding variables (employment, smoking, alcohol consumption, number of children, and menstrual irregularity), it is not explicitly clear that they controlled for the age of the women in the study (which ranged from 20-40 years) in the proportional hazards regression model.  However, the authors did explicitly state that age was controlled for in the other analyses which were presented.   It is well known that age is negatively correlated with female fertility. Consequently, if, for any reason, older women tended to have higher exposures and they did not control for age, then this may lead to a misattribution of the fertility effect to formaldehyde rather than age.  Exposure to solvents, wood dust and other dusts, and phenols was not associated with decreased fecundability and these agents would not be expected to have been confounders.  Xylene was reported to be associated with an increased risk of spontaneous abortion in an earlier study in laboratory workers (Taskinen et al., 1994) but was not mentioned as an exposure for the wood workers.
As noted at the outset of this section, the database on the effects of formaldehyde exposure on the female reproductive system was limited.  The available evidence from epidemiologic studies is suggestive of an association with an increased risk of spontaneous abortion, which is coherent with and contributory to diminished fertility and increased infertility since the loss of a pregnancy delays the time until delivery of a live born child.  Evidence from animal toxicology studies is also supportive of the observed association in humans.  While the evidence base is small and somewhat varied, the potential impact of the suggested association, however uncertain, remains important.  In their peer-review of the draft IRIS assessment, the NAS (2011) affirmed that the derivation of quantitative concentration-response estimates from such available evidence is in keeping with EPA's non-cancer practices even if there is uncertainty about the effect (U.S. EPA, 2002).
In summary, Taskinen et al. (1999) reported a finding of an association between formaldehyde exposure and reduced fertility that appeared to be concentration dependent.  While this may only be suggestive of an association, it does appear to be consistent with the relatively small data base of other studies of female reproductive toxicity.  Evidence that formaldehyde could be associated with reduced fertility (subfertility) is a serious concern and more research would be helpful in reducing uncertainty in the hazard identification and quantifying any concentration-response relationship.  The available data from Taskinen et al. (1999) do allow for the derivation of a concentration-response function which can provide a basis for use in the economic analyses.  
2.4 References
Akinbami LJ. (2006) The State of childhood asthma, United States, 1980 - 2005. Advance data from vital and health statistics; no 381, Hyattsville, MD: National Center for Health Statistics.  
Alexandersson, R; Hedenstierna, G. (1988) Respiratory hazards associated with exposure to formaldehyde and solvents in acid-curing paints.  Arch Environ Health 43:222 - 227.
Andersen, I; Mølhave, L. (1983) Controlled human studies with formaldehyde.  In: Gibson, JE; ed.  Formaldehyde toxicity.  Washington, DC: Hemisphere Publishing Corporation; pp. 154 - 165.
	Arts, JH; Dröge, SC; Spanhaak, S; et al. (1997) Local lymph node activation and IgE responses in brown Norway and Wistar rats after dermal application of sensitizing and non-sensitizing chemicals.  Toxicology 117:229 - 234.
Axelsson, G; Lűtz, C; Rylander, R. (1984) Exposure to solvents and outcome of pregnancy in university laboratory employees.  Br J Ind Med 41:305 - 312.
Baird, DD; Wilcox, AJ. (1985) Cigarette smoking associated with delayed conception.  J Am Med Assoc 253:2979-2983.
Bateson, TF; Wright JM. (2010) Regression calibration for classical exposure measurement error in environmental epidemiology studies using multiple local surrogate exposures. Am J Epidemiology 172: 344-52.
Bolumar, F; Olsen, J; Boldsen, J. (1996) Smoking reduces fecundity: A European multicenter study on fertility and subfecundity.  The European study group on infertility and subfecundity.  Am J Epidemiol 143:578 - 587.
CDC.(2009) http://www.cdc.gov/mmwr/preview/mmwrhtml/mm6017a4.htm?s_cid=mm6017a4_w
Cometto-Muňiz, JE; Cain, WS. (1992) Sensory irritation.  Relation to indoor air pollution.  Ann NY Acad Sci 641:137 - 151.
Feron, VJ; Arts, JH; Kuper, CF; et al. (2001) Health risks associated with inhaled nasal toxicants.  Crit Rev Toxicol 31:313 - 347.
Garrett, MH; Hooper, MA; Hooper, BM; et al. (1999a) Increased risk of allergy in children due to formaldehyde exposure in homes.  Allergy 34:330 - 337.
Glinianaia, S.V.; Rankin, J.; Bell, R.; et al. (2004a) Particulate Air Pollution and Fetal Health: a Systematic Review of the Epidemiologic Evidence. Epidemiology 15, 36-45. 
Glinianaia, S.V.; Rankin, J.; Bell, R.; et al. (2004b) Does Particulate Air Pollution Contribute to Infant Death? A Systematic Review. Environ. Health Perspect. 112, 1365-1371. 
Hanrahan, LP; Dally, KA; Anderson, HA; et al. (1984) Formaldehyde vapor in mobile homes: a cross sectional survey of concentrations and irritant effects.  Am J Public Health 74(9):1026 - 27.
Hemminki, K; Kyyrönen, P; Lindbohm, ML. (1985) Spontaneous abortions and malformations in the offspring of nurses exposed to anaesthetic gases, cytostatic drugs, and other potential hazards in hospitals, based on registered information of outcome.  J Epidemiol Community Health 39:141 - 147.
Hemminki, K; Mutanen, P; Salonienmi, I; et al. (1982) Spontaneous abortions in hospital staff engaged in sterilizing instruments with chemical agents.  Br Med J 285:1461 - 1463.
Holmström, M; Wilhelmsson, B. (1988) Respiratory symptoms and pathophysiological effects of occupational exposure to formaldehyde and wood dust.  Scand J Work Environ Health 14:306−311.
Horvath, E, Jr; Anderson, J; Pierce, WE; et al. (1988) Effects of formaldehyde on the mucous membranes and lungs: A study of an industrial population.  JAMA 259:701 - 707.
John, EM; Savitz, DA; Shy, CM. (1994) Spontaneous abortions among cosmetologists.  Epidemiology 5:147 - 155.
Jurvelin, J; Vartiainen, M; Jantunen, M; et al. (2001) Personal exposure levels and microenvironmental concentrations of formaldehyde and acetaldehyde in the Helsinki metropolitan area.  J Air Waste Manag Assoc 51:17 - 24.
Kline J, Stein Z, Susser M. Conception to birth: epidemiology of prenatal development. New York: Oxford University Press, 1989.
Kriebel, D; Sama, SR; Cocanour, B. (1993) Reversible pulmonary responses to formaldehyde.  A study of clinical anatomy students.  Am Rev Respir Dis 148:1509 - 1515.
Kriebel, D; Myers, D; Cheng, M; et al. (2001) Short-term effects of formaldehyde on peak expiratory flow and irritant symptoms.  Arch Environ Health 56(1):11 - 18.
Krzyzanowski, M; Quackenboss, JJ; Lebowitz, MD. (1990) Chronic respiratory effects of indoor formaldehyde exposure.  Environ Res 52:117 - 125.
Kulle, TJ. (1993) Acute odor and irritation response in healthy nonsmokers with formaldehyde exposure.  Inhal Toxicol 5:323 - 332.
Lacasana, M.; Esplugues, A.; Ballester, F. (2005) Exposure to Ambient Air Pollution and Prenatal and Early Childhood Health Effects. Eur. J. Epidemiol. 20, 183-199. 
Liu, KS; Huang, FY; Hayward, SB; et al. (1991) Irritant effects of formaldehyde exposure in mobile homes.  Environ Health Perspect 94:91 - 94.
Maisonet, M.; Correa, A.; Misra, D.; Jaakkola, J.J. (2004) A Review of the Literature on the Effects of Ambient Air Pollution on Fetal Growth. Environ. Res. 95, 106-115. 
McGwin, G; Lienert, J; Kennedy, JI. (2010) Formaldehyde Exposure and Asthma in Children: A Systematic Review. Environ Health Perspect 118:313 - 317.
National Academy of Science. (2011) Review of the Environmental Protection Agency's Draft IRIS Assessment of Formaldehyde. National Research Council.
Nielsen, GD. (1991) Mechanisms of activation of the sensory irritant receptor by airborne chemicals.  Crit Rev Toxicol 21:183 - 208.
Ritchie, IM; Lehnen, RG. (1987) Formaldehyde-related health complaints of residents living in mobile and conventional homes.  Am J Public Health 77:323 - 328.
Rothman, KJ; Greenland, S. (1998) Modern Epidemiology, 2[nd] edition.  Lippincott Williams & Wilkins, Baltimore.
Rumchev, KB; Spickett, JT; Bulsara, MK; et al. (2002) Domestic exposure to formaldehyde significantly increases the risk of asthma in young children.  Eur Respir J 20:403 - 408.
Sallmén, M; Lindbohm, ML; Kyyronen, P; et al. (1995) Reduced fertility among women exposed to organic solvents.  Am J Ind Med 27(5):699 - 713.
Seitz, T; Baron, S. (1990) Health hazard evaluation report: Rockcastle Manufacturing, Mount Vernon, Kentucky.  National Institute for Occupational Safety and Health, U.S. Department of Health and Human Services, Cincinnati, OH; HETA 87-349-2022.
Sram, R.J.; Binkova, B.; Dejmek, J.; Bobak, M. (2005) Ambient Air Pollution and Pregnancy Outcomes: a Review of the Literature. Environ. Health Perspect. 113, 375-382. 
Stephen E.H.; Chandra A. (1998) Updated projections of infertility in the
United States: 1995 - 2025.  Fertility and Sterility 10:30-34.
Taskinen, H; Kyyronen, P; Hemminki, K. (1994) Laboratory work and pregnancy outcome.  J Occup Med 36:311-319.
Taskinen, HK; Kyyronen, P; Sallmen, M; et al. (1999) Reduced fertility among female wood workers exposed to formaldehyde.  Am J Ind Med 36:206 - 212.
U.S. EPA. (2010) Toxicological Review of Formaldehyde  -  Inhalation Assessment. EPA/635/R-10/002A.  Integrated Risk Information System (IRIS).  National Center for Environmental Assessment, Washington, DC.  Available online at http://www.epa.gov/iris.
U.S. HHS. (2007) Asthma Education and Prevention Program Expert Panel Report 3: Guidelines for the Diagnosis and Management of Asthma. National Institutes of Health. National Heart Lung and Blood Institute. NIH Publication Number 08-5846.
Wilcox, AJ; Horney, LF. (1984) Accuracy of spontaneous abortion recall.  Am J Epidemiol 120:727 - 733.
Zhao, Z; Zhang, Z; Wang, Z; et al. (2008) Asthmatic symptoms among pupils in relation to winter indoor and outdoor air pollution in schools in Taiyaun, China.  Environ Health Perspect 116:90 - 97.
Section 3: Benefits Assessment Approach
3.1 Introduction/Background
The economic benefit of a risk reduction to an individual can be approximated by his or her willingness to pay to avoid a small change in the risk times the reduction in risk. This willingness to pay is denominated in dollars and represents the amount of money the individual would pay to obtain the risk reduction and be just as well off as before the change. For example, if an individual would pay $0.10 to avoid an additional 1% risk of having a bad headache on the job and some policy reduced the chance of experiencing that headache by 25%, then the value of that policy change to the individual would be $2.50. In some cases, the cost of the illness can be used as a proxy for the willingness to pay but, as should be obvious in the case of a headache, this cost of illness may be less than the true willingness to pay to avoid the outcome. This is all relatively straightforward if the risk reduction occurs in the current time period. Evaluating the economic value of a series of changes in risk that occur to a number of individuals in the future, however, can be tricky because one must keep track of the benefit to each individual over time and then discount back to the present. 

3.1.1 General Model
Following the life-cycle consumption literature (Cropper and Portney 1990; Cropper and Sussman 1990), an individual's willingness to pay for a future risk reduction is the discounted willingness to pay in the period in which the risk reduction occurs, discounted at the consumption rate of interest, which could vary over time. This must be done for all risk reductions throughout an individual's life. From an intergenerational standpoint, a future individual's discounted willingness to pay must be discounted back to the present using a social rate of discount, which could also vary over time.
	Mathematically, the total willingness to pay by an individual, n, at time 0 for a risk reduction at age a is
	,	
	where WTPn,a is the marginal willingness to pay of individual n for a risk reduction at age a. λ is a standard exponential discount factor equal to 1/(1+δ), where δ is a constant consumption rate of discount. Δrn,a(en,0,...,en,a) is the change in risk at age a, which could depend upon the exposure, en,t, from the beginning of the individual's life, k=0, until age a. 
If we look at the total willingness to pay from an intergenerational perspective, then we further discount the individual's value back to the present using the social rate of discount. For simplicity, we assume that the social rate of discount equals the consumption rate of discount, and that both are constant over time. If we denominate each generational cohort, g, by the year in which the cohort was born, with g=0 for individuals born this year, then the total willingness to pay at time 0 for a risk reduction for individual ng (that is, individual n of generation g) at age a would be
	.	
The willingness to pay for all risk reductions that this individual will receive over his or her lifetime, from age 0 to death at age An, would be 
	.	
To get a comprehensive measure of the total willingness to pay for any set of future risk reductions, this exercise must be carried out for all individuals in a generation, ng = 1,...,Ng, for every year of each individual's life, a=0,...,An, and across all generations, g = 0,...,G. The total willingness to pay for all future risk reductions would then be
	.	

