  SEQ CHAPTER \h \r 1 APPENDIX J__

ADDITIONAL SENSITIVITY ANALYSES RELATED TO THE BENEFITS ANALYSIS  TC \l1
" 

The analysis presented in Chapter 5 __ is based on our current
interpretation of the scientific and economic literature.  That
interpretation requires judgments regarding the best available data,
models, and modeling methodologies and the assumptions that are most
appropriate to adopt in the face of important uncertainties.  The
majority of the analytical assumptions used to develop the primary
estimates of benefits have been reviewed and approved by EPA’s SAB. 
Both EPA and the SAB recognize that data and modeling limitations as
well as simplifying assumptions can introduce significant uncertainty
into the benefit results and that alternative choices exist for some
inputs to the analysis, such as the mortality C-R functions.  

This appendix supplements our primary analysis of benefits with three
additional sensitivity calculations.  These supplemental estimates
examine sensitivity to both valuation issues (e.g., the appropriate
income elasticity) and for physical effects issues (e.g., the structure
of the cessation lag and the sensitivity of the premature mortality
estimate to the presence of a presumed threshold).  These supplemental
estimates are not meant to be comprehensive.  Rather, they reflect some
of the key issues identified by EPA or commentors as likely to have a
significant impact on total benefits.  The individual adjustments in the
tables should not simply be added together because 1) there may be
overlap among the alternative assumptions and 2) the joint probability
among certain sets of alternative assumptions may be low. 

J.1	Premature Mortality Cessation Lag Structure

Over the last ten years, there has been a continuing discussion and
evolving advice regarding the timing of changes in health effects
following changes in ambient air pollution.  It has been hypothesized
that some reductions in premature mortality from exposure to ambient
PM2.5 will occur over short periods of time in individuals with
compromised health status, but other effects are likely to occur among
individuals who, at baseline, have reasonably good health that will
deteriorate because of continued exposure.  No animal models have yet
been developed to quantify these cumulative effects, nor are there
epidemiologic studies bearing on this question.  The SAB-HES has
recognized this lack of direct evidence.  However, in early advice, they
also note that “although there is substantial evidence that a portion
of the mortality effect of PM is manifest within a short period of time,
i.e., less than one year, it can be argued that, if no lag assumption is
made, the entire mortality excess observed in the cohort studies will be
analyzed as immediate effects, and this will result in an overestimate
of the health benefits of improved air quality.  Thus some time lag is
appropriate for distributing the cumulative mortality effect of PM in
the population” (EPA-SAB-COUNCIL-ADV-00-001, 1999, p. 9).  In recent
advice, the SAB-HES suggests that appropriate lag structures may be
developed based on the distribution of cause-specific deaths within the
overall all-cause estimate (  XE "EPA-SAB-COUNCIL-ADV-04-002, 2004" 
EPA-SAB-COUNCIL-ADV-04-002, 2004).  They suggest that diseases with
longer progressions should be characterized by longer-term lag
structures, while air pollution impacts occurring in populations with
existing disease may be characterized by shorter-term lags.  

A key question is the distribution of causes of death within the
relatively broad categories analyzed in the long-term cohort studies. 
Although it may be reasonable to assume the cessation lag for lung
cancer deaths mirrors the long latency of the disease, it is not at all
clear what the appropriate lag structure should be for cardiopulmonary
deaths, which include both respiratory and cardiovascular causes.  Some
respiratory diseases may have a long period of progression, while
others, such as pneumonia, have a very short duration.  In the case of
cardiovascular disease, there is an important question of whether air
pollution is causing the disease, which would imply a relatively long
cessation lag, or whether air pollution is causing premature death in
individuals with preexisting heart disease, which would imply very short
cessation lags.  The SAB-HES provides several recommendations for future
research that could support the development of defensible lag
structures, including using disease-specific lag models and constructing
a segmented lag distribution to combine differential lags across causes
of death (  XE "EPA-SAB-COUNCIL-ADV-04-002, 2004" 
EPA-SAB-COUNCIL-ADV-04-002, 2004).  The SAB-HES indicated support for
using “a Weibull distribution or a simpler distributional form made up
of several segments to cover the response mechanisms outlined above,
given our lack of knowledge on the specific form of the distributions”
(  XE "EPA-SAB-COUNCIL-ADV-04-002, 2004"  EPA-SAB-COUNCIL-ADV-04-002,
2004, p. 24).  However, they noted that “an important question to be
resolved is what the relative magnitudes of these segments should be,
and how many of the acute effects are assumed to be included in the
cohort effect estimate” (  XE "EPA-SAB-COUNCIL-ADV-04-002, 2004" 
EPA-SAB-COUNCIL-ADV-04-002, 2004, p. 24-25).  Since the publication of
that report in March 2004, EPA has sought additional clarification from
this committee.  In its followup advice provided in December 2004, this
SAB suggested that until additional research has been completed, EPA
should assume a segmented lag structure characterized by 30 percent of
mortality reductions occurring in the first year, 50 percent occurring
evenly over years 2 to 5 after the reduction in PM2.5, and 20 percent
occurring evenly over the years 6 to 20 after the reduction in PM2.5
(EPA-COUNCIL-LTR-05-001, 2004).  The distribution of deaths over the
latency period is intended to reflect the contribution of short-term
exposures in the first year, cardiopulmonary deaths in the 2- to 5-year
period, and long-term lung disease and lung cancer in the 6- to 20-year
period.  Furthermore, in their advisory letter, the SAB-HES recommended
that EPA include sensitivity analyses on other possible lag structures. 
In this appendix, we investigate the sensitivity of premature
mortality-reduction related benefits to alternative cessation lag
structures, noting that ongoing and future research may result in
changes to the lag structure used for the primary analysis. 

