A correction to the excess risk estimates presented in the 2004 report
by ENVIRON International Corporation titled “Preliminary Quantitative
Risk Assessment for Beryllium”

Submitted by:

Roslyn A. Stone, PhD 

Consulting Statistician

139 Alleyne Drive

Pittsburgh, PA 15215-1450

Submitted to:

Occupational Safety and Health Administration Under the Toxachemica,
Int. Contract with OSHA (Contract No. XXXXXXXX)

Draft Report

September 19, 2005

I.	Introduction

The U.S. Occupational Safety and Health Administration (OSHA) is
conducting a quantitative assessment of lung cancer mortality risk as a
function of beryllium exposure, based on published epidemiologic data.
The primary data source useful for this purpose is the nested
case-control study of Sanderson et al. (2001a), which was conducted in
one of the beryllium processing facilities that participated in a larger
lung cancer cohort mortality study (Ward et al., 1992).  The Reading,
PA, plant was chosen because it had a large number of lung cancer cases
(deaths), as well as adequate personnel records and 7000 historical
beryllium exposure measurements on which to base an extensive
retrospective exposure assessment (Sanderson et a. (2001b)).  The
Reading, PA, cohort included 3,569 male workers employed at that plant
between 1/1/1940 and 12/31/1969.

The case-control study included the 142 lung cancer deaths at the
Reading, PA, plant identified in the larger cohort study; cases were
individually matched to 5 controls of the same race at that plant who
were alive at the age of death of the corresponding case.  Exposures
were estimated for the members of each matched set as of the age of
death of the case, based on a retrospective exposure assessment linked
to a job-exposure matrix.  

Cases had significantly higher cumulative, average, and maximum
exposures to beryllium 10 and 20 years before death than controls of the
same age, based on conditional logistic regression analyses using
log-transformed exposure metrics. No significant associations were
observed using any of these metrics when the exposures were not lagged
10 or 20 years.  Cases also appeared to have higher lagged exposures to
beryllium oxide, beryllium-copper alloy, copper, and fluorides.  Based
on an indirect argument, these results do not appear to be confounded by
smoking.

In 2004, ENVIRON International Corporation submitted a preliminary
quantitative lung cancer risk assessment for beryllium to the
Occupational Safety and Health Administration (OSHA) based on the
Sanderson et al. (2001a) log cumulative exposure data.  They summarize
the design and results of the Sanderson et al. study (2001a), and
describe their estimation of the excess risk for several levels of
cumulative exposure to beryllium on pp. 13-19 of their report.  

In the present report, we present a reanalysis that addresses a
technical error in the 2004 ENVIRON report.  In particular, we summarize
their analytic approach, correct errors in their calculation of standard
errors based on data reported in Sanderson et al. (2001a), and generate
corrected interval estimates for the estimated additional lung cancer
deaths per 1000 workers.  In addition, we summarize the strengths,
limitations, and uncertainties in this analysis and the underlying
epidemiologic data.

Estimating excess risk

Summary of ENVIRON approach.  Although the 2004 ENVIRON report motivated
their approach in terms of a prospective logistic regression model, the
key results hold true for the conditional logistic regression model that
was in fact used.  A unique feature of the odds ratio is that the odds
of disease given exposure is equal to the odds of exposure given
disease.  Therefore the same odds ratio is obtained whether one samples
on the basis of exposure (as in a prospective study) or on the basis of
disease status (as in a case-control study).  The conditional logistic
regression likelihood essentially compares the exposure of the case to
the average exposure in the corresponding matched set (including the
case), and averages the estimated log odds ratios across all matched
sets using the following equation:

(Eq. 1)			∏	exp(Ziβ)

				∑ exp(Zjβ)

In Equation 1, i indexes the ith case, i=1…I, the sum in each
denomination is over the j members of the ith matched set, and the
product is over the I matched sets.  The parameter β represents the log
odds ratio, and Z is some measure of exposure (e.g. log cumulative
exposure lagged 10 years).  For a quantitative predictor Z, exp(β) is
the odds ratio associated with a 1 unit change in Z.

An artifact of log-transforming the exposure is that log(1) =0, so a
“0” predictor actually corresponds to an exposure of 1 μg/m3days.
In both the ENVIRON report and the corrected analyses, it is assumed
that an “unexposed” worker has an exposure of 1 μg/m3days, and that
the odds of lung cancer for such an “unexposed” worker is
approximately equal to the odds for a truly unexposed worker. It is
impossible to accurately quantify log(0) = -∞.