3.1.2 Simplified Model
Equation (4) represents the general model, in which the willingness to pay for each individual is calculated as the sum of discounted willingness to pay for the risk reduction experienced in each period. The difficulty with equation (4) is that is requires us to know both the risk reduction and the willingness to pay for each individual in each period. Given that this is generally impractical, we modify the problem to make it tractable. For example, if every individual in a given generation were to experience the same risk reduction, and if we assume that the real (as opposed to nominal) willingness to pay value is constant across time and individuals, then equation (4) simplifies to
	,	
where Popg is the population of individuals of generation g. An example might be the value of a reduction in exposure to a uniformly mixed pollutant in an airshed. Each individual experiences the same exposure reduction and, by assumption, the same risk reduction. If we use an average marginal willingness to pay to obtain this risk reduction, then we can estimate the economic benefit of the action using equation (5). This is important because we no longer have to aggregate across individuals. Instead, we can simply calculate the average benefits in any given year, , multiply times the population in that year, Ng, and discount back to the present using the discount factor λ[(][a+g][)].
In the case of formaldehyde exposure, however, we cannot assume that each individual experiences the same risk reduction. However, we can still avoid aggregating across individuals through two simplifying assumptions. First, if the risk reduction is only a function of the exposure at age a rather than the lifetime exposure, then the change in risk for individual ng, is . Second, if we assume a linear concentration-response function (or approximate linearity around the change in exposure), then the change in risk is some proportion of the change in exposure. That is, . With these two changes, equation (4) simplifies to
	.	
This is the correct formula if every individual experiences the same change in exposure at the same age, but can be expanded if different groups experience different exposure changes. For formaldehyde, individuals in different housing types (e.g., detached single family homes, attached single family homes, apartments, mobile homes, and campers/RVs) experience different levels of formaldehyde based on the amount of composite wood products in these housing units and the air volume. In addition, different age groups (infants, children, adult workers, and retirees) experience different exposure levels based on the amount of time they are in the home and where they go when they are not in the home. 
Dividing the population up into exposure groups based on age cohorts, c=0,...,C, and housing type, h = 1,...,H, and letting t=a+g, the simplified equation for total willingness to pay can be written as
	,	
where Poph,c,t is the population in each exposure group at time t and Δeh,c,t is the change in exposure experienced by that group. The advantage to this approach is that the willingness to pay can be calculated for each year individually and the total willingness to pay will be calculated as the sum of discounted values. 
Equation (7) can now be applied to each endpoint to obtain the total willingness to pay for a policy change. The change in exposure in any given year will vary by individual depending on the type of housing structure, the age of that housing, and the climate (specifically, the temperature and humidity). The complete benefits analysis will use approximately 220 exposure scenarios associated with four housing types (mobile homes, apartments, single family attached homes, and single family detached homes), eleven age-of-unit profiles (new structure, 1-year-old structure, ..., 10 year-old structure), and five geographic climate zones. (illustrated in Figure 8).


Figure 8. The U.S. Energy Information Administration's five climate zones based on the average number of heating degree-days (HDD) and cooling degree-days (CDD) over a 30-year period. Climate zones do not necessarily follow State boundaries, because climate is affected by elevation, proximity to coast lines, latitude, and other physical features. 

To simplify this exposition, however, we illustrate the benefits analysis using just three housing profiles: a new mobile home in climate zone 1, a 1-year-old mobile home in climate zone 1, and a new single family detached home in climate zone 1. The population in each housing type will be the population for that climate zone, estimated from the Residential Energy Consumption Survey (EIA 2008) and scaled by aged to match the age distribution for the general population (U.S. Bureau of Census 2009). An example of this application is given below for each of the three endpoints (sensory irritation, asthma incidence, and reduced fertility). The discussion for each endpoint is organized into four parts: monetization; the application of the annual approach, a worked example, and a discussion of the uncertainties. These three endpoints represent the non-cancer effects for which a quantitative concentration exposure-response relationship can be derived.  It is possible, even likely, that there are other non-cancer health impacts associated with formaldehyde exposure for which concentration exposure-response relationships cannot derived due to lack of data or sufficient research. If this is true, then the total economic benefits may be underestimated in the analysis here.

3.2 Sensory Irritation
The valuation of sensory irritation is the most straightforward of the three non-cancer endpoints because the monetization has been used in numerous EPA rules and the concentration-response relationship is for a time period less than the one year time step of the exposure model.
3.2.1 Monetization
Loehman and others conducted a survey of 396 respondents to estimate the willingness to pay to avoid one symptom-day of shortness of breath, coughing and sneezing, and head congestion (including eye, ear, and throat irritation).  A survey of this sort, in which respondents are asked to state their willingness to pay based on the policy described is called stated preference survey. Loehman used a specific type of stated preference survey called a contingent valuation survey. They report a median willingness to pay of $2 - $79 per avoided symptom-day. The value for severe head congestion (which includes eye irritation) was $8.17 for one symptom-day. (Green et al. 1978; Loehman et al.1979)
Tolley et al. (1986) conducted a contingent valuation study from the personal interviews of 176 respondents in 1984-1985 regarding the willingness to pay to avoid seven "light" (i.e., less severe) symptoms. The symptoms were coughing, stuffed sinuses, throat congestion, itching eyes, drowsiness, headache, and nausea. The willingness to pay to relieve one symptom-day of a light symptom ranged from $25 to $50, with a mean value of $27.73 and a median value of $12.50. (Kenkel, Berger, and Blomquist 1994) Berger et al. (1987) reanalyzed these data to compare the mean willingness to pay and the private cost of illness for these symptoms and found similar values. Dickie and Gerking (1991 and 1998) used a household production function approach to estimate the willingness to pay to avoid 26 respiratory symptoms related to air pollution in 1985 and 1986. The symptoms included were cough; throat irritation; husky voice; phlegm, sputum or mucous; chest tightness; could not take a deep breath; pain on deep respiration; out of breath easily; breathing sounds, wheezing or whistling; eye irritation; could not see as well as usual; eyes sensitive to bright light; ringing in ears; pain in ears; sinus pain; nosebleed; dry and painful nose; runny nose; fast heartbeat at rest; tired easily; faintness or dizziness; felt spaced out or disoriented; headache; chills or fever; nausea; and swollen glands. They found a range of estimates between $0.49 and $190 to relieve one symptom for one day. 
Industrial Economics Incorporated, IEc (1993a and 1993b), conducted a survey of the literature and provided a range of willingness to pay estimates for a variety of morbidity effects, including throat congestion, head and sinus congestion, coughing, asthma attack, chronic allergy attack, eye irritation, headache, shortness of breath, chest tightness, nausea, drowsiness, chronic bronchitis, and angina pectoris. While IEc recommend averaging a number of studies for many of the health effects, they relied only on Tolley et al. (1986) for the value for eye irritation.  Based on these estimates, eye irritation had the highest (mid-range) estimate of the willingness to pay for to avoid a single symptom for one day. 
IEc 1993a, 1993b also estimated the willingness to pay to avoid a minor respiratory restricted activity day using the willingness to pay estimates from Tolley et al. (1986) assuming a combination of three symptoms: coughing, throat congestion, and sinusitis. The assumption behind a minor restricted activity day is that it is a combination of symptoms, but the term is not exactly defined. Krupnick and Kopp (1988) previously suggested that a reasonable lower bound for the willingness to pay for a minor respiratory restricted activity day would be the willingness to pay to avoid a single mild symptom, since any combination of symptoms and various levels of restriction might be considered part of a restricted day. Since a restricted activity day is something less than a lost work day, an upper bound would be the value of a work loss day. Based on IEc's (1993) average values, eye irritation has the highest (mid-range) willingness to pay value. Therefore, the value to avoid eye irritation serves as the best single mild symptom to use to represent a lower bound on a combination of symptoms.
These results have been used by EPA in a number of contexts. In 1997, EPA conducted a retrospective analysis of the benefits and costs of the Clean Air Act (EPA 1997), including the benefits of reduced upper respiratory symptoms associated with air pollution. The upper respiratory symptoms are defined by Pope et al. (1995) as consisting of one or more of the following symptoms: runny or stuffy nose; wet cough; and burning, aching, or red eyes. A central estimate of $19 (in 1990 dollars), with a range from $7 to $33, was developed for one symptom-day, based on the mid-range estimate produced by IEc (1993). The value for a minor restricted activity day is $38, with a range between $16 and $61 (and an assumption of a triangular distribution). The lower bound of $16 is based on the IEc estimate of eye irritation.
In 1999, EPA conducted a prospective analysis of the Clean Air Act (EPA 1999) and used the same values as it used in the 1997 retrospective analysis. In 2011, EPA conducted a second prospective analysis of the Clean Air Act from 1990 to 2020 (EPA 2011a). In this second prospective analysis, the values were updated to 2006 dollars and were adjusted to reflect the expected rise in income level between 1990 and 2020. The value for upper respiratory symptoms was $28.80 at 1990 income levels (in 2006$) and $30.70 at 2020 income levels, with a range of $10.80 to $50.50. The value for a Minor Restricted Activity Days is $59 at 1990 income levels and $64 at 2010 income levels, a range of $24 to $94. As before, the lower bound of the minor restricted activity days of $24 is based on the highest estimate for a single symptom, which is for eye irritation. 
These values are also used for regulatory analysis by EPA's Office of Air and Radiation. While the Economic Analysis for each regulation includes a comprehensive discussion of the willingness to pay values used, the Office of Air and Regulation (EPA 2011b) describes the most common values in its Environmental Benefits Mapping and Analysis Program (BenMAP) program. BenMAP is a publicly available GIS-based program distributed by the EPA to estimate the health impacts and economic benefits from air quality improvements.  Table 3 reports the median values as given in the BenMAP documentation (EPA 2011a)
The value for eye irritation is listed as $20.03 in 1999 dollars, based on the median value of Tolley et al. (1986). 
Table 3: Median Willingness to Pay Estimates for Morbidity Symptoms


Source: Table J-10 in EPA BenMAP documentation ((EPA 2011a).
In summary, the willingness to pay to avoid eye irritation has been used in a number of EPA studies. The use of different base years for different analyses obscures the fact that the value used is almost always based on the IEc (1993) estimate derived from Tolley et al. (1986). Therefore, a value of $24 in 2006 dollars, as was used in the last EPA study to use this number (EPA 2011a), is the value that will be used here as the willingness to pay to reduce eye irritation from formaldehyde exposure. 

3.2.2 Annual approach
The concentration-response function for the prevalence of eye irritation (as a proxy for sensory irritation, as described in Section 2.1 of this document) takes the form. Because this relationship is modeled for a time of less than one year, the total willingness to pay to reduce eye irritation for one year, t, is a straight-forward application of equation (7) above. 
,	
where 
		
is the willingness to pay for any given housing and age cohort. Poph,c,t is the population in that particular cohort, and WTP is the estimate of the WTP for eye irritation (described above). This willingness to pay can then be calculated for each year of analysis. If we were to assess the total benefits of a policy action, we would need to discount each year's benefits back to the base year using the discount factor λ.
.	
3.2.3 Example calculation
The concentration-response function for the prevalence of eye irritation given in Section 2.1 of this document is  based on Hanrahan et al. (1984). While Hanrahan does not provide the relevant time period for this relationship, Liu et al. (1991) produced qualitatively similar results for a two-week time period. Therefore, the following development assumes that the concentration-response relationship for eye irritation is for a two-week period. This means that for one year, 26 two-week periods, the concentration-response function would be .
Table 4, below, lists the exposure for three housing profiles for both the baseline and a "CARB2" policy scenario (i.e., emission limits set at the California phase 2 levels, which are also the emission limits mandated by FSCWPA). This exposure assessment comes from a spreadsheet model based on an application of the Matthews model (Hawthorne and Matthews 1987). A model housing structure is simulated for each housing profile using assumptions about the emissions from the wood found in each housing type for the baseline scenario. The policy scenario is then simulated by assuming that any composite wood in the baseline scenario that is not compliant with California's CARB phase 2 standard is made to be compliant. Any wood [product] that already meets and has lower emissions than specified by CARB2 is assumed to remain the same. In spreadsheet form the formaldehyde exposure results are reported in mg/m[3]; for display in Table 1, the results have been converted to ppb by assuming that 814 ppb formaldehyde = 1 mg/m3. This assumption corresponds to a temperature of 25°C, a pressure of 1 atm, and a molecular weight for formaldehyde of 30.03 g/mol., which is line with the approach for performing unit conversions as described by the National Research Council's standing operating procedures for developing acute exposure guideline levels for hazardous chemicals (NRC 2001).
Table 4: Illustrative formaldehyde exposure scenarios using three housing profiles
                                   Scenario
                                Housing Profile
                               Infants Avg. ADC
                       Preschool / School Child Avg. ADC
                        Non-Industrial Worker Avg. ADC
                               Retirees Avg. ADC
Weighted average ADC (mg/m[3]) during current exposure year


Baseline
New Mobile Home
                                    0.0394
                                    0.0344
                                    0.0349
                                    0.0419

1-year-old Mobile Home
                                    0.0280
                                    0.0248
                                    0.0256
                                    0.0296