In previous advice from the SAB-HES, they recommended an analysis of 0-,
8-, and 15-year lags, as well as variations on the proportions of
mortality allocated to each segment in the segmented lag structure (  XE
"EPA-SAB-COUNCIL-ADV-00-001, 1999"  EPA-SAB-COUNCIL-ADV-00-001, 1999,
(EPA-COUNCIL-LTR-05-001, 2004).  The 0-year lag is representative of
EPA’s assumption in previous RIAs.  The 8- and 15-year lags are based
on the study periods from the   XE "Pope et al. (1995"  Pope et al.
(1995) and   XE "Dockery et al. (1993"  Dockery et al. (1993) studies,
respectively.  However, neither the Pope et al. nor Dockery et al.
studies assumed any lag structure when estimating the relative risks
from PM exposure.  In fact, the Pope et al. and Dockery et al. analyses
do not supporting or refute the existence of a lag.  Therefore, any lag
structure applied to the avoided incidences estimated from either of
these studies will be an assumed structure.  The 8- and 15-year lags
implicitly assume that all premature mortalities occur at the end of the
study periods (i.e., at 8 and 15 years).  

In addition to the simple 8- and 15-year lags, we have added three
additional sensitivity analyses examining the impact of assuming
different allocations of mortality to the segmented lag of the type
suggested by the SAB-HES.  The first sensitivity analysis assumes that
more of the mortality impact is associated with chronic lung diseases or
lung cancer and less with acute cardiopulmonary causes.  This
illustrative lag structure is characterized by 20 percent of mortality
reductions occurring in the first year, 50 percent occurring evenly over
years 2 to 5 after the reduction in PM2.5, and 30 percent occurring
evenly over the years 6 to 20 after the reduction in PM2.5.  The second
sensitivity analysis assumes the 5-year distributed lag structure used
in previous analyses, which is equivalent to a three-segment lag
structure with 50 percent in the first 2-year segment, 50 percent in the
second 3-year segment, and 0 percent in the 6- to 20-year segment.  The
third sensitivity analysis assumes a negative exponential relationship
between reduction in exposure and reduction in mortality risk.  This
structure is based on an analysis by   XE "Röösli et al. (2004" 
Röösli et al. (2004), which estimates the percentage of total
mortality impact in each period t as

		(C.1)

The   XE "Röösli et al. (2004"  Röösli et al. (2004) analysis
derives the lag structure by calculating the rate constant 

(–0.5) for the exponential lag structure that is consistent with both
the relative risk from the cohort studies and the change in mortality
observed in intervention type studies (e.g.,   XE "Pope et al., 1992" 
Pope et al. [1992] and   XE "Clancy et al., 2002"  Clancy et al.
[2002]).  This is the only lag structure examined that is based on
empirical data on the relationship between changes in exposure and
changes in mortality.  

The estimated impacts of alternative lag structures on the monetary
benefits associated with reductions in PM-related premature mortality
(estimated with the Pope et al. ACS impact function) are presented in
Table J-1.  These estimates are based on the value of statistical lives
saved approach (i.e., $5.5 million per incidence) and are presented for
both a 3 and 7 percent discount rate over the lag period. 