Key steps of the estimation:

1.  Source of epidemiologic data.  Extrapolations are based on the
estimated log odds ratios (βs) reported in Table IV of Sanderson et al.
(2001a), the relevant section of which is reproduced below:

Sanderson et al. (2001a) Table IV.  Conditional logistic regression
analysis of logs of continuous exposure variables (Beryllium workers
case-control study, USA)

 						β		Wald statistic	        p-value

Log cumulative exposure (μg/m3days), 	0.060		5.35			0.021

Lagged 10 years

Log cumulative exposure (μg/m3days), 	0.041		5.62			0.018

Lagged 20 years

2.  Calculation of confidence bounds.  Calculate the lower and upper
bounds of 95% Wald confidence intervals for these log odds ratios (cL,
cU), where cL= β -1.96 s.e. (β) and cU= β +1.96 s.e. (β) .  The
required standard errors were calculated from the reported Wald test
statistics in Table IV of Sanderson et al. (2001a) under the assumption
that these statistics had Normal distributions (i.e. 0.060/s.e. = 5.35
for the 10-year lag and 0.041/s.e.=5.62 for the 20-year lag). However,
the p-value of 0.021 for the 10-year lagged cumulative exposure
corresponds to a Normal cutpoint of 2.03 and the p-value of 0.018 for
the 20-year lagged cumulative exposure corresponds to a Normal cutpoint
of 2.10, neither of which matches the reported Wald statistic in Table
IV of Sanderson et al. (2001).  These derivations are summarized in the
table on p. 16 of the ENVIRON report, reproduced below:

ENVIRON (2004) Table I, p. 16.

Lag for cumulative	Estimate of β		Standard error (se)	95% C.I. for βa

exposure (years)	parameter		of β

(per μg-days/m3)

10			0.060			0.011			(0.038, 0.082)

20			0.041			0.0073			(0.027, 0.055)

aThe confidence intervals were calculated assuming normality of the
estimated βs.  The interval was estimated to be β ± 1.96 se.

3.  Life table approach to estimating excess risk.  The point estimates
of β in the previous table and the corresponding 95% confidence bounds
were used to estimate the additional lung cancer deaths per 1000 workers
exposed to beryllium at a specified concentration for 45 years starting
at age 20 and the associated confidence bounds. The hypothetical worker
was followed until age 100, and baseline rates were estimated by the
2000 all-cause and lung cancer mortality rates (both sexes, all races). 
In these extrapolations the “rare disease” assumption was invoked,
that the odds ratio approximates the relative risk.

In this lifetable approach, the estimated relative risk associated with
the age-dependent cumulative exposure was multiplied by the age-specific
conditional probability of dying from lung cancer given survival to that
age.  The relevant lagged age-specific cumulative exposure was
calculated by multiplying the number of years of exposure (as of that
age) minus the lag, and multiplying by the product of the hypothesized
daily exposure concentration and the assumed 250 working days per year. 
These estimated additional lung cancer deaths per 1000 workers exposed
for 45 years starting at age 20 were summarized in Table II of the 2004
ENVIRON report.  This table is reproduced below:

ENVIRON (2004) Table II, p. 19 

Lag for cumulative 	Exposure concentration 	Estimated additional 

exposure (years)	μg/m3				lung cancer deaths per 1000 

workers exposeda

10			2				47 	(27-71)

			1				43 	(25-64)

			0.5				39	(22-58)

			0.2				34	(20-50)

			0.1				30	(18-44)

20			2				28	(17-40)

			1				26	(16-37)

			0.5				24	(15-33)

			0.2				21	(13-29)

			0.1				18	(12-16)

aWorkers assumed to be exposed for 45 years starting at age 20.  Best
estimates and bounds (in parentheses) are shown, corresponding to the
estimates presented by Sanderson et al (2001a) and the uncorrected 95%
confidence intervals derived above using the Wald statistics.

III.	Corrected standard errors and confidence intervals for estimated
excess risk

 The correct formulas used to calculate the s.e. (β) are:

for the 10-year lag		0.060/s.e.(β) = √5.35, 		so s.e.(β) = 0.026

and for the 20-year lag	0.041/s.e.(β) = √5.62, 		so s.e.(β) = 0.017.

Both of these estimated standard errors are more than double the
corresponding values in Table I of the 2004 ENVIRON report. 

The corresponding 95% confidence limits based on the corrected standard
errors are:

for the 10-year lag		0.006  ±  1.96 (0.026)  	(cL= 0.009, cU=0.111)

and for the 20-year lag	0.041  ±  1.96 (0.017)  	(cL= 0.008, cU=0.074).

Both of these confidence intervals are considerably wider than those
reported in Table I of the 2004 ENVIRON report.