New Detached Home
                                    0.0356
                                    0.0312
                                    0.0319
                                    0.0381
CARB2
New Mobile Home
                                    0.0375
                                    0.0328
                                    0.0333
                                    0.0398

1-year-old Mobile Home
                                    0.0268
                                    0.0238
                                    0.0247
                                    0.0283

New Detached Home
                                    0.0354
                                    0.0311
                                    0.0318
                                    0.0379
Weighted average ADC (ppb) during current exposure year


Baseline
New Mobile Home
                                     32.07
                                     28.00
                                     28.41
                                     34.11

1-year-old Mobile Home
                                     22.79
                                     20.19
                                     20.84
                                     24.09

New Detached Home
                                     28.98
                                     25.40
                                     25.97
                                     31.01
CARB2
New Mobile Home
                                     30.53
                                     26.70
                                     27.11
                                     32.40

1-year-old Mobile Home
                                     21.82
                                     19.37
                                     20.11
                                     23.04

New Detached Home
                                     28.82
                                     25.32
                                     25.89
                                     30.85
Weighted average ADC (ppb) during current exposure year


Change
New Mobile Home
                                     -1.55
                                     -1.30
                                     -1.30
                                     -1.71

1-year-old Mobile Home
                                     -0.98
                                     -0.81
                                     -0.73
                                     -1.06

New Detached Home
                                     -0.16
                                     -0.08
                                     -0.08
                                     -0.16
* Note: These are preliminary estimates and will likely change in the final exposure and benefits assessments.
ADC = Average Daily Concentration.
The average daily concentration (ADC) for four categories of classes of individuals (infants, age 0-2; preschool and school-aged children, age 2-16; non-industrial workers, age 16-65; and retirees, age 65-100) are reported in Table 1. Each individual is assumed to enter the next age group at the birthday on the lower bound of the age category. So, for example, an individual is classified as an infant until his or her second birthday, whereupon that individual is classified as a preschool/school-aged child. Individuals in different age categories but living in the same housing type have different ADCs because they have different levels of exposure to formaldehyde outside of the home. The exposure model accounts for formaldehyde concentrations in schools and daycare, in automobiles, workplace exposure, outside. The final benefits analysis will include exposure for a larger group of individuals (e.g., workers exposed to higher levels of formaldehyde in the workplace), but the four classifications given here are sufficient to illustrate the benefits methodology.
Individuals in a new mobile home have the highest baseline exposure of these three profiles, based on ppb, ranging from 34.11 ppb for retirees (in the last column of Table 1) to 28.00 ppb for school-aged children (in the fourth column of Table 1). The exposure is different for each individual because of the amount of time each individual spends in the home compared to other activities. For example, children spend more time outside where formaldehyde exposure is comparatively lower than in the home. The policy scenario results in a reduction of 1.71 ppb to 1.30 ppb for new mobile homes.
Individuals in new single-family detached home have the next highest exposure in this example, ranging from 31.01 ppb to 25.40 ppb. New single family homes have lower emissions than new mobile homes because of the larger ratio of air volume to surface area of wood in the home. A 1-year-old mobile home has a baseline range of exposure from 24.09 ppb to 20.19 ppb. The 1-year-old mobile home has lower emissions than a new mobile home because the stepwise approximation of off-gassing of formaldehyde, with the largest emissions coming from the first year and declining exponentially thereafter. Notice, however, that even though a new detached home has higher overall emissions than a 1-year-old mobile home, the emissions reductions from the policy scenario are larger in the 1-year-old mobile home. This is because the volume of wood which is assumed to be affected by the rule and the effect that it has in the unit differs by housing type, as predicted by the Matthews model.
Table 5, below, illustrates how this exposure assessment and the concentration-response function for eye irritation would be used in a benefits analysis for these three housing profiles in climate zone 1. Each profile has an 8-column block in the table.  The first column block represents the population of 21,670 individuals living in new mobile homes (EIA 2008). This population is distributed across ages (represented by rows) in proportion to the age distribution for the nation as a whole (U.S. Bureau of Census 2009). The baseline exposure, policy scenario exposure, and associated change in ppb are listed for each age. The number of cases for the baseline, policy, and the change in cases (in absolute value) for each age is then calculated using the difference in the concentration-response function at baseline and CARB2 exposure levels. Using a willingness to pay of $24 per case, the willingness to pay at any age is given by equation (9). For example, for an individual age 0 (that is, an infant before his or her first birthday) living in a new mobile home, this would be 

In total, 129.3 cases (the sum of all rows from age 0 on) of eye irritation would be avoided from formaldehyde exposure reduction in new mobile homes in climate zone 1 for one year. The total willingness to pay for this housing profile across all ages would be $3,103.

Table 5: Illustrative benefits calculations for sensory irritation using three housing profiles

Table 5: Illustrative benefits calculations for sensory irritation using three housing profiles (cont.)


The second column block of Table 5 represents the benefits to individuals living in a 1-year-old mobile home. Here assume again that there are 21,670 individuals living in this type of structure (an assumption of convenience due to lack of data), so the population distribution across ages is exactly the same as for new mobile homes. In fact, the only change between column block 1 and column block 2 is the smaller exposure due to the fact that the wood in a one-year-old structure has had time to off-gas. In total, a projected 48.9 cases of eye irritation annually would be reduced in this housing profile, with a total benefit of $1,174 for any year of analysis.
The third column block of Table 5 represents the benefits to individuals living in a new single-family detached home. An estimated 302,507 individuals live in this type of home. Even though the magnitude of the exposure reduction experienced in new detached homes is smaller than that experienced in either mobile home profile presented, the number of cases reduced is larger because the exposure reduction is applied to a larger population. An estimated 115.4 cases of eye irritation are projected to be reduced each year by this policy change, with a benefit of $2,770.
The benefits of all housing profiles are then summed to produce the total benefits in one year. If we assume that the populations and distributions across housing types are stable, then the benefits value for each housing cohort will the same for every year except the first one. In other words, individuals may move from one house to another and we are not capable of predicting those movements, but, if we assume that there will be 21,670 individuals living in a new mobile home in climate zone 1 during every year of our analysis, then we will continue to see $3,149 worth of benefits from this housing profile every year.
An additional conclusion from this analysis is that even after the policy is implemented, there will be a lag in its effect based on the age of the housing structure. This is why, in the example here, the first year is different from the others. A policy requiring "CARB2" compliant wood will affect new houses immediately. It will, however, not affect the existing housing stock, unless those existing houses are remodeled with new wood products. (The proposed rule will include this remodeling impact, but it has not been included here to simplify the exposition.) The effect of the policy will not be seen in one-year-old homes until one year after its implementation. 
Table 6, to the right, illustrates how the total estimated benefits of the rule will be calculated for 30 years using a discount rate of 3% (implying a discount factor of 0.9709). In the year immediately following the policy implementation, year 0 in Table 3, the annual benefits are the sum of the benefits for new mobile homes and new detached houses, which is ($3,103 + $2,770 =) $5,873. The benefits in the second year, and each year thereafter are the benefits from all three housing types, ($3,103 + $1,174 + $2,770 =) $7,048. Discounting these benefits to present value terms by multiplying them times 0.9709[t], where t is the year, produces total benefits of $144,009 for this policy change.

3.2.4 Discussion of uncertainties
The example above assumes that the population is constant from year to year (births = deaths + net migrations) and that the future distribution across housing types is exactly the same as the present distribution, neither of which is likely to be true. However, the method described above can be modified to accommodate a growing population and a different housing and age distribution by changing the population values for each year. 
The concentration-response function used here is non-linear. This means that annual approach may not produce an exact measure of the benefits. However, given that the change in exposure is relatively small, the results from using the non-linear concentration-response function are probably very similar to the results if we were to use a linear function. Furthermore, because the non-linear concentration-response function applies to a period of time less than one year, there should be no problems in applying the annual approach.
The contingent valuation estimates of willingness to pay to avoid eye irritation are rather dated. The values obtained by Tolley et al., which are the underlying values used in the analysis, are 25 years old.  While EPA still uses these estimates, there have been a number of advances over the years in the application of stated preference methods aimed at reducing hypothetical bias which causes stated preference estimates of willingness to pay to be too high. On the other hand, the same willingness to pay value is attributed to both adults and children. There is some evidence that parents are willing to pay more to avoid adverse health effects in their children than they are to avoid the same adverse health effects in themselves (Dickie and Gerking, 2003; Dickie and Ulery, 2002; Liu et al., 2000).  EPA (2000a) reviewed the results of several contingent valuation studies (Loehman et al. 1979, 1979; Rowe and Chestnut 1986; and Tolley et al. 1986) for various symptoms. Both Loehman et al. (1979) and Tolley et al. (1986) found that the willingness to pay to avoid multiple days of a condition is greater than the willingness to pay to avoid one symptom-day. However, the willingness to pay per symptom-day declined as the number of symptom-days avoided increased. In other words, the value to reduce two symptom-days of some effect is generally less than two times the value for one symptom-day. This point was also made in Kenkel, Berger, and Blomquist (1994) and declining marginal willingness to pay for avoided illnesses was also found more recently in Bosworth, Cameron, DeShazo (2009). Therefore, multiplying the marginal willingness to pay for one symptom-day times the number of symptom-days, as has been done here, may overstate the total value and, hence, the benefit of the policy change. However, a reasonable upper bound of the annual value of the total effect for one symptom-day would be the sum of the willingness to pay for one symptom-day of each effect individually. This would be what have reported in Table 5 if we assume that a different set of people experience these symptoms in each of the two week periods.
This analysis only valued one symptom, eye irritation, largely because this is the only symptom for which an effective concentration-response function could be derived. However, there is evidence that there are other forms of irritation (e.g. nose, throat irritation) associated with formaldehyde exposure. If this is true and the reduction of formaldehyde exposure reduces these symptoms concurrently, then the values of those other minor effects should, in theory, be included in the analysis. This limitation will be acknowledged qualitatively in the economic analysis for the proposed rule.
The report by Tolley et al. (1986) suggested that the impact of multiple symptoms is close to, but slightly lower than the aggregate sum of the willingness to pay for individual effects. That is, the willingness to pay for a group of three to five symptoms jointly was slightly less than the sum of the willingness to pay for each symptom individually. Therefore, if we were to produce a concentration-response function for all of these symptoms of sensory irritation associated with formaldehyde exposure, then a reasonable upper bound of the total effect for one symptom-day would be the sum of the willingness to pay for one symptom-day of each effect individually.  EPA (2000a) suggested that a reasonable lower bound would be the high-end value for one symptom. Since eye irritation is the lower end of the median values as reported by IEc (1993a and 1993b), the values used here likely probably represent a lower bound on the true effect of multiple symptoms.

3.3 Asthma incidence
Valuing asthma incidence is more difficult than sensory irritation. First, monetization is more difficult because the valuation is based on the incidence of asthma. Most economic analysis of asthma value the exacerbation of asthma symptoms rather than development of new cases. Second, the concentration-response relationship is based on an odds ratio for asthma prevalence, whereas we are need an annual incidence rate. Third, as illustrated in the sensory irritation section, the exposure model produces results for one-year of exposure to formaldehyde for each age, housing type, climate cohort. If the concentration-response relationship produces an incidence rate for a time period longer than this one year window, then an adjustment to the simple model given by equation (7) needs to be made.

3.3.1 Monetization
EPA has included asthma as a health effect in many of its economic analyses. However, this valuation usually takes the form of valuing an increase, or exacerbation, of asthma symptoms rather than an increase in the incidence of asthma. The Office of Air uses two values to monetize the effect of asthma exacerbation in adults and three values for asthma exacerbation in children.  Rowe and Chestnut (1986) estimate a mean willingness to pay of $43 in 2000$ for avoiding a "bad asthma day" as $43 in 2000$, with a range of $16 to $71. This unit value is applicable to both adults and children. A second value for adults is $74, derived from Dickie and Ulery (2002) and Dickie and Messman (2004), assuming that asthma exacerbation consists of 1 symptom-day. Two unit values for children are available from Dickie and Ulery (2002) and Dickie and Messman (2004). One of these is $86 , twice the adult unit value for adults based on evidence that parents are willing to pay about twice as much to avoid symptoms and illness in their children as in themselves. The other value for children is $156, based on a statistical model including a dummy variable for children. These values were used in all three analyses of the benefits and costs of the Clean Air Act (EPA 1997, 1999, and 2011a) and are summarized in the EPA's Office of Air's BenMAP program (EPA 2011b). The problem with applying these values to formaldehyde exposure is that, as of yet, a statistical relationship between formaldehyde exposure and asthma exacerbation has not been sufficiently well established to develop a concentration-response function. 
As described in the section on concentration-response functions, however, there is a statistical relationship between formaldehyde exposure and asthma occurrence or incidence. While valuing asthma incidence is less common in EPA analyses than valuing asthma exacerbation, it has been done. This approach was used in the first prospective study of the benefits and costs of the Clean Air Act (EPA 1999). The number of new cases of chronic asthma as a function of ozone exposure was estimated based on a study by McDonnell et al. (1999). Using an approach similar to the one that EPA uses to value reductions in chronic bronchitis, the willingness to pay to avoid chronic asthma was based as the net present value of a willingness to pay to avoid the disease over a lifetime. The central estimate (in 1990 dollars) was $25,000, with a triangular distribution and a range between $19,000 and $30,000. 
This range and distribution was based on two studies that estimated the willingness to pay to avoid chronic asthma in adults. Blumenschein and Johannesson (1998) used two different contingent valuation methods to estimate mean willingness to pay for a cure for asthma. Using their mean estimate of $2,268 per year, a three percent discount rate, and 1997 life expectancies for males in the United States, they estimated a present discounted value of the stream of annual willingness to pay values of $47,637 (in 2000$). O'Conor and Blomquist (1997) estimated the willingness to pay to avoid chronic asthma by offering respondents a choice between hypothetical medications which differed in safety and efficacy. They then combined this risk-risk tradeoff with a statistical value of life to derive an annual willingness to pay to avoid asthma. EPA (2011b) reports that, using a value of a statistical life of $5,894,400 (in 1997$), the implied annual value of avoiding chronic asthma, based on O'Conor and Blomquist, would be $1,474. Assuming a three percent discount rate and 1997 life expectancies for males in the United States, the present discounted value of the stream of annual WTPs would be $30,257 (in 2000$). The implied annual value of asthma control of $1,474 (in 1995$) is also close to the best estimates from more recent work by Blomquist, Dickie, and O'Conor (2011). For the average age adult (45 years old) the annual value of asthma control is $1,960 in 2007 dollars, or $1,441 in 1995 dollars.
These willingness to pay values are higher, in real terms, than the direct medical costs for an average asthma patient reported by EPA (2000d) and repeated below in Table 7.