Table J_-1.  Sensitivity of Benefits of Premature Mortality Reductions
to Alternative Cessation Lag Structures, Using Pope et al (2002) Effect
Estimate

Alternative Lag Structures for PM-Related Premature Mortality 	15/35

Alternative Lag Structures for PM-Related Premature Mortality	Value 

(billion 1999$)a.b	Percent Difference from Base Estimate

None	Incidences all occur in the first year



		3% discount rate	$16.53.5	10.4%

		7% discount rate	$$3.516.5	31.2%

8-year	Incidences all occur in the 8th year



		3% discount rate	$2.913.4	-10.3%

		7% discount rate	$2.210.3	-18.3%

15-year	Incidences all occur in the 15th year



		3% discount rate	$2.310.9	-27.0%

		7% discount rate	$6.41.4	-49.1%

Alternative Segmented	20 percent of incidences occur in 1st year, 50
percent in years 2 to 5, and 30 percent in years 6 to 20



		3% discount rate	$14.53.1	-3.2%

		7% discount rate	$11.52.5	-8.7%

5-Year Distributed	50 percent of incidences occur in years 1 and 2 and
50 percent in years 2 to 5



		3% discount rate	$15.73.4	4.9%

		7% discount rate	$14.73.1	17.1%

Exponential	Incidences occur at an exponentially declining rate
following year of change in exposure



		3% discount rate	$15.83.4	5.6%

		7% discount rate	$14.43.1	14.8%

a	Dollar values rounded to two significant digits.

   TC \l1 " 

The results of this sensitivity analyses demonstrate that because of
discounting of delayed benefits, the lag structure may also have a large
impact on monetized benefits, reducing benefits by 30 percent if an
extreme assumption that no effects occur until after 15 years is
applied.  However, for most reasonable distributed lag structures,
differences in the specific shape of the lag function have relatively
small impacts on overall benefits.  For example, the overall impact of
moving from the previous 5-year distributed lag to the segmented lag
recommended by the SAB-HES in 2004 in the primary estimate is relatively
modest, reducing benefits by approximately 5 percent when a 3 percent
discount rate is used and 15 percent when a 7 percent discount rate is
used.  If no lag is assumed, benefits are increased by around 10 percent
relative to the segmented lag with a 3 percent discount rate and 30
percent with a 7 percent discount rate.  

X. 2	Threshold Sensitivity Analysis

Chapter __ presents the results of the PM2.5 premature mortality
benefits analysis based on an assumed cutpoint in the long-term
mortality concentration-response function at 10 µg/m3, and an assumed
cutpoint in the short-term morbidity concentration-response functions at
10 µg/m3. There is ongoing debate as to whether there exists a
threshold below which there would be no benefit to further reductions in
PM2.5.  Some researchers have hypothesized the presence of a threshold
relationship.  The nature of the hypothesized relationship is the
possibility that there exists a PM concentration level below which
further reductions no longer yield premature mortality reduction
benefits.  EPA’s most recent PM2.5 Criteria Document concludes that
“the available evidence does not either support or refute the
existence of thresholds for the effects of PM on mortality across the
range of concentrations in the studies” (U.S. EPA, 2004b  XE "U.S.
EPA, 2004"  , p. 9-44).  EPA’s Science Advisory Board (SAB) that
provides advice on benefits analysis methods has been to model premature
mortality associated with PM exposure as a non-threshold effect, that
is, with harmful effects to exposed populations regardless of the
absolute level of ambient PM concentrations.

For these reasons we provide the results of a sensitivity analysis in
which we estimate the change in reduction in incidence of PM2.5-related
premature mortality resulting from changes in the presumed threshold. We
also provide a corresponding estimate of the valuation of these changes
in incidence.

Table _-2:  Mortality Threshold Sensitivity Analysis for 0.070 ppm Ozone
Scenario (Using Pope et al., 2002 Effect Estimate with Slope Adjustment
for Thresholds Above 7.5 ug) 90th Percentile Confidence Intervals
Provided in Parentheses a



East	Western U.S. Excluding CA	California	Total

Less Certainty That Benefits Are at Least as Large	No Threshold	570

(230—920)	30

(11—45)	53

(21—85)	650

	Threshold at 7.5 µg	580

(230—930)	15

(6—24)	51

(20—85)	650

(250—1,000)

	Threshold at 10 µg	510

(200—810)	0.2

(0.07—0.3)	47

(18—75)	550

(220—890)

	Threshold at 12 µg	100

(40—160)	0.03

(0.01—0.04)	42

(16—67)	140

(56—230)

More Certainty That Benefits are at Least as Large	Threshold at 14 µg
---	---	36

(14—59)	36

(14—59)



a  All estimates are rounded to 2 significant digits.  All rounding
occurs after final summing of unrounded estimates.  As such, totals will
not sum across columns. 

