Health Effects of Exposure to Radon BEIR VI (1999) / Chapter Skim
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Appendix A Risk Modeling and Uncertainty Analysis
Appendix A Risk Modeling and Uncertainty Analysis
Pages 129-175
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From page 129... ...
of lung cancer and cumulative exposure to radon progeny was generally consistent with linearity within each cohort. However, estimates of the excess relative risk (ERR)
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We begin with a review of risk models developed by other investigators. In order to lay the foundation for the committee's risk model, we then discuss methods for combining data from different sources, including random-effects and two-stage methods.
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131 Cq Cq a' o be a' o Cq Cq .= a' ¢ E¢ca o · ~ o ~ o o o H.~ z ~ o En ~ to ~o O ~13R ° ca ~ o C ~ ~ o o o ~ ~ ~o .
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In addition to identifying sources of uncertainty, the committee attempted a quantitative analysis of uncertainty in radon risk estimates. This analysis is conducted within the general framework developed by Rai and others (1996)
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Here, w denotes cumulative exposure, x is a vector of covariates which affect the background lung-cancer rate, and z is a vector of covariates that may modify the exposure-response relationship. The excess risk varied by categories of attained age, <35, 35-49, 50-65, >65 yrs, with 0, 10, 20, 30 excess cases per 106 personyears per unit of exposure in WLM.
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The ICRP model was based on a simple constant excess relative risk model of the form RR(w)
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. That committee conducted a pooled analysis of data from four cohort studies of underground miners including the studies of Colorado, Ontario, Beaverlodge, and Sweden (NRC 1988~.
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The ICRP approach was notable in two respects. First, in contrast to the earlier ICRP risk model, which was based on a constant relative risk in cumulative exposure (ICRP 1987)
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for the cross-classification variables, such as cumulative exposure, exposure duration, attained age, and age at first exposure, were computed. For pooling purposes, data were further cross-classified by cohort.
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This general relative risk model can be written as r~x,z,w)
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With the two-stage clonal expansion model, separate parameters are used to describe the first and second stage mutation rates as well as the birth and death rates of initiated cells. Third, a validated biologic-based model is likely to enjoy greater acceptance when used for the quantitative estimation and prediction of cancer risks.
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From page 141... ...
The Colorado uranium miners' data used in this analysis were described by Hornung and Meinhard (1987) , and included the information on the age at which exposure to radon progeny and cigarette smoke began, the ages at which these exposures stopped, the cumulative exposure to radon progeny, the number of cigarettes smoked per day, the age at last observation or death, and information on whether or not the individual had died of lung cancer by that time.
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From page 142... ...
Estimates of the spontaneous mutation rates aO and be were almost equal, and the second mutation rate v appears to be unaffected by either radon progeny or cigarette smoke. Since the likelihood is little changed by setting a0 = be and be = br = 0, a reduced form of model A with only 12 parameters was therefore considered.
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From page 143... ...
The second mutation rate was found to be independent of radon progeny and cigarettesmoke exposures. With both models, the age-specific relative risks associated with joint exposure were supra-additive but sub-multiplicative, confirming previous findings by Whittemore and McMillan (1983)
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From page 144... ...
where pk is the excess relative risk of lung cancer associated with exposure to radon progeny for the kth cohort, Wjk denotes the cumulative radon exposure within the jth stratum of the kth cohort, °a denotes the modifying effect of attained age, and ~z denotes the effect of either exposure duration or exposure
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Wang and others (1995) provide a detailed discussion of how this approximation random effects model may be fit to data from the 11 miner cohorts using generalized estimating equations (GEEs)
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An overall estimate of ~ is then obtained as a simple linear combination of the cohort-specific estimates. Details of the two-stage regression method have been given by Laird and Mosteller (1990)
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Consequently, the committee focused primarily on two-stage regression methods for model fitting. Combined Analysis of Miner Cohorts The updated data on the 11 miner cohorts were summarized in the form of a multi-way table prior to analysis.
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Consequently, the overall estimate of ~ was obtained using the twostage method with associated standard errors reflecting variation within and between cohorts. We also used the random-effects method to obtain the overall estimate of p.
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(The difference in standard errors for the two-stage and random-effects methods is due to the different approaches used to estimate the standard error, and the small number of cohorts involved in the analysis.) The cohort-specific estimates of the excess relative risk per unit exposure are shown graphically in Figure A-1.
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obtained by fitting a constant excess relative risk model to each cohort separately (overall estimate based on the 2-stage method) and 95% confidence intervals.
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TABLE A-4 Estimates of the parameters in the committee' s two preferred risk models Exposure-age-duration modela Exposure-age-concentration modela x 100 0.55b (2.03)
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Adjustments for Smoking Status The data on smoking are generally too sparse to model the joint effects of smoking and radon exposure. However, using the results of analyses of the effect of radon-progeny exposure among never-smokers and among ever-smokers, it is possible to adjust the committee's preferred models to account for smoking status.