Table 7: Lifetime Direct Medical Costs for Asthma (in 1999$)


Source: Table IV.2-17 in EPA 2000d
The cost-of-illness estimates in this table are based on the cost of medical services, reimbursement by Medicare, and national recommendations and private sector costs regarding drug therapy. The values were obtained by multiplying the probabilities of patients utilizing various services times the cost per service, and then discounting over time to form a present value at various discount rates. One important assumption embedded in the estimate for the average patient is that 30 percent will become asymptomatic as they move into adulthood, so they do not incur costs beyond their seventeenth year, and 70 percent will have the disease throughout their life. All of the high-use patients are assumed to have asthma throughout their life. 
It is not necessarily surprising that the direct medical costs are below the willingness to pay estimates. In general, cost-of-illness estimates understate the willingness to pay to avoid a given health effect because they often omit averting expenditures and the value of lost utility associated with pain and suffering. Although the cost-of-illness approach could be used to value asthma incidence, the use of willingness to pay values is considered to be a more appropriate measure (EPA 2010).
Curiously, beside the prospective analysis of the Clean Air Act, monetization of asthma incidence has not been used in economic analyses of regulatory action. This is probably due to a lack of an appropriate concentration-response relationship. Nevertheless, the EPA's Office of Air includes recommended values for the monetization of chronic asthma in its BenMAP documentation (EPA 2011b) based on Blumenschein and Johannesson (1998) and O'Conor and Blomquist (1997). The value of avoiding one statistical case of chronic asthma is the average of the two estimates, based on a three percent discount rate, or $38,947 (in 2000$). This is the value that will be used as the willingness to pay for reduced asthma incidence from formaldehyde exposure.
There are two reasons why this is not the appropriate value to use for an asthma case developed in the 6-17 age range. First, the value reported in BenMAP represents the average value for adult-onset asthma. The method used to calculate the willingness to pay is based on the present discounted value of a stream of annual values derived from Blumenschein and Johannesson (1998) and O'Conor and Blomquist (1997). Using this method, the willingness to pay to avoid child-onset asthma should be larger because of more years associated with having asthma. 
The present discounted value of the stream of annual WTPs for someone who gets asthma at age a is		
where
       denotes the annual WTP,
	 denotes the age at onset of asthma (e.g.,  = 6, 7, ..., or 17),
	denotes the life expectancy for an individual age a, and
	dr denotes the discount rate,
Note that this implicitly assumes that an individual who develops asthma will suffer with the disease for the rest of his or her life (i.e., he or she will never become asymptomatic). A weighted average pdv can be calculated using the percentages of the population in the age categories as the weights. If denotes the percent of children in the age range [6-17] who are age j,  j = 6, ..., 17 and assuming that any child in the age range is equally likely to have asthma, then 
	 	
Inflating the willingness to pay values for adult-onset asthma derived from the annual values of Blumenschein and Johannesson (1998) and O'Conor and Blomquist (1997) using the CPI-U implies values of $60,322 and $38,314 (2010$) respectively. In contrast, the willingness to pay to avoid child onset-asthma between the ages of 6 and 17 using equation (12) would be $93,341  and $59,287 (2010$) respectively.
The second reason why the values reported in BenMAP may not be appropriate is that there is substantial evidence that non-trivial percentages of asthmatics become asymptomatic at some point in their lives. The 2009 population and prevalence rate results for the total U.S. population in the current asthma and lifetime asthma tables are available online  from the Centers for Disease Control, National Health Interview Survey (NHIS) and are shown in Table 8 below.
Table 8: Results of the 2009 National Health Interview Survey Questions on Asthma and Implied Percentage of Asymptomatic Individuals
Characteristic
Total Population
Children (<18)
Adults (18+)




Lifetime asthma population (in 1000s) (CDC Table 1-1 )
                                                                         39,930
                                                                         10,196
                                                                         29,734
Current asthma population (in 1000s) (CDC Table 3-1 )
                                                                         24,567
                                                                          7,111
                                                                         17,456
Percent of asthmatics who still have asthma:
                                                                          61.5%
                                                                          69.7%
                                                                          58.7%
Percent of asthmatics who are now asymptomatic:
                                                                          38.5%
                                                                          30.3%
                                                                          41.3%
Source: Centers for Disease Control and Prevention 2009

The percent of asthmatics who still have asthma can be calculated by dividing the "current asthma population" by the "lifetime asthma population." The percent of asthmatics that are asymptomatic is found by subtracting this value from 100%.  For example, the adult age group (age 18+), 29,734,000 individuals said they had been diagnosed with asthma; of these, 17,456,000   -  or 58.7% -- said they still have asthma. That implies that 100% - 58.7% = 41.3% of asthmatics in this age group are asymptomatic.
For simplicity, we assume that an asthmatic child who becomes asymptomatic is equally likely to do so at any age after childhood. However, rather than calculate this probability for each age, we discretely represent this equal probability 10 year intervals, starting with age 17  -  ages 17, 27, 37, 47, 57, and 67.  Since the total proportion of child asthmatics who will become asymptomatic at some point after childhood is assumed to be 41%, and each age is assumed to have an equal probability of being the age at which the individual becomes asymptomatic, we assume that (41%/6 =) 6.8% of child asthmatics become asymptomatic at each of the 6 representative ages (17, 27, 37, 47, 57, and 67).
For each of the representative ages (17, 27, 37, 47, 57, and 67), the analysis calculated  , given that age-when-asthma-stops, using equations (27) and (28) above and replacing  in equation (27) with the representative age, for all values of a.  If we assume that asthma starts at the beginning of an age and stops in the middle of an age, then if a child gets asthma at age x and becomes asymptomatic at age y, the number of years the child has asthma is y  -  x + 0.5.   For example, the present discounted value of willingness to pay values for an asthmatic child of age a that become asymptomatic at age 27 is  
	 
		
Equation Error! Reference source not found. can then be used to calculate the resulting value for.  The weighted PDV (in 2010$) of willingness to pay values using this method is $79,214 and $50,314 using the derived annual values of Blumenschein and Johannesson (1998) and O'Conor and Blomquist (1997) respectively. The average of two studies is $64,764 (in 2010$). This is the value that will be used in this analysis.

3.3.2 Annual approach
The concentration-response relationship for asthma incidence is given as an odds ratio for children exposed to formaldehyde. An odds ratio is a way of comparing the probability of an event, in this case asthma diagnosis, occurring between two groups and is commonly used in epidemiology and risk assessment. Mathematically, "odds" is the ratio of the probability that an event will occur, P, to the probability that the event will not occur, (1-P).  That is, odds = P/(1-P). The "odds ratio" is simply the ratio of the odds of the event occurring to an exposed group to the odds of the event occurring in the control group. That is
		
An odds ratio is used to estimate how strongly exposure is associated with the probability that an event, such as asthma diagnosis, occurs. For example, if the odds ratio is 1.027 for a 1 ppb change in formaldehyde exposure and we see 100,000 cases of asthma in our control population, then we would expect to see 102,700 cases of asthma in a population exposed to one additional ppb of formaldehyde.
The odds ratio can be related to the logistic model. The logistic function varies between 0 and 1 and is used to represent the cumulative density function of some event occurring. y(x) is often expressed as a linear function of the form y = β0 + β1∙x. So, in our case, F(x) is the probability of being diagnosed with asthma, P, and x is exposure to formaldehyde. The logit of P is then defined as the natural logarithm of the odds. That is, 
logit(P) = ln(P/(1-P)) = β0 + β1∙x.
Therefore, the odds of asthma incidence for the entire population is e[(][β0 + β1∙x)], and the log-odds is β0 + β1∙x. This means that the result of a logistic regression is nothing more than the log of the odds, or the log-odds. 

The odds ratio of an exposed group, x = x1, to some control group, x = x0, is then 
		 
So β1 gives the impact of a one unit change in exposure (that is, where x1  - x0 = 1). Furthermore, β1 can be recovered by taking the log of the odds ratio given in the epidemiology literature. So, if the odds ratio of a 1 ppb increase in formaldehyde is 1.027, then the β1 in the implied logistic model would be ln(1.027) = 0.0266.
This can be used to determine the willingness to pay for any change in emissions. Given a fixed willingness to pay for one case of asthma, the willingness to pay for a change in exposure over some period of time, t0-t1, is given by a modified version of equation (7).
		
The willingness to pay for any given housing and age cohort is
      		
The "effective odds ratio" is defined here as the odds ratio for a given change in exposure based on the odds ratio from the literature
		
So, continuing with the example above, if the odds ratio is 1.02 for a 1 ppb change in formaldehyde exposure and we would like to determine the effect of a -1.28 ppb change, the effective odds ratio would be e [ln][(1.02][7][)*(-1.28)] = 0.966. 
A problem arises when the time period, t, is longer than the time step of the exposure model. This can be illustrated using childhood asthma incidence and formaldehyde exposure.  The odds ratio for asthma prevelance is based on the random effects model of McGwin et al. (2010), excluding Rumchev et al. (2002). The mean age for the six remaining studies in McGwin et a.. ranges from 8 to 14 years old. The minimum age across the six studies was 6 and the maximum was 17. This is the age range for which we estimate benefits in this analysis.  
We assume that probability of being diagnosed with asthma can be taken from the prevalence rate reported in the 2008 National Health Interview Survey and reported in Table 9. 
Table 9: Lifetime Asthma Prevalence, 2008

All ages
 0 - 4
 5 - 14
 15 - 19
 20 - 24
 25 - 34
 35 - 64
 65+
Asthmatics
38,450
1,499
6,576
3,653
3,609
5,119
13,887
4,107
Prevalence Rate
12.9
7.2
16.4
17.4
17.4
12.7
11.7
11
Population
298,062
20,819
40,098
20,994
20,741
40,307
118,692
37,336
Percentage
100.00%
3.90%
17.10%
9.50%
9.39%
13.31%
36.12%
10.68%
Source: CDC 2008 (Tables 1-1 and 2-1)

The data indicate that the asthma prevalence among 0-4 years olds is 7.2 percent and asthma prevalence among 5-14 year olds is 16.2 percent. We assumes that once a child gets asthma, he or she does not outgrow it within that age range.  For example, for ages 0-4, the prevalence rate is 7.2%.  This means that 7.2% of individuals ages 0-4 have asthma.  Since this age range starts at birth, all of these asthma cases must have started within the age range  -  i.e., in this case, prevalence equals cumulative incidence.  For any age range that starts at an age greater than 0, however, prevalence does not equal incidence, since some of the prevalent cases may have started at an age less than the lower bound of the age range.  For example, the 16.4% of individuals with asthma between the ages of 5 and 14 include those individuals whose asthma started during ages 0-4.  The incidence rate for the age range 5-14 was estimated by subtracting 7.2 percent from 16.4 percent to estimate that 9.2 percent of individuals in the age range of 5-14 are newly diagnosed with asthma. For this analysis, we assume that this 9.2 percent applies to the 12 years that we are analyzing and that new cases are uniformly distributed over these 11 years. Thus, the annual incidence rate for our analysis is 0.092/12 = 0.0076, or 0.76% for children aged 6 to 17.  
Using this assumption, the expected number of asthma cases that we would expect to see in the baseline per 100,000 children age 6 to 17 is illustrated by the red and blue areas in Figure 9. We would expect 760 cases per year each year for twelve years, for a sum total of 9,200 cases of 
If the odds ratio for a 1 ppb reduction is 1.027, then we would expect a 2.7% reduction in the area under this curve for a 1 ppb reduction in exposure. That is, we would see 242 fewer asthma cases, found by multiplying 9,200 times the effective odds ratio for a 1 ppb reduction, [1 - e [ln][(1.02][7][)∙(-1)]].  If we had a 10 ppb reduction, we would see 9,200∙[1 - e [ln][(1.02][7][)∙(-10)]] = 2,152 fewer cases, an 23% reduction. If we were to allocate these 2,152 fewer cases uniformly then we would see approximately 179 fewer cases in each. This is illustrated by the dark red areas in Figure 9.