Table __-3:  Sensitivity of Monetized Benefits of Reductions in
Mortality Risk to Assumed Thresholds for 15/35 Scenario (Using Pope et
al., 2002 Effect Estimate with Slope Adjustment for Thresholds Above 7.5
ug) 90th Percentile Confidence Intervals Provided in Parentheses a

Less Certain that Benefits Are at Least as Large	No Threshold	3%	$3,300

($830--$6,900)	$160

($41--$340)	$310

($77--$630)	$3,800

($950--$7,900)



7%	$2,800

($700--$5,800)	$140

($34--$280)	$260

($64--$530)	$3,200

($800--$6,200)

 	Threshold at 7.5 ug	3%	$3,400

($840--$7,000)	$86

($22--$$180)	$300

($74--$620)	$3,700

($940--$7,800)

 

7%	$2,800

($710--$5,900)	$72

($18--$150)	$250

($63--$520)	$3,200

($790--$6,600)

 	Threshold at 10 ug	3%	$2,900

($730--$6,100)	$1

($0.2--$2)	$270

($67--$560)	$3,200

($800--$6,600)

 

7%	$2,500

($620--$5,100)	$0.8

($0.2--$1.7)	$230

($57--$470)	$2,700

($670--$5,600)

 	Threshold at 12 ug	3%	$590

($150--$1,200)	$0.2

($0.04--$0.3)	$240

($61--$500)	$830

($210--$1,700)



7%	$490

($120--$1,000)	$0.1

($0.03--$0.3)	$200

($51--$420)	$700

($180--$1,500)

	Threshold at 14 ug	3%	--	--	$210

($53--$440)	$210

($53--$440)

More Certain that Benefits Are at Least as Large

7%	--	--	$180

($44--$370)	$180

($44--$370)

a  All estimates are rounded to 2 significant digits.  All rounding
occurs after final summing of unrounded estimates.  As such, totals will
not sum across columns. 

J.2	Visibility Benefits in Additional Class I Areas  TC \l1 " 

The Chestnut and Rowe (1990a) study from which the primary valuation
estimates are derived only examined WTP for visibility changes in Class
I areas (national parks and wilderness areas) in the southeast,
southwest, and California.  To obtain estimates of WTP for visibility
changes at national parks and wilderness areas in the northeast,
northwest, and central regions of the U.S., we have to transfer WTP
values from the studied regions.  This introduces additional uncertainty
into the estimates.  However, we have taken steps to adjust the WTP
values to account for the possibility that a visibility improvement in
parks in one region is not necessarily the same environmental quality
good as the same visibility improvement at parks in a different region. 
This may be due to differences in the scenic vistas at different parks,
uniqueness of the parks, or other factors, such as public familiarity
with the park resource.  To take this potential difference into account,
we adjusted the WTP being transferred by the ratio of visitor days in
the two regions.

Based on this benefits transfer methodology (implemented within the
preference calibration framework discussed in Chapter 5 and Appendix I),
estimated additional visibility benefits in the northwest, central, and
northeastern U.S. are provided in Table J-2.

Table J-2:  Monetary Benefits Associated with Improvements in Visibility
in Additional Federal Class I Areas in 2020 Incremental to 15/65
Attainment Strategy (in millions of 1999$)a 

Suite of Standards	Northwestb	Centralc	Northeastd	Total

15/35	$96	$130	$6	$240

14/35	$67	$140	$44	$250

	a  	All estimates are rounded to 2 significant digits.  All rounding
occurs after final summing of unrounded estimates.  As such, totals will
not sum across columns

	b	Northwest Class I areas include Crater Lake, Mount Rainier, North
Cascades, and Olympic national parks, and Alpine Lakes, Diamond Peak,
Eagle Cap, Gearhart Mountain, Glacier Peak, Goat Rocks, Hells Canyon,
Kalmiopsis, Mount Adams, Mount Hood, Mount Jefferson, Mount Washington,
Mountain Lakes, Pasayten, Strawberry Mountain, and Three Sisters
wilderness areas.