Corrected Table I of the 2004 ENVIRON report.

f β		Standard error (se)	95% C.I. for βa

exposure (years)	parameter		of β

(per μg-days/m3)

10			0.060			0.026			(0.009, 0.111)

20			0.041			0.017			(0.008, 0.074)

aThe confidence intervals were calculated assuming normality of the
estimates, β.  The interval was estimated to be β ± 1.96 se.

Using the Excel spreadsheet “lung cancer lifetable.xls”, which was
provided to OSHA by ENVIRON, the revised estimates based on the
corrected confidence limits are:

Corrected Table II of the 2004 ENVIRON report	

Lag for cumulative	Exposure concentration	Estimated additional lung
cancer

exposure (years) 	μg/m3				deaths per 1000 workers exposeda

10			2				47 	(6-110)

			1				43 	(5-98)

			0.5				39	(5-88)

			0.2				34	(4-75)

			0.1				30	(4-65)

20			2				28	(5-59)

			1				26	(4-53)

			0.5				23	(4-48)

			0.2				20	(3-41)

			0.1				18	(3-36)

aWorkers assumed to be exposed for 45 years starting at age 20.  Best
estimates and bounds (in parentheses) are shown, corresponding to the
estimates presented by Sanderson et al (2001a) and the corrected 95%
confidence intervals derived above using the Wald statistics.

The point estimates are the same as in the 2004 ENVIRON report, but the
corrected confidence intervals are considerably wider.  All of the
exposure levels and lags considered are consistent with a minimum excess
risk of no more than 6 workers/1000 workers exposed, although the upper
limit decreases as exposure concentration decreases and as time lag
increases. 

IV.	Discussion

Strengths.  This quantitative risk assessment is based on a published
epidemiologic study with a large number of lung cancer cases and an
extensive retrospective exposure assessment based on 7000 historical
measurements and detailed work histories.  Time-specific job-exposure
matrices were constructed to estimate age-specific exposures.  All-cause
mortality and lung cancer mortality rates for unexposed persons were
estimated using 2000 U.S. population rates. In addition, the excess risk
estimates are based on a relevant exposure scenario (45 years of
exposure starting at age 20); however, the excess risk associated with
other exposure scenarios of interest could be extrapolated using the
same approach. 

Limitations.  Several limitations of this quantitative risk assessment
are due to characteristics of the workers in the underlying
epidemiologic study.  For example, the Sanderson et al. (2001a) study is
relatively uninformative with respect to long-term exposures:  almost
2/3 of cases and more than half of the controls were employed at this
plant <1 year. In addition, a majority of both cases and controls were
hired during the 1940’s, with about 60% hired between 1941-1945. 
These workers newly hired during World War II are likely to differ from
workers hired before or after, and exposures are known to be lower
post-1950.  As in most such studies, no data were available on
occupational exposures prior or subsequent to employment in the study
plant.  Finally, a potentially important confounder for lung cancer,
smoking, was not ascertained directly in the Sanderson et al. (2001a)
study.  However, an indirect assessment provided no evidence of major
confounding by smoking.

One potential limitation of the cause-specific lifetable approach in the
2004 ENVIRON report is that the problem of competing risks is ignored;
the excess risks are estimated under the assumption that beryllium
exposure is not associated with other causes of mortality. To the extent
that beryllium is associated with causes of mortality other than lung
cancer, these estimated excess risks would be too low. A somewhat
similar quantitative risk assessment for acrylonitrile based on
occupational cohort data does take competing risks into account (Starr
et al. 2004).

Uncertanties.  Reconstructing exposures using a retrospective exposure
assessment is likely to underestimate variability in exposure across
workers as well as uncertainties in the retrospective exposure
assessment process itself.  The confidence intervals for the estimated
odds ratios in Sanderson et al. Table IV do not account for the inherent
uncertainty in the retrospective exposure assessment.  The already wide
confidence intervals in the Corrected Table II are likely to
underestimate the true uncertainty in these estimated excess risks. It
is also possible that the Wald confidence is not accurate, and that a
non-symmetric interval would fit these data better.

In the absence of an underlying mechanistic model, the choice of the
exposure metric and the form of the exposure-response were specified
based on empirical grounds.  The present quantitative risk assessment is
based on log-transformed cumulative exposure lagged 10 or 20 years, and
the conditional logistic regression model assumes that the effect of
exposure is linear in a logit scale.  Although the log transform is
problematic at 0, this transformation does down-weight the influence of
extremely high exposure values. In addition, the role of co-exposures
and alternative characterizations of exposure in terms of particle size
and parent compound could be assessed. 