Figure 8. Number of asthma cases per 100,000 from ages 6 to 17, assuming an odds ratio of 1.02 and a 10 ppb change in formaldehyde exposure 
Allocating cases uniformly across the age brackets given by the CDC data provides us with a way to calculate the annual benefits of any exposure reduction that occurs for the entire time period. We now ask the more difficult question of how to model the annual reduction if the representative individual does not experience the exposure reduction over the entire time period. For example, how do we calculate the benefits to an individual who is 15 years old at the beginning of the policy and experiences only one year of the 10 ppb exposure reduction. We consider two possible approaches.
The first approach is to assume that the odds ratio can be applied to the one year reduction in the same fashion as it was applied for the 12 year time period. This is illustrated in Figure 9. In the baseline, we expect 760 cases of asthma among 17 year-olds. Applying the odds ratio to the one year interval implies that a 10 ppb reduction would produce 760∙[1 - e [ln][(1.02][7][)∙(-10)]] = 178 fewer cases, represented by the red area in Figure 9. This is same area as the red area for the 15 to 16 age bracket in Figure 8. 


Figure 8. Upper bound estimate of the reduced number of asthma cases per 100,000, assuming an odds ratio of 1.02 and a 10 ppb change in formaldehyde exposure for one year
The problem with this first approach is that it effectively treats the exposure as an one year effect. The odds ratio that indicated an 23% reduction in asthma cases from a 10 ppb reduction in formaldehyde exposure over 16 years is treated as implying an 23% reduction in asthma case for a 10 ppb reduction in formaldehyde in one single year. However, it serves as an upper bound to the number of asthma cases that might be avoided by an exposure reduction of one year.
At the other extreme, we might assume that the exposure reduction of 10 ppb for one year produces the same effect as if that 10 ppb was spread out over the entire 12 year time period. In other words, a 10 ppb reduction in one year is modeled like a 10/12 = 0.833 ppb reduction for 12 years. This is illustrated in Figure 8. The baseline is represented by the red and blue areas. A 0.625 ppb exposure reduction experienced over 16 years would result in 9,200∙[1 - e [ln][(1.02][7][)∙(-][0.833][)]] = 202 fewer cases, represented by the light and dark red areas. However, only 17 of those cases would occur in the 17[th] year. This would be the number of fewer asthma cases we would see in a population of 760 fifteen-year-old children who experience only one year of a 10 ppb exposure reduction. This second approach provides a lower bound to the number of asthma cases that might be avoided from an exposure reduction over one year.


Figure 8. Lower bound estimate of the reduced number of asthma cases per 100,000, assuming an odds ratio of 1.02 and a 10 ppb change in formaldehyde exposure for one year
This same logic for both the upper and lower bound can be used to determine the benefits of an exposure reduction for any individual who does not experience the exposure reduction for the full period. Mathematically, this means that for any time period , the willingness to pay for an individual who is age k at the time of policy implementation would be 
Upper bound:
	
Lower bound:
	
The reason that this adjustment is necessary is because there are individuals between the ages of 6 and 17 who are alive when the policy is implemented and we must calculate the benefits of the exposure reduction to them. In other words, we need this to model the transition path as we move from the year after policy implementation, where the benefits are presumably lower, to a time when everyone is enjoying the full benefit of the policy. After 12 years, every individual will experience the full 12 years of exposure reduction (in one housing type or another), so won't need to worry about bounding the willingness to pay. Note that the upper bound estimate reflects full benefit for the 17[th] year, so it is the same as if the individual had experienced the full exposure reduction for the 11 years prior.
While we allocated the cases proportionally across age brackets in this case, calculating the transition path of the willingness to pay as the rule is fully phased may be important if the probability of the outcome is small in the final years. For example, consider the case of lifetime cancer risk. The risk of being diagnosed with cancer is greatest in the middle years and smaller in the last year of one's life. If we were to stop dosing an individual with a carcinogen in the final year of his or her life, the upper bound estimate suggests that he or she would receive the same benefit in this last year of life as an individual who had experienced the exposure reduction for his or her entire life. The lower bound estimate would treat this final year exposure reduction as if it had been spread out over the entire lifetime and then allocates the last year's benefit.
Table 10: Illustrative formaldehyde exposure scenarios using three housing profiles
                                   Scenario
                                Housing Profile
                       Preschool / School Child Avg. ADC
                        Non-Industrial Worker Avg. ADC
Weighted average ADC (mg/m3) during current exposure year
                                   Baseline
New Mobile Home
                                                                         0.0344
                                                                         0.0349
                                       
1-year-old Mobile Home
                                                                         0.0248
                                                                         0.0256
                                       
New Detached Home
                                                                         0.0312
                                                                         0.0319
                                     CARB2
New Mobile Home
                                                                         0.0328
                                                                         0.0333
                                       
1-year-old Mobile Home
                                                                         0.0238
                                                                         0.0247
                                       
New Detached Home
                                                                         0.0311
                                                                         0.0318
Weighted average ADC (ppb) during current exposure year
                                   Baseline
New Mobile Home
                                                                          28.00
                                                                          28.41
                                       
1-year-old Mobile Home
                                                                          20.19
                                                                          20.84
                                       
New Detached Home
                                                                          25.40
                                                                          25.97
                                     CARB2
New Mobile Home
                                                                          26.70
                                                                          27.11
                                       
1-year-old Mobile Home
                                                                          19.37
                                                                          20.11
                                       
New Detached Home
                                                                          25.32
                                                                          25.89
Weighted average ADC (ppb) during current exposure year
                                    Change
New Mobile Home
                                                                          -1.30
                                                                          -1.30
                                       
1-year-old Mobile Home
                                                                          -0.81
                                                                          -0.73
                                       
New Detached Home
                                                                          -0.08
                                                                          -0.08


3.3.3 Example calculationThe odds ratio for asthma incidence given earlier in the document is 1.027 per one ppb increase in formaldehyde exposure over a 16 year period. Using the CDC data from Table 9, above, we assume that the probability of being diagnosed with asthma between ages 6 and 17 is 9.2% and that this probability is uniformly distributed across the age bracket. This can now be used for the benefits analysis using equations (19) and (20) above.For this example, we will use the same three housing profiles in climate zone 1 that we used for sensory irritation: a new mobile home; a 1-year-old mobile home; and a new single family detached. We also use the same exposure changes for these three housing profiles, listed in Table 10 for the demographics of interest: school-aged children, age 2-16, and non-industrial workers.
Table 11 lists the benefits for the assumed exposure reductions in these three housing profiles. The first block represents the 3,436 children living in new mobile homes in climate zone 1 (EIA 2008, U.S. Bureau of Census 2009). Notice that the population assumptions are the same as those that we assumed for the sensory irritation analysis, but we are only concentrating on the children age 6-17. Under the baseline, we expect 26.34 asthma cases for this housing profile. Given the assumed exposure reductions, we would expect 0.898 fewer asthma cases. 
Table 11: Illustrative benefits calculations for asthma incidence using three housing profiles.
                        New Mobile Home, Climate Zone 1
                                      Age
                                  Population
                            Baseline Exposure (ppb)
                             CARB2 Exposure (ppb)
                           Exposure Reduction (ppb)
                            Expected Baseline Cases
                             Effective Odds Ratio
                                 Cases Avoided
                                      WTP
                                                                               
                                                                          3,436
                                                                               
                                                                               
                                                                               
                                                                          26.34
                                                                               
                                                                          0.898
                                                                        $58,181
                                                                              6
                                                                            294
                                                                          28.00
                                                                          26.70
                                                                          -1.30
                                                                         2.2524
                                                                         0.9659
                                                                          0.077
                                                                         $4,975
                                                                              7
                                                                            290
                                                                          28.00
                                                                          26.70
                                                                          -1.30
                                                                         2.2270
                                                                         0.9659
                                                                          0.076
                                                                         $4,919
                                                                              8
                                                                            288
                                                                          28.00
                                                                          26.70
                                                                          -1.30
                                                                         2.2104
                                                                         0.9659
                                                                          0.075
                                                                         $4,882
                                                                              9
                                                                            292
                                                                          28.00
                                                                          26.70
                                                                          -1.30
                                                                         2.2421
                                                                         0.9659
                                                                          0.076
                                                                         $4,952
                                                                             10
                                                                            281
                                                                          28.00
                                                                          26.70
                                                                          -1.30
                                                                         2.1574
                                                                         0.9659
                                                                          0.074
                                                                         $4,765
                                                                             11
                                                                            277
                                                                          28.00
                                                                          26.70
                                                                          -1.30
                                                                         2.1234
                                                                         0.9659
                                                                          0.072
                                                                         $4,690
                                                                             12
                                                                            277
                                                                          28.00
                                                                          26.70
                                                                          -1.30
                                                                         2.1204
                                                                         0.9659
                                                                          0.072
                                                                         $4,683
                                                                             13
                                                                            278
                                                                          28.00
                                                                          26.70
                                                                          -1.30
                                                                         2.1288
                                                                         0.9659
                                                                          0.073
                                                                         $4,702
                                                                             14
                                                                            283
                                                                          28.00
                                                                          26.70
                                                                          -1.30
                                                                         2.1704
                                                                         0.9659
                                                                          0.074
                                                                         $4,794
                                                                             15
                                                                            288
                                                                          28.00
                                                                          26.70
                                                                          -1.30
                                                                         2.2052
                                                                         0.9659
                                                                          0.075
                                                                         $4,871
                                                                             16
                                                                            290
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         2.2270
                                                                         0.9659
                                                                          0.076
                                                                         $4,919
                                                                             17
                                                                            297
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         2.2777
                                                                         0.9659
                                                                          0.078
                                                                         $5,031
                    1 Year Old Mobile Home, Climate Zone 1
                                      Age
                                  Population
                            Baseline Exposure (ppb)
                             CARB2 Exposure (ppb)
                           Exposure Reduction (ppb)
                            Expected Baseline Cases
                             Effective Odds Ratio
                                 Cases Avoided
                                      WTP
                                                                               
                                                                          3,436
                                                                               
                                                                               
                                                                               
                                                                          26.34
                                                                               
                                                                          0.556
                                                                        $35,980
                                                                              6
                                                                            294
                                                                          20.19
                                                                          19.37
                                                                          -0.81
                                                                         2.2524
                                                                         0.9785
                                                                          0.048
                                                                         $3,129
                                                                              7
                                                                            290
                                                                          20.19
                                                                          19.37
                                                                          -0.81
                                                                         2.2270
                                                                         0.9785
                                                                          0.048
                                                                         $3,094
                                                                              8
                                                                            288
                                                                          20.19
                                                                          19.37
                                                                          -0.81
                                                                         2.2104
                                                                         0.9785
                                                                          0.047
                                                                         $3,071
                                                                              9
                                                                            292
                                                                          20.19
                                                                          19.37
                                                                          -0.81
                                                                         2.2421
                                                                         0.9785
                                                                          0.048
                                                                         $3,115
                                                                             10
                                                                            281
                                                                          20.19
                                                                          19.37
                                                                          -0.81
                                                                         2.1574
                                                                         0.9785
                                                                          0.046
                                                                         $2,998
                                                                             11
                                                                            277
                                                                          20.19
                                                                          19.37
                                                                          -0.81
                                                                         2.1234
                                                                         0.9785
                                                                          0.046
                                                                         $2,950
                                                                             12
                                                                            277
                                                                          20.19
                                                                          19.37
                                                                          -0.81
                                                                         2.1204
                                                                         0.9785
                                                                          0.045
                                                                         $2,946
                                                                             13
                                                                            278
                                                                          20.19
                                                                          19.37
                                                                          -0.81
                                                                         2.1288
                                                                         0.9785
                                                                          0.046
                                                                         $2,958
                                                                             14
                                                                            283
                                                                          20.19
                                                                          19.37
                                                                          -0.81
                                                                         2.1704
                                                                         0.9785
                                                                          0.047
                                                                         $3,015
                                                                             15
                                                                            288
                                                                          20.19
                                                                          19.37
                                                                          -0.81
                                                                         2.2052
                                                                         0.9785
                                                                          0.047
                                                                         $3,064
                                                                             16
                                                                            290
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         2.2270
                                                                         0.9807
                                                                          0.043
                                                                         $2,788
                                                                             17
                                                                            297
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         2.2777
                                                                         0.9807
                                                                          0.044
                                                                         $2,851
                New Single Family Detached Home, Climate Zone 1
                                      Age
                                  Population
                            Baseline Exposure (ppb)
                             CARB2 Exposure (ppb)
                           Exposure Reduction (ppb)
                            Expected Baseline Cases
                             Effective Odds Ratio
                                 Cases Avoided
                                      WTP
                                                                               
                                                                         47,964
                                                                               
                                                                               
                                                                               