	c	Central Class I areas include Craters of the Moon, Glacier, Grand
Teton, Theodore Roosevelt, Badlands, Wind Cave, and Yellowstone national
parks, and Anaconda-Pintlar, Bob Marshall, Bridger, Cabinet Mountains,
Fitzpatrick, Gates of the Mountain, Lostwood, Medicine Lake, Mission
Mountain, North Absaroka, Red Rock Lakes, Sawtooth, Scapegoat,
Selway-Bitterroot, Teton, U.L. Bend, and Washakie wilderness areas.

	d 	Northeast Class I areas include Acadia, Big Bend, Guadalupe
Mountains, Isle Royale, Voyageurs, and Boundary Waters Canoe national
parks, and Brigantine, Caney Creek, Great Gulf, Hercules-Glades, Lye
Brook, Mingo, Moosehorn, Presidential Range-Dry Roosevelt Campobello,
Seney, Upper Buffalo, and Wichita Mountains wilderness areas.

J.3	Income Elasticity of Willingness to Pay  TC \l1 " 

As discussed in Chapter 5, our estimates of monetized benefits account
for growth in real GDP per capita by adjusting the WTP for individual
endpoints based on the central estimate of the adjustment factor for
each of the categories (minor health effects, severe and chronic health
effects, premature mortality, and visibility).  We examined how
sensitive the estimate of total benefits is to alternative estimates of
the income elasticities.  Table J-3 lists the ranges of elasticity
values used to calculate the income adjustment factors, while Table J-4
lists the ranges of corresponding adjustment factors.  The results of
this sensitivity analysis, giving the monetized benefit subtotals for
the four benefit categories, are presented in Table J-5.



Table J_-34.  Ranges of Elasticity Values Used to Account for Projected
Real Income Growtha  TC \l2 " 

Benefit Category	Lower Sensitivity Bound	Upper Sensitivity Bound

Minor Health Effect	0.04	0.30

Severe and Chronic Health Effects	0.25	0.60

Premature Mortality	0.08	1.00

Visibilityb	—	—

a	Derivation of these ranges can be found in   XE "Kleckner and Neumann
(1999"  Kleckner and Neumann (1999) and   XE "Chestnut (1997"  Chestnut
(1997).  COI estimates are assigned an adjustment factor of 1.0. 

b	No range was applied for visibility because no ranges were available
in the current published literature.

Table J_-45.  Ranges of Adjustment Factors Used to Account for Projected
Real Income Growtha  TC \l2 " 

Benefit Category	Lower Sensitivity Bound	Upper Sensitivity Bound

Minor Health Effect	1.018	1.147

Severe and Chronic Health Effects	1.121	1.317

Premature Mortality	1.037	1.591

Visibilityb	—	—

a	Based on elasticity values reported in Table C-4, U.S. Census
population projections, and projections of real GDP per capita.

b	No range was applied for visibility because no ranges were available
in the current published literature.

Table J_-6.  Sensitivity of Monetized Benefits to Alternative Income
Elasticitiesa  TC \l2 " 



Severe and Chronic Health Effects	--$1,400	$1,600--	$160$2,500
$190$2,700

Premature Mortalityb 	$2,000$13,000	$3,000$20,000	$2,800$23,000
$3,600$34,000

Visibility and Other Welfare Effectsc	$530	$530	$1,200	$1,200

Total Benefitsb	$2,000$15,000	$3,100$22,000	$2,900$26,000	$3,800$37,000

a	All estimates rounded to two significant digits.

b	Using mortality effect estimate from Pope et al (2002) to estimate
PM2.5 mortality and a 3 percent discount rate and mortality effect
estimate from Bell (2004)and 3 percent discount rate.

c	No range was applied for visibility because no ranges were available
in the current published literature.

	Consistent with the impact of mortality on total benefits, the
adjustment factor for mortality has the largest impact on total
benefits.  The value of mortality in 2020 ranges from 90 percent to 130
percent of the primary estimate based on the lower and upper sensitivity
bounds on the income adjustment factor.  The effect on the value of
minor and chronic health effects is much less pronounced, ranging from
98 percent to 105 percent of the primary estimate for minor effects and
from 93 percent to 106 percent for chronic effects.

C_.4	References  TC \l1 " 

Chestnut, L.G.  1997.  “Draft Memorandum:  Methodology for Estimating
Values for Changes in Visibility at National Parks.”  April 15.

Chestnut, L.G., and R.D. Rowe.  1990a.  Preservation Values for
Visibility Protection at the National Parks:  Draft Final Report. 
Prepared for Office of Air Quality Planning and Standards, U.S.
Environmental Protection Agency, Research Triangle Park, NC and Air
Quality Management Division, National Park Service, Denver, CO.