Other uncertainties pertain to the choice of the time frame for the
case-control comparisons.  Sanderson et al. (2001a) sampled non-cases
from the risk set at the age the case died, and evaluated cumulative
exposures for both the case and the matched controls as of that age. 
This specifies age as the primary time dimension, as is usually done for
lung cancer because mortality depends so strongly on age.  An
alternative time frame would be time since first employment, so that
cases and controls would be compared after the same duration of
employment.  Some researchers adjust for year of hire as a covariate to
adjust for “cohort” effects.  However, if exposures are similar
across a plant at a given time but vary over time, adjusting for year of
hire could be over-adjusting for exposure.  

As Deubner (2001) points out, adjusting for attained age does not
necessarily adjust for age at hire.  However, age at hire does not
provide a useful time scale in which to compare the exposures of cases
and controls.  In a hypothetical example, Kolanz (2005) compared cases
and controls at different ages, which is not what was done by Sanderson
et al. (2001a).  The Kolanz example is reproduced below (2005, p. 18):

Case/		Age employment		Age diagnosed			Exposure

,

+

,

g

ç

õ

hD

hD

hÃ

h¸5

=or ascertained		years	lag 10 		lag 10 

									from age 40	true

Case		20	35		40			15	10		10

Control		30	45		50			15	0		10

This example purports to show that cases are expected to have different
lagged exposures than controls under the (unspecified) null hypothesis. 
In the Sanderson et al. (2001a) study, exposures were ascertained as of
the age of death of the case.  The table above would be modified as
follows:

Case/		Age employment		Age diagnosed			Exposure

control		began	terminated	or ascertained		years	lag 10 		lag 10 

									from age 40	true

Case		20	35		40			15	10		10

Control		30	45		40			10	0		0

In this second example, the true lag 10 exposure matches the lag 10 from
age 40 because the case and control are being compared at the same age. 
If the purpose of the 10 year lag is to discount recent exposures, then
the control truly does have 0 exposure outside of this 10-year window
from the age of interest (i.e. 40).  This is not a bias but a
consequence of the definition of a lagged exposure.

Some of these uncertainties can be addressed easily by conducting
additional analyses using the published data.  For example,
log-transformed average or maximum exposure, or different time lags,
could be assessed with only minor modifications to the existing
programs. 

However, addressing other uncertainties would require re-analysis of the
full data from the Sanderson et al. (2001a) study.  For example, the
analysis presented here could be re-done using exact confidence
intervals, which would be valid for sparse data and not presume
symmetric limits. To the extent possible, alternative functional forms
of the relationship between lung cancer mortality and exposure to
beryllium could be explored, and co-exposures taken into account.
Influence diagnostics could provide insight into the stability of the
model and identify any influential points. Exposure-response
relationships for subgroups of workers could be assessed, such as
short-term and longer-term workers or workers hired after 1950. 
Finally, the impact of adjusting for age at hire could be assessed. 
Depending on how smoking was ascertained for a subsample of cases and
controls in the Sanderson thesis, as suggested by Deubner (2001), it may
be feasible to include such “validation” data in a more
comprehensive analysis of the case-control data.

However, some uncertainties remain that cannot be addressed with the
data and statistical methods considered here.  Assessing the role of
particle size or compound would likely involve reconstructing the
initial job-exposure matrix of Sanderson et al. (2001b), which may not
be feasible.  Subsequent analyses would involve linking the job-exposure
matrix to the entire Reading cohort, not just the cases and matched
controls.  Addressing the impact of competing risks would also require
the full cohort data and the linked job-exposure matrix.

VI.	References

Sanderson WT, Ward EM, Steenland K, Petersen MR (2001a).  Lung cancer
case-control study of beryllium workers.  Am J Ind Med 39:133-144.

Ward E, Okun A, Ruder A. Fingerhut M, Steenland K (1992).  A mortality
study of workers at seven beryllium processing plants.  Am J Ind Med
22:885-904.

Sanderson WT, Petersen MR, Ward EM (2001b).  Estimating historical
exposures of workers in a beryllium manufacturing plant. Am J Ind Med
39:145-157. 

ENVIRON International Corporation (2004). Preliminary Quantitative Risk
Asssessment for Beryllium.  Report submitted to OSHA.

Deubner DC (2001).  Re: Lung cancer case-control study of beryllium
workers. Sanderson WT, Ward EM, Steenland K, Petersen MR. Am J Ind Med
2001. 39:133-144 (Letter to the editor). Am J Ind Med 40:284-285.

Kolanz ME (2005).  Comments of Brush Wellman Inc. to the ACGIH TLV
Committee regarding the ACGIH 2005 Notice of Intended Change for
Beryllium and Compounds.

Starr TB, Gause C, Youk AO, Stone R, Marsh GM (2004).  A risk assessment
for occupational acrylonitrile exposure using epidemiology data.  Risk
Analysis 24:587-601.  

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