                                                                         367.72
                                                                               
                                                                          0.797
                                                                        $51,591
                                                                              6
                                                                          4,101
                                                                          25.40
                                                                          25.32
                                                                          -0.08
                                                                        31.4420
                                                                         0.9978
                                                                          0.068
                                                                         $4,411
                                                                              7
                                                                          4,055
                                                                          25.40
                                                                          25.32
                                                                          -0.08
                                                                        31.0871
                                                                         0.9978
                                                                          0.067
                                                                         $4,361
                                                                              8
                                                                          4,025
                                                                          25.40
                                                                          25.32
                                                                          -0.08
                                                                        30.8555
                                                                         0.9978
                                                                          0.067
                                                                         $4,329
                                                                              9
                                                                          4,082
                                                                          25.40
                                                                          25.32
                                                                          -0.08
                                                                        31.2980
                                                                         0.9978
                                                                          0.068
                                                                         $4,391
                                                                             10
                                                                          3,928
                                                                          25.40
                                                                          25.32
                                                                          -0.08
                                                                        30.1165
                                                                         0.9978
                                                                          0.065
                                                                         $4,225
                                                                             11
                                                                          3,866
                                                                          25.40
                                                                          25.32
                                                                          -0.08
                                                                        29.6410
                                                                         0.9978
                                                                          0.064
                                                                         $4,159
                                                                             12
                                                                          3,861
                                                                          25.40
                                                                          25.32
                                                                          -0.08
                                                                        29.5995
                                                                         0.9978
                                                                          0.064
                                                                         $4,153
                                                                             13
                                                                          3,876
                                                                          25.40
                                                                          25.32
                                                                          -0.08
                                                                        29.7162
                                                                         0.9978
                                                                          0.064
                                                                         $4,169
                                                                             14
                                                                          3,952
                                                                          25.40
                                                                          25.32
                                                                          -0.08
                                                                        30.2970
                                                                         0.9978
                                                                          0.066
                                                                         $4,251
                                                                             15
                                                                          4,015
                                                                          25.40
                                                                          25.32
                                                                          -0.08
                                                                        30.7836
                                                                         0.9978
                                                                          0.067
                                                                         $4,319
                                                                             16
                                                                          4,055
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                        31.0880
                                                                         0.9978
                                                                          0.067
                                                                         $4,362
                                                                             17
                                                                          4,147
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                        31.7959
                                                                         0.9978
                                                                          0.069
                                                                         $4,461

 The effective odds ratio and willingness to pay are calculated using the upper bound, equation (16) above, assuming a willingness to pay to avoid one asthma case of $64,764. For example, the willingness to pay for a six-year old child in this housing profile would be

The total willingness to pay for this housing profile would be $58,181.
The second block of Table 11 represents the benefits to individuals living in a 1-year-old mobile home. As with sensory irritation, we assume that the population distribution across ages is exactly the same as for new mobile homes but the exposure profile is different. In total, 26.34 asthma cases would be expected in the baseline (the same as for new mobile homes because the age distribution is the same). 0.556 cases would be avoided from the policy intervention, and the total willingness to pay for this intervention would be $35,980.
The third block of Table 11 represents the benefits to individuals living in a new single-family detached home. An estimated 47,964 children live in this type of home and the exposure reduction expected from the policy is smaller than for mobile homes. An estimated 367.72 asthma cases would be expected in the baseline, 0.797 cases would be avoided from the policy intervention, and the total benefits of this action would be $51,591.
As was true in the case for sensory irritation, the sum of these willingness to pay values for new mobile homes and new detached houses ($58,181 + $51,591= $109,772) is the willingness to pay for the reduction in asthma incidence in the first year. The sum of the willingness to pay for all three housing types ($58,181 + $35,980 + $51,591= $145,751) is the willingness to pay for any given year of analysis after the first year, assuming that the population remains constant and the distribution across housing types is the same in the future as it is now. 
These aggregate results are appropriate for the case where every individual is afforded the exposure reduction over their entire 12 year exposure, but it may not be valid for the early years of policy implementation. To calculate the transition path from initial to full policy implantation, we use the upper and lower bound equations, equations (19) and (20) respectively. The results of these calculations are given in Table 12. 
The left hand block of Table 12 gives the upper bound estimate of the policy for thirty years of implementation. In this case, the undiscounted willingness to pay is the same value, $145,751, for each year after the first year. This is because the upper bound estimate assumes that the odds ratio is appropriate for an exposure reduction experience for one year. So, for example, a child who is seventeen years old in the first year of policy implementation will only enjoy one year of exposure reduction associated with this concentration-response function. In the upper bound estimate, that child receives the same benefit in that year as all seventeen-year-old children do in every year thereafter. Assuming a discount rate of 3%, the present discounted value of 30 years of the policy is about $2.9 million dollars for these three housing profiles. 
Table 12: Upper and lower bound benefits calculations for asthma incidence using three housing profiles
                                                                               
                             Upper  Bound Estimate
                             Lower  Bound Estimate
                                     Year
                                New Mobile Home
                            1-Year Old Mobile Home
                             New SF Detached Home
                                   Total WTP
                             Total Discounted WTP
                                New Mobile Home
                            1-Year Old Mobile Home
                             New SF Detached Home
                                   Total WTP
                             Total Discounted WTP

                                                                     $1,803,609
                                                                     $1,079,385
                                                                     $1,599,309
                                                                     $4,482,303
                                                                     $2,966,556
                                                                     $1,681,291
                                                                     $1,023,670
                                                                     $1,496,535
                                                                     $4,201,497
                                                                     $2,706,869
0
                                                                        $58,181
                                                                               
                                                                        $51,591
                                                                       $109,772
                                                                       $109,772
                                                                        $31,019
                                                                               
                                                                        $27,971
                                                                        $58,990
                                                                        $58,990
1
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                       $141,506
                                                                        $35,452
                                                                        $22,080
                                                                        $31,902
                                                                        $89,434
                                                                        $86,829
2
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                       $137,384
                                                                        $39,455
                                                                        $24,607
                                                                        $35,470
                                                                        $99,532
                                                                        $93,818
3
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                       $133,383
                                                                        $43,082
                                                                        $26,878
                                                                        $38,676
                                                                       $108,636
                                                                        $99,417
4
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                       $129,498
                                                                        $46,279
                                                                        $28,887
                                                                        $41,517
                                                                       $116,683
                                                                       $103,671
5
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                       $125,726
                                                                        $49,067
                                                                        $30,646
                                                                        $44,005
                                                                       $123,718
                                                                       $106,720
6
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                       $122,064
                                                                        $51,461
                                                                        $32,158
                                                                        $46,147
                                                                       $129,766
                                                                       $108,677
7
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                       $118,509
                                                                        $53,454
                                                                        $33,425
                                                                        $47,942
                                                                       $134,822
                                                                       $109,622
8
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                       $115,057
                                                                        $55,059
                                                                        $34,447
                                                                        $49,390
                                                                       $138,896
                                                                       $109,646
9
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                       $111,706
                                                                        $56,271
                                                                        $35,218
                                                                        $50,485
                                                                       $141,974
                                                                       $108,811
10
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                       $108,452
                                                                        $57,073
                                                                        $35,735
                                                                        $51,219
                                                                       $144,027
                                                                       $107,170
11
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                       $105,294
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                       $105,294
12
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                       $102,227
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                       $102,227
13
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $99,249
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $99,249
14
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $96,359
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $96,359
15
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $93,552
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $93,552
16
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $90,827
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $90,827
17
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $88,182
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $88,182
18
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $85,613
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $85,613
19
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $83,120
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $83,120
20
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $80,699
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $80,699
21
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $78,348
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $78,348
22
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $76,066
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $76,066
23
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $73,851
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $73,851
24
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $71,700
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $71,700
25
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $69,612
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $69,612
26
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $67,584
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $67,584
27
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $65,616
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $65,616
28
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $63,704
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $63,704
29
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $61,849
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $61,849
30
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $60,048
                                                                        $58,181
                                                                        $35,980
                                                                        $51,591
                                                                       $145,751
                                                                        $60,048


The right hand block of Table 12 gives the lower bound of the policy. The undiscounted total willingness to pay in the first year, $58,990, reflects the fact that most of the individuals receiving benefits have already been exposed to the baseline level of formaldehyde for part of their life and will not experience the full benefit of the program. Each year, a new cohort of children is added who will experience the full exposure reduction, so the undiscounted willingness to pay grows for the next 12 years, until it stabilizes at $145,751. The present discounted value of 30 years of the policy in this case would be about $2.7 million.

3.3.4 Discussion of uncertainties
As with sensory irritation, this example assumes that the population is constant and that the future distribution across housing types is exactly the same as the present distribution. Accommodating a growing population and a different housing and age distribution would be implemented in the same way as described above, by simply by changing the population values for each year.
As with sensory irritation, the concentration-response function is non-linear. One way to deal with this would be to linearize this concentration-response function over the relevant range of exposure, for example with a first order Taylor approximation. However, given that the upper and lower bound calculations require us to form an annual change in risk and the change in exposure is relatively small, the results from using the non-linear concentration-response function are probably very similar to the results if we were to use a linear function.
The prevalence rates from the CDC are higher than those used for the most recent prospective analysis of the benefits and costs of the Clean Air Act (EPA 2011a) as reported by IEc (2011). IEc assumed a prevalence rate of 5.27% for children less than 18 years of age, based on data from the American Lung Association (2002). The rates are also higher than the prevalence rates recommended by the EPA's Office of Air for their BenMAP program (EPA 2011b).  The Office of Air suggests a prevalence rate of 6.14% for children less than 5 years old and 10.7% for children 5-17 based on current prevalence rates in 2008 American Lung Association (2010).

3.4 Reduced Fertility
Valuing reductions in fertility is the most difficult of the three non-cancer effects. Similar to valuing asthma incidence, the concentration-response relationship is based on a period of time longer than the modeled one year exposure window, so adjustments will have to be made similar to those for asthma incidence. Monetization, based on either the cost of illness or a willingness to pay framework, has been discussed in the literature but has not been included in EPA rules.