Chestnut, L.G., and R.D. Rowe.  1990b.  “A New National Park
Visibility Value Estimates.”  In Visibility and Fine Particles,
Transactions of an AWMA/EPA International Specialty Conference, C.V.
Mathai, ed. Air and Waste Management Association, Pittsburgh.

Clancy, L., P. Goodman, H. Sinclair, and D.W. Dockery.  2002.  “Effect
of Air-pollution Control on Death Rates in Dublin, Ireland:  An
Intervention Study.”  Lancet Oct 19;360(9341):1210-4.

Desvousges, W.H., F.R. Johnson, and H.S. Banzhaf.  1998.  Environmental
Policy Analysis With Limited Information: Principles and Applications of
the Transfer Method (New Horizons in Environmental Economics.)  Edward
Elgar Pub:  London. 

EPA-SAB-COUNCIL-ADV-00-001.  October 1999.  The Clean Air Act Amendments
(CAAA) Section 812 Prospective Study of Costs and Benefits (1999): 
Advisory by the Health and Ecological Effects Subcommittee on Initial
Assessments of Health and Ecological Effects.  Part 2. 

EPA-SAB-COUNCIL-ADV-99-012.  July 1999.  The Clean Air Act Amendments
(CAAA) Section 812 Prospective Study of Costs and Benefits (1999): 
Advisory by the Health and Ecological Effects Subcommittee on Initial
Assessments of Health and Ecological Effects.  Part 1. 

EPA-SAB-COUNCIL-ADV-01-004.  September 2001.  Review of the Draft
Analytical Plan for EPA’s Second Prospective Analysis—Benefits and
Costs of the Clean Air Act 1990-2020:  An Advisory by a Special Panel of
the Advisory Council on Clean Air Compliance Analysis. 

EPA-SAB-COUNCIL-ADV-04-002.  March 2004.  Advisory on Plans for Health
Effects Analysis in the Analytical Plan for EPA’s Second Prospective
Analysis—Benefits and Costs of the Clean Air Act, 1990-2020:  Advisory
by the Health Effects Subcommittee of the Advisory Council on Clean Air
Compliance Analysis.

Kleckner, N., and J. Neumann.  June 3, 1999.  “Recommended Approach to
Adjusting WTP Estimates to Reflect Changes in Real Income.” 
Memorandum to Jim Democker, US EPA/OPAR.

Roosli M, Kunzli N, Braun-Fahrlander C, Egger M. 2005. “Years of life
lost attributable to air pollution in Switzerland: dynamic
exposure-response model.” International Journal of Epidemiology
34(5):1029-35.

U.S. Environmental Protection Agency (EPA).  2004.  Air Quality Criteria
for Particulate Matter, Volume II.  Office of Research and Development. 
EPA/600/P-99/002bF, October 2004.

Although these studies were conducted for 8 and 15 years, respectively,
the choice of the duration of the study by the authors was not likely
due to observations of a lag in effects but is more likely due to the
expense of conducting long-term exposure studies or the amount of
satisfactory data that could be collected during this time period.

 The advice from the 2004 SAB-HES (U.S. EPA-SAB, 2004b) is characterized
by the following: “For the studies of long-term exposure, the HES
notes that Krewski et al. (2000  XE "Krewski et al. (2000"  ) have
conducted the most careful work on this issue.  They report that the
associations between PM2.5 and both all-cause and cardiopulmonary
mortality were near linear within the relevant ranges, with no apparent
threshold.  Graphical analyses of these studies (Dockery et al., 1993 
XE "Dockery et al., 1993"  , Figure 3, and Krewski et al., 2000  XE
"Krewsk⁩瑥愠⹬‬〲〰•Ⱅ瀠条⁥㘱⤲愠獬⁯畳杧獥⁴
⁡潣瑮湩畵⁭景攠晦捥獴搠睯⁮潴氠睯牥氠癥汥⹳†桔
牥晥牯ⱥ椠⁴獩爠慥潳慮汢⁥潦⁲偅⁁潴愠獳浵⁥⁡潮
琠牨獥潨摬洠摯汥搠睯⁮潴‬瑡氠慥瑳‬桴⁥潬⁷湥⁤
景琠敨挠湯散瑮慲楴湯⁳敲潰瑲摥椠⁮桴⁥瑳摵敩⹳ඔ
̍഍ഄ̍഍ഄऍ഍ഉ

഍

R