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153 to g ~A .m ;> o e ~ ~ .!
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QUALITATIVE UNCERTAINTY ANALYSIS In the remainder of this appendix, we focus on sources of uncertainty and variability in radon risk estimates. Clearly, lack of accurate information on a number of variables that affect radon risk, including critical variables such as radon exposure and tobacco consumption, confers uncertainty on committee projections of risk.
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155 + 11 ho U]
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The committee attempted to identify the main sources of uncertainty in assessing the lung-cancer risk from radon exposure. The committee also conducted a limited quantitative analysis of the uncertainty in estimates of both relative risk and attributable risk.
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were obtained using the committee's preferred risk models (chapter 3, Table 3-6~. These estimates reflect the lifetime relative risk (ERR)
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As Morgan and others note, the distinction between parameter and model uncertainties is somewhat blurred, since the selected model can be viewed as a special case of a much richer model with many of the risk factors omitted. For example, the linear model used in this report is a special case of more general non-linear models, and was chosen because more general models did not provide significantly better fits to the underground miner data (Lubin and others 1994a)
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From page 159... ...
However, because the population attributable risk is a complex function of the estimated parameters, and because the distributions of the statistics involved may not be adequately approximated by multivariate normal distributions, the committee conducted Monte Carlo simulations to obtain uncertainty distributions and confidence intervals for attributable risks as described later in this appendix. Errors in the Underground Miner Data In the three sections that follow, errors in the data from the 11 miner cohorts used to determine the committee's risk model are discussed.
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Relative to other sources of error, bias from errors in health outcome data is not thought to be large, and no attempt has been made to quantify it. Errors in the Underground Miner Data on Exposure to Radon and Radon Progeny The exposure estimates used in the committee's analyses of the 11 miner cohorts are subject to many sources of error, as discussed in detail in appendix F
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From page 161... ...
A portion of the uncertainty resulting from exposure-measurement error may thus be included in the heterogeneity component of the variance for the risk coefficient based on the combined analyses. However, it is unlikely that this takes account of all uncertainty from this source, and no account has been taken of the tendency for random error to bias risk estimates downward.
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More than a third of the lung-cancer deaths in the exposure restricted analyses came from the Ontario cohort, where exposure assessment methods were among the best of the 11 cohorts. Lifetime risk estimates based on models developed from these analyses were very similar to those obtained using the committee's recommended models.
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From page 163... ...
Temporal Expression of Risks The committee's risk models provide for a decline in risk with time since exposure and with age at risk. Although these patterns were consistently identified in nearly all of the underground miner cohorts, it is possible that the estimates of these effects could have been biased by time-dependent errors in both
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The statistical uncertainty in estimating the parameters quantifying age at risk effects was included in the Monte Carlo simulations that were conducted, but the uncertainty in estimating the parameters quantifying the time since exposure parameters was not included. Dependence of Risks on Sex The cohorts used to develop the committee's risk models included only male miners.
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These differences must be accounted for in using risk estimates based on underground miners to estimate risks for persons exposed in homes. The parameter summarizing these differences is often referred to as the K-factor.
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Thus, the variability in K is larger than its uncertainty. Uncertainties Relating to Background Exposures The risk models developed by the committee based on its analysis of data from the 11 miner cohorts are based on occupational radon exposures.
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Rather than evaluate uncertainty from this source, it seems preferable simply to state that the lifetime risk estimates presented in this report are appropriate only for a population with these demographic characteristics. If changes occur in the future, or risk projection for other populations are desired, these estimates will need to be recalculated to reflect these modifications.
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Though convenient and easy to use with modern computing technology, Monte Carlo methods should be carefully monitored to ensure the integrity of the results (Burmaster and Anderson 1994~. Distinguishing between uncertainty and variability is necessary but sometimes difficult (Hoffman and Hammonds 1994; Bogen 1995~.
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, the attributable risk of lung cancer due to radon exposure is defined as the proportion of lung-cancer deaths attributable to radon progeny. For continuous risk factors, the AR can be written as 00 | it(w)
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Furthermore, let ei be the excess relative risk due to exposure w to radon progeny for age group i. Here, we consider two types of models for ei: ei = ,Bofi~w (i)
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and (40) express the age-specific excess relative risk using a risk factor Owl for exposure concentration and an alternative risk factor Spur for exposure duration, respectively.
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gm = 1.00, gsd~LUe (1.2, 2.2) TABLE A-8b Uncertainty and variability distributions for risk factors in the exposure-age-duration model for excess relative risk Risk Factor Variability Uncertainty Model parameters ~ = (F3, (a, 'Yz)
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174 a' o o so a' be a' Cat o x a' ·_4 Cal so o C)
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0.111 (0.081, 0.194) TABLE A-lOb Impact of uncertainty and variability on uncertainty intervals for population attributable risk for females Exposure-ageconcentration model Exposure-ageduration model Source ARa 95%U.I.
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