3.4.1 Monetization
The effect of pollution on pregnant women is a legitimate economic endpoint and has been included qualitatively in a number of contexts. The Safe Drinking Water Act (SDWA 1974) explicitly mentions special consideration of pregnant women when setting priorities for maximum contaminant level goals for public drinking water systems. However, this is generally interpreted as evaluating the health impact on the mother rather than the ability to become pregnant. For example, EPA's Ground Water Rule (EPA 2006) and Proposed Revised Total Coliform Rule (EPA 2010) both evaluate the effect of pollutants on the health of pregnant women but do not discuss potential impacts on fertility or other reproductive issues.
When reproductive issues are monetized, they almost always take the form of valuing the health impact on the fetus rather than the ability to become pregnant. For example, both the Lead-Based Paint Hazard Standards (EPA 2000c) and the EPA Clean Air Mercury Rule (EPA 2005a) monetize the impact of IQ losses from in utero exposure to the pollutant, but not fertility effects. In the case of lead, there was an explicit recognition that exposure can cause reproductive difficulty in both men and women (EPA, CPSC, and HUD 2003), but the endpoint was not included in the quantitative analysis. 
In a few cases, fertility impacts have been included in the economic analysis, but without full monetization. For example, the Arsenic in Drinking Water rule explicitly mentioned "reproductive and developmental effects" (including spontaneous abortions, perinatal death, and stillbirth) as "potential non-quantifiable health benefit" (EPA 2000b). This was based on a National Research Council review of the EPA's 1988 risk assessment for arsenic in drinking water (NRC 1999). However, the EPA chose not to monetize the endpoint because of a lack of human data or strong evidence on the risks of this health effect. 
The furthest that the EPA has gone in the past in valuing fertility impacts is the quantification, but not monetization, of fetal losses in the Stage 2 Disinfectants and Disinfection Byproducts Rule (EPA 2005b). In this analysis, EPA calculated the odds-ratio or relative risk ratio for fetal loss from four population-based epidemiological studies. Because the exposure in these four studies was significantly greater than the exposure for the general population, survey data were used to derive a Population Attributable Risk (PAR) values for the general population. Using the annual incidence of fetal loss, EPA estimated a range of 0 to 18,700 annual fetal losses attributable to exposure to chlorinated drinking water. 
EPA chose neither to monetize these impacts nor to include them in the primary benefits analysis because it believed that the scientific knowledge on reproductive and developmental health effects was not strong enough to quantify risk in the primary benefits analysis. In particular, the lower 95 percent confidence intervals for the PAR for all four studies were less than zero, meaning that the possibility of no effect could not be ruled out with 95 percent confidence. However, the calculations did indicate that the potential monetized value of this effect could be significant. In the same rule, EPA also mentioned other potential adverse reproductive impacts. For example, disinfectants are associated with miscarriages, which have associated medical costs as well as associated pain, suffering, and loss. These costs were estimated to range from $5,000 to $11,000 depending on the conditions of the miscarriage. 
For the case of formaldehyde, exposure has been associated with delayed conception (Taskinen et al. 1999) rather than fetal loss. Fertility problems are not uncommon during an individual's reproductive cycle. Garceau et al. (2002) claims that one in six couples experience fertility difficulty at some point in time in their reproductive lives. The CDC (2005) reports that 7% of married couples of reproductive age reported not using contraception for 12 months and not becoming pregnant and 12% of women of childbearing age in the United States have used an infertility service at some point in their reproductive cycle. While obtaining some fertility service is common, only 3.8 percent obtain ovulation drugs, 1.1 percent undergo artificial insemination and 0.3 percent engages in assisted reproductive technology, primarily in-vitro fertilization (IVF). The remainder seeks advice, undergoes tests, or obtains medical help to prevent miscarriages or surgery for blocked tubes.
Ovulation drugs, artificial insemination, and IVF are considered cycle-based treatments (Katz 2011). Artificial insemination is a process in which the sperm is placed in either the cervix (intracervical insemination, or ICI) or the uterus (intrauterine insemination, or IUI) by artificial means. IVF is a process by which human egg cells are fertilized by sperm outside the body and then transferred back to the patient's uterus. Success rates have been rising over time, with about 40% of couples undergoing IVF ultimately becoming pregnant (de La Rochebrochard 2009). In an 18 month cohort study, Katz (2011) finds a 23.5% success rate for medication only; a 38.5-55.6% success rate for IUI, depending on the accompanying fertility drug used; and a 47.3-52.4% rate for IVF, depending on whether or not donor eggs were used. 
Katz (2011) reports median treatment costs, successful or not, of $1,182 for medication only; $3,595-$8,594 for IUI; and $24,373-$38,015 for IVF. The median treatment costs per successful outcome were $925 for medication; $4,124-$8,542 for IUI; and $24,010-$38,545 for IVF.   This is roughly consistent with the cost estimates reported from other studies. The average cost per IVF cycle and per live-birth were estimated by Omurtag (2009) to be $9,226 and $56,419, respectively, and were estimated by Chambers (2009) to be $12,513 and $41,132, respectively. 
While there appear to be good data on the cost of treatment, there are few studies on the willingness to pay to reduce delayed conception. Most economic valuation studies regarding fertility focus on an individual or a couples' willingness to pay for infertility treatment, particularly in-vitro fertilization (IVF).  
Granberg et al. (1995) conducted a study of 40 couples in Sweden using open-ended questions about the maximum number of treatments that they would be willing to undergo at various price level and their willingness to pay to have a child. The combined direct and indirect cost at the time of the study was ₤3,880 per treatment and ₤11,490 per delivery. The willingness to pay for a child ranged from ₤0 to ₤25,000, with more than half of the couple's willing to pay more than ₤10,000.
Ryan (1996) conducted a contingent valuation survey of 339 women seeking fertility services in Australia and found a mean willingness to pay of about $2,500 per IVF attempt. Because this study included a subset of women who had completed their treatment, it allowed Ryan to estimate the willingness to pay with certainty and to distinguish between undergoing treatment and having a child versus completing the treatment but ending childless. Having a child increased the willingness to pay by about 30%. 
A second study (Ryan, 1997) surveyed 458 women using a fertility service in Scotland. Using a randomized bid and a dichotomous choice model, Ryan estimates a mean willingness to pay of just over ₤5,000 per IVF attempt. There was a lower willingness to pay among individuals who had completed their treatment, likely reflecting the lower value associated with undergoing the treatment with the certainty of ending the process with no child. 
Note that both Ryan studies reflect a sample of individuals who are already seeking infertility services. This suggests a potential sample selection bias for individuals with a preference for increasing their chances of having a child.
Neumann and Johannesson (1994) conducted a study of 231 nurses, doctors, parents, students, and administrative staff in the Boston area. The contingent valuation survey used a payment card and a randomized bid to obtain the willingness to pay for IVF treatment with varying probabilities of success. The survey compared the respondents' willingness to pay for treatment in the event that they are infertile (an ex-post analysis) with the willingness to pay for insurance, assuming that they do not know their infertility status (an ex-ante analysis). The ex-post willingness to pay for a 10% chance of success was $17,730, suggesting about $175,000 per statistical pregnancy. The mean ex-ante willingness to pay was $865 per IVF treatment with a 10% chance of success. The authors take this latter value to imply a willingness to pay of $1.7 million per statistical pregnancy, but this is based on the authors' subjective assumption about couples' ex-ante belief that they will need IVF treatment. Curiously, the willingness to pay per statistical successful outcome drops as the level of certainly of success rises. The authors estimate a willingness to pay of $40,000 per statistical pregnancy in the ex-post case and $216,000 in the ex-ante case given 100% certainty of ending with a child. Again, the ex-ante value is based on the author's assessment of a couple's ex-ante belief that they will need IVF treatment.
All of these studies reflect willingness to pay for fertility treatment. The one study that comes close to valuing a reduction in delayed conception is Van Houtven and Smith (1999). They conducted a pilot study of 188 individuals in four cities using a mall intercept survey. Respondents were asked to consider taking a completely safe medication on a weekly basis which would delay the increase in infertility risk for up to five years based on randomly assigned monthly payment amounts. They found a willingness to pay of willingness to pay of $16,500 to $49,400 per statistical pregnancy using a 3% discount rate (and $15,200 to $45,700 using a 5% rate).
Valuing difficulty in conceiving due to formaldehyde exposure could be done using either the cost of treatment or some measure of the willingness to pay. Conceptually, the willingness to pay approach is preferable and could be deduced from the studies described above. For example, the van Houtven and Smith (1999) value of approximately $15,000 - $50,000 for a statistical pregnancy and a probability of success of 25% from ovulation drugs suggests a willingness to pay of between $3,750 and $12,500 for fertility treatment. Alternatively, the Ryan (1996) willingness to pay of $2,500 per IVF attempt plus 30% for certainty, an average of 3.5 IVF cycles per patient, and a 50% success rate for IVF suggests a willingness to pay of just under $6,000. 
However, given that there is there has been less research on these willingness to pay values than other values and the fact that the values have not been used in previous economic analysis, it may be more straight-forward to use a cost of illness approach. Futhermore, many of these willingness to pay studies apply to the more serious infertility rather than to the delayed fertility being modeled here.  In this respect, the willingness to pay studies are not suitable for benefits transfer. For this analysis, we will use rounded values of the midpoint from the median cost of treatment values for fertility services taken from Katz (2011): $1,000 for medication; $6,000 for IUI; and $30,000 for IFV.
 
3.4.2 Annual Approach
The linear concentration-response function accounting for background exposures based on Taskinen et al. (1999) provides the most direct application of equation (7).
	
And the willingness to pay for any given housing and age cohort is
	
The number of women in the U.S. wishing to become pregnant can be estimated using the number of women of child-bearing age and information on pregnancy and contraception use (CDC 2010). The Taskinen (1999) study examined the fecundity of women age 20-40, so this is the age group which we will consider. The percentage of women seeking pregnancy over the course of a year can be estimated as the sum of the percentage of women who reported not using contraception because they were seeking pregnancy and the percentage who are intentionally pregnant or postpartum after an intentional pregnancy.  The percentages of women who reported not using contraception because they were seeking pregnancy were 4.3%, 6.3%, 5.9%, and 5.1% for age ranges 20-24, 25-29, 30-34, and 35-39, respectively.  The percentages of women who were pregnant or postpartum were 10.0%, 7.7%, 8.1%, and 1.9% for age ranges 20-24, 25-29, 30-34, and 35-39, respectively.  Since half of pregnancies are intended, according to CDC (2010), the percentage of women seeking pregnancy over the course of a year was estimated as the percentage of women currently seeking pregnancy plus half of the percentage of women who are pregnant or postpartum.  These estimates are 9.3%, 10.2%, 10.0%, and 6.1% for age ranges 20-24, 25-29, 30-34, and 35-39, respectively.
The percent of women seeking fertility treatment varies by age group.  Table 13 presents the probabilities of seeking pregnancy and of obtaining cycle-based treatment based on tables provided by the CDC (2005 and 2010). Note that the last three columns, which present the percentages of women using a particular fertility treatment conditional on seeking some fertility treatment, do not sum to one hundred percent.  This is because the costs associated with fertility treatments other than the three presented in the table were not estimated.  Thus, these costs are implicitly assumed to be zero for the purpose of this analysis.

Table 13: Probability of Obtaining Cycle-Based Treatment by Age Group
      
      
Percent Obtaining Treatment
Percent Obtaining Treatment Conditional on Some Fertility Treatment Being Sought
Age Group
Percent Seeking Pregnancy
Any Fertility Service
Ovulation drugs
IUI
IVF
Ovulation drugs
IUI
IVF
                                                                          20-24
                                                                           9.3%
                                                                           4.9%
                                                                           1.0%
                                                                           0.2%
                                                                           0.0%
                                                                         20.41%
                                                                          4.08%
                                                                          0.00%
                                                                          25-29
                                                                          10.2%
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                          30-34
                                                                          10.0%
                                                                          17.7%
                                                                           5.3%
                                                                           1.8%
                                                                           0.4%
                                                                         29.94%
                                                                         10.17%
                                                                          2.26%
                                                                          35-39
                                                                           6.1%
                                                                          17.3%
                                                                           4.6%
                                                                           1.4%
                                                                           0.3%
                                                                         23.96%
                                                                          7.29%
                                                                          3.65%
Source: Percent seeking pregnancy is from CDC 2010 and percent obtaining treatment is from CDC 2005

The willingness to pay for an exposure change for some time period, t0 to t1, would then be:
	
where Pr(∙) is the probability of needing the cycle-based treatment conditional upon requiring fertility assistance.
As with asthma prevalence, the time period associated with the exposure-response relationship is longer than the 20 year time step examined by Taskinen (1999). Therefore, the linear model estimated above would be the probability of having difficulty conceiving based on an exposure for that time period. As before, this causes a problem if we have an individual who does not experience the exposure reduction for the full time period. We can form an upper and lower bound of this willingness to pay as we did for asthma prevalence. The upper bound is based on the assumption that the linear concentration-response function holds for an exposure reduction of one year. The lower bound assumes that an exposure reduction for one year represents 1/20[th] of an exposure reduction for the entire 20 year time period. (For convenience, the 20-40 time period is considered to be inclusive, so we are only modeling up to the individual's 40[th] birthday.) This means that for any time period , the willingness to pay for an individual who is age k at the time of policy implementation would be 

Upper bound:
	
Lower bound:
	
Table 14: Illustrative formaldehyde exposure (is ppb) using three housing profiles
                                   Scenario
                                Housing Profile
                        Non-Industrial Worker Avg. ADC
Weighted average ADC (ppb) during current exposure year
                                   Baseline
New Mobile Home
                                                                          28.41
                                       
1-year-old Mobile Home
                                                                          20.84
                                       
New Detached Home
                                                                          25.97
                                     CARB2
New Mobile Home
                                                                          27.11
                                       
1-year-old Mobile Home
                                                                          20.11
                                       
New Detached Home
                                                                          25.89


3.4.3 Example Calculation
The linear concentration-response function for the risk of having difficulty conceiving is 
Risk = 0.056 + 0.0016∙(exposure)
We will use the same three housing profiles as we did in the previous examples. The assumed ADC for formaldehyde exposure for a woman age 20-40 is given in Table 14. This can be combined with the probability of reduced fecundity to produce a probability of undergoing fertility treatment.
The willingness to pay for fertility treatment will be treated in an expected value context. The average cost and probability of obtaining various cycle-based fertility treatments at various ages is given in Table 14. The first column gives the age ranges and the second column provides the proabililty that a woman is seeking pregnancy. Women between 20 and 34 years old have around a 10% probability of seeking pregnancy. From 35 to 40, the probability of a woman seeking pregnancy drops to 6.1%. The final three columns give the probability of obtaining treatment, conditional upon seeking some fertility treatment. Women seeking fertility treatment have no chance of being recommended for the more invasive and expensive IVF in their 20s, but have an increasing chance of obtaining this procedure in their 30s. In contrast, obtaining medication and IUI peaks between ages 30-34. It is true that women older than age 39 also obtain fertility treatment, but the costs and probabilities have been truncated at age 39 to remain consistent with Taskinen et al. (1999). The average cost of the three types of cycle-based fertility treatment, based on Katz (2010), is given in the final row.
Table 15: Average cost and probability of obtaining cycle-based fertility treatment
                                   Age Group
                           Percent Seeking Pregnancy
Percent Obtaining Treatment Conditional on Some Fertility Treatment Being Sought
                                       
                                       
                                Ovulation drugs
                                      IUI
                                      IVF
                                                                          20-24
                                     9.30%
                                                                         20.41%
                                                                          4.08%
                                                                          0.00%
                                                                          25-29
                                    10.20%
                                                                               
                                                                               
                                                                               
                                                                          30-34
                                    10.00%
                                                                         29.94%
                                                                         10.17%
                                                                          2.26%
                                                                          35-39
                                     6.10%
                                                                         23.96%
                                                                          7.29%
                                                                          3.65%
                                 Average Cost
                                                                         $1,000
                                                                         $6,000
                                                                        $30,000
Source: Percent seeking pregnancy is from CDC 2010 and percent obtaining treatment is from CDC 2005
Table 16 shows the illustrative benefits calculation for fertility effects in women living in the three housing types in climate zone 1. The population size is assumed to be half of the total population living in this housing structure because we are only dealing with women.The first seven columns of Table 16 represents the 2,943 women living in new mobile. Given reduced emissions of 1.30 ppb for every year, we would expect 0.548 fewer cases of women having difficulty conceiving for this housing profile. The total willingness to pay to obtain this reduction is $543. The next six columns represent women living in one year old mobile homes. Since the emission reduction is smaller, we expect to see 0.308 fewer cases, with a willingness to pay of $300. The last six columns reflect the impact on women of child-bearing age in new homes. Here we expect 0.478 fewer cases and estimate a total willingness to pay of $465.
Table 17 gives the upper and lower bound estimate of the policy for the three housing types for thirty years of implementation. As before, the first year of implementation (year 0) does not affect individuals in 1-year-old homes.  The upper bound estimate (left hand block of Table 17) produces the same willingness to pay for each year after the first year. The lower bound estimate (right hand block of Table 17) produces steadily increasing undiscounted willingness to pay estimates until the 20[th] year, reflecting the fact that earlier years were accounting for women who only experience part of the benefit of the exposure reduction. Discounting these values at 3%, the total discounted willingness to pay from this illustration is between $26,461 and $21,779.

Table 16: Illustrative benefit calculations for reduced fertility effects to women living in new mobile homes

                                                                               
                        New Mobile Home, Climate Zone 1
                    1 Year Old Mobile Home, Climate Zone 1
                New Single Family Detached Home, Climate Zone 1
Age
                                  Population
                            Baseline Exposure (ppb)
                             CARB2 Exposure (ppb)
                           Exposure Reduction (ppb)
                                 Cases Avoided
                                      WTP
                                  Population
                            Baseline Exposure (ppb)
                             CARB2 Exposure (ppb)
                           Exposure Reduction (ppb)
                                 Cases Avoided
                                      WTP
                                  Population
                            Baseline Exposure (ppb)
                             CARB2 Exposure (ppb)
                           Exposure Reduction (ppb)
                                 Cases Avoided
                                      WTP
                                                                               
                                                                          2,943
                                                                               
                                                                               
                                                                               
                                                                          0.548
                                                                           $533
                                                                          2,943
                                                                               
                                                                               
                                                                               
                                                                          0.308
                                                                           $300
                                                                         41,081
                                                                               
                                                                               
                                                                               
                                                                          0.478
                                                                           $465
                                                                             20
                                                                            158
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0306
                                                                            $14
                                                                            158
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0172
                                                                             $8
                                                                           2204
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0267
                                                                            $12
                                                                             21
                                                                            153
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0296
                                                                            $13
                                                                            153
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0167
                                                                             $7
                                                                           2134
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0258
                                                                            $12
                                                                             22
                                                                            151
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0293
                                                                            $13
                                                                            151
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0165
                                                                             $7
                                                                           2110
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0256
                                                                            $11
                                                                             23
                                                                            150
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0291
                                                                            $13
                                                                            150
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0164
                                                                             $7
                                                                           2098
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0254
                                                                            $11
                                                                             24
                                                                            152
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0294
                                                                            $13
                                                                            152
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0165
                                                                             $7
                                                                           2117
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0256
                                                                            $12
                                                                             25
                                                                            153
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0325
                                                                            $15
                                                                            153
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0183
                                                                             $8
                                                                           2132
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0283
                                                                            $13
                                                                             26
                                                                            150
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0319
                                                                            $14
                                                                            150
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0179
                                                                             $8
                                                                           2096
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0278
                                                                            $12
                                                                             27
                                                                            152
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0324
                                                                            $15
                                                                            152
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0182
                                                                             $8
                                                                           2127
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0283
                                                                            $13
                                                                             28
                                                                            153
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0325
                                                                            $15
                                                                            153
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0183
                                                                             $8
                                                                           2136
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0284
                                                                            $13
                                                                             29
                                                                            154
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0327
                                                                            $15
                                                                            154
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0184
                                                                             $8
                                                                           2150
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0286
                                                                            $13
                                                                             30
                                                                            153
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0319
                                                                            $51
                                                                            153
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0179
                                                                            $28
                                                                           2136
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0278
                                                                            $44
                                                                             31
                                                                            145
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0303
                                                                            $48
                                                                            145
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0170
                                                                            $27
                                                                           2029
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0264
                                                                            $42
                                                                             32
                                                                            141
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0294
                                                                            $47
                                                                            141
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0165
                                                                            $26
                                                                           1968
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0256
                                                                            $41
                                                                             33
                                                                            139
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0289
                                                                            $46
                                                                            139
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0163
                                                                            $26
                                                                           1936
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0252
                                                                            $40
                                                                             34
                                                                            135
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0281
                                                                            $45
                                                                            135
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0158
                                                                            $25
                                                                           1883
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0245
                                                                            $39
                                                                             35
                                                                            138
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0176
                                                                            $31
                                                                            138
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0099
                                                                            $18
                                                                           1931
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0153
                                                                            $27
                                                                             36
                                                                            134
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0170
                                                                            $30
                                                                            134
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0096
                                                                            $17
                                                                           1872
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0149
                                                                            $26
                                                                             37
                                                                            137
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0174
                                                                            $31
                                                                            137
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0098
                                                                            $17
                                                                           1913
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0152
                                                                            $27
                                                                             38
                                                                            143
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0182
                                                                            $32
                                                                            143
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0103
                                                                            $18
                                                                           2002
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0159
                                                                            $28
                                                                             39
                                                                            151
                                                                          28.41
                                                                          27.11
                                                                          -1.30
                                                                         0.0192
                                                                            $34
                                                                            151
                                                                          20.84
                                                                          20.11
                                                                          -0.73
                                                                         0.0108
                                                                            $19
                                                                           2110
                                                                          25.97
                                                                          25.89
                                                                          -0.08
                                                                         0.0168
                                                                            $30

Table 17: Upper and Lower bound benefits for reduced fertility effects using three housing profiles
                                                                               
                             Upper  Bound Estimate
                                       
                                       
                                       
                             Lower  Bound Estimate
                                       
                                       
                                       
Year
                                New Mobile Home
                            1-Year Old Mobile Home
                             New SF Detached Home
                                   Total WTP
                             Total Discounted WTP
                                New Mobile Home
                            1-Year Old Mobile Home
                             New SF Detached Home
                                   Total WTP
                             Total Discounted WTP
                                                                               
                                                                        $16,538
                                                                         $9,003
                                                                        $14,429
                                                                        $39,970
                                                                        $26,461
                                                                        $14,272
                                                                         $7,901
                                                                        $12,450
                                                                        $34,623
                                                                        $21,779
                                                                              0
                                                                           $533
                                                                               
                                                                           $465
                                                                           $999
                                                                           $999
                                                                           $226
                                                                               
                                                                           $197
                                                                           $422
                                                                           $422
                                                                              1
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                         $1,261
                                                                           $252
                                                                           $141
                                                                           $219
                                                                           $612
                                                                           $595
                                                                              2
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                         $1,224
                                                                           $277
                                                                           $156
                                                                           $242
                                                                           $674
                                                                           $635
                                                                              3
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                         $1,189
                                                                           $302
                                                                           $170
                                                                           $263
                                                                           $734
                                                                           $672
                                                                              4
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                         $1,154
                                                                           $317
                                                                           $178
                                                                           $284
                                                                           $779
                                                                           $692
                                                                              5
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                         $1,121
                                                                           $349
                                                                           $196
                                                                           $304
                                                                           $850
                                                                           $733
                                                                              6
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                         $1,088
                                                                           $372
                                                                           $209
                                                                           $324
                                                                           $905
                                                                           $758
                                                                              7
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                         $1,056
                                                                           $393
                                                                           $221
                                                                           $343
                                                                           $958
                                                                           $779
                                                                              8
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                         $1,025
                                                                           $415
                                                                           $233
                                                                           $362
                                                                         $1,010
                                                                           $797
                                                                              9
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $996
                                                                           $446
                                                                           $251
                                                                           $380
                                                                         $1,077
                                                                           $826
                                                                             10
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $967
                                                                           $455
                                                                           $256
                                                                           $397
                                                                         $1,107
                                                                           $824
                                                                             11
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $938
                                                                           $472
                                                                           $265
                                                                           $412
                                                                         $1,149
                                                                           $830
                                                                             12
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $911
                                                                           $487
                                                                           $274
                                                                           $425
                                                                         $1,185
                                                                           $831
                                                                             13
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $885
                                                                           $499
                                                                           $281
                                                                           $436
                                                                         $1,215
                                                                           $828
                                                                             14
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $859
                                                                           $509
                                                                           $286
                                                                           $444
                                                                         $1,240
                                                                           $820
                                                                             15
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $834
                                                                           $517
                                                                           $291
                                                                           $451
                                                                         $1,259
                                                                           $808
                                                                             16
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $810
                                                                           $524
                                                                           $295
                                                                           $457
                                                                         $1,275
                                                                           $795
                                                                             17
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $786
                                                                           $528
                                                                           $297
                                                                           $461
                                                                         $1,287
                                                                           $779
                                                                             18
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $763
                                                                           $532
                                                                           $299
                                                                           $464
                                                                         $1,295
                                                                           $761
                                                                             19
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $741
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $741
                                                                             20
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $719
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $719
                                                                             21
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $698
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $698
                                                                             22
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $678
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $678
                                                                             23
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $658
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $658
                                                                             24
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $639
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $639
                                                                             25
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $620
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $620
                                                                             26
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $602
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $602
                                                                             27
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $585
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $585
                                                                             28
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $568
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $568
                                                                             29
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $551
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $551
                                                                             30
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $535
                                                                           $533
                                                                           $300
                                                                           $465
                                                                         $1,299
                                                                           $535


3.4.4 Discussion of uncertainties
As with the previous endpoints, this example assumes that the population is constant and that the future distribution across housing types is exactly the same as the present distribution. Correcting for trends in population and housing could be done in the same fashion as for the other endpoints.
The willingness to pay estimates above reflects the positive value that women who have trouble conceiving would obtain by not suffering this difficulty. However, it should be pointed out that there is probably a much smaller opposite effect associated with an increase in pregnancy by women who do not want to become pregnant. A complete analysis would incorporate this opposite effect, but is much more difficult and controversial to estimate and value.
The equation for probability of having trouble conceiving is used to produce an estimate of the number of women who whose time to pregnancy will exceed 12 months. The valuation treated this estimate as equal to the number of women who seek fertility treatment. This might be justified as an upper bound estimate, but there are certainly women to have trouble becoming pregnant and do not seek fertility treatment. This is not reflected in this analysis.
The willingness to pay values are based on the average cost of obtaining fertility services. While this is not the theoretically correct value to use for monetization, it is a reasonable estimate if most fertility treatment costs are paid for out-of-pocket by the patients rather than by insurance.  In actually paying the cost, the patient reveals that the treatments is worth at least as much as she paid.  The maximum willingness to pay, however, would be expected to be greater than these costs because many consumers receive more utility from service than they pay for it. Note that this does not take into account any utility or disutility of treatments.  This suggests using cost-of-illness will produce an underestimate. 
On the other hand, these values are being applied to all women who are exposed to formaldehyde, but not all of the women whose fertility is affected will pay the market prices for the treatments.  In other words, we have an estimate of the willingness to pay for the women who choose to undergo these treatments. However, we do not have an estimate of the willingness to pay for the women whose fertility is affected but choose not to undertake the treatment. Their values are likely to be positive, but they are less than the costs.  For example, it may be that women with lower household incomes are less likely to pay for treatments at the going prices.  In this sense, the estimate of fertility benefits using the average cost of obtaining fertility service may be biased upward.
Also, all of the women in the Taskanen study whose pregnancies were delayed ultimately had successful pregnancies.  The "health endpoint" being modeled is therefore delayed fertility, not infertility.  If women would be willing to pay more to increase the chance of getting pregnant than they would to decrease the time to pregnancy then the cost-of-illness estimates based on a successful pregnancy used here would overstate the true willingness to pay.
The willingness to pay for reduced time to conceive could, theoretically, be estimated with a stated preference survey, but this would require women to place an ex-ante value on their willingness to pay to undergo various types of fertility treatment, each with an uncertain outcome. Since the women producing this ex-ante value will likely have had little or no experience with the various fertility treatments, such a study would require extensive pre-testing to assure that the women understand the commodity.  
There are also reasons to believe that the cost of treatment may not even reflect the correct endpoint. For example, women are willing to pay to reduced time to conceive but, at the same time, are reluctant to undergo fertility treatment. Furthermore, the cycle-based treatments described here may not even be the appropriate treatment to reduce delayed fertility associated with formaldehyde exposure.
Finally, the values reflect that ages reported in the Taskinen (1999) study, ages 20-40. However, women older than age 40 obtain fertility treatment. The CDC (2005) study that was used to produce probabilities for the 20-40 age group reports 19.2% of the women studied who were age 40 to 44 had obtained some type of infertility treatment, with 8.4% obtaining ovulation drugs, 2.6% undergoing artificial insemination, and 0.7% utilitizing assisted reproductive technology (assumed to be IVF). The value of reduced infertility effects from reduced formaldehyde exposure is not reflected in this analysis in order to remain consistent with Taskinen (1999), but could be included by simply extending the ages considered.
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Volume 1: http://yosemite.epa.gov/ee/epa/eerm.nsf/vwAN/EE-0092a-1.doc/$file/EE-0092a-1.doc
Volume 2: http://yosemite.epa.gov/ee/epa/eerm.nsf/vwAN/EE-0092B-01.pdf/$file/EE-0092B-01.pdf
Volume 3: http://yosemite.epa.gov/ee/epa/eerm.nsf/vwAN/EE-0092C.pdf/$file/EE-0092C.pdf
Volume 4: http://yosemite.epa.gov/ee/epa/eerm.nsf/vwAN/EE-0092C.pdf/$file/EE-0092C.pdf

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U.S. Environmental Protection Agency (EPA). 2011a. The Benefits and Costs of the Clean Air Act: 1990 to 2020. U.S. EPA, Office of Air and Radiation. Washington, DC. March. http://www.epa.gov/airprogm/oar/sect812/prospective2.html

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