Accounting for Uncertainty in Systematic Bias in Exposure Estimates Used in Relative Risk Regression

Transcription

1 PNL UC-605 Accounting for Uncertainty in Systematic Bias in Exposure Estimates Used in Relative Risk Regression E. S. Gilbert December 1995 The study was funded by Grant R01 OH03270 from the National Institute for Occupational Safety and Health of the Centers for Disease Control and Prevention Pacific Northwest Laboratory Rich1 and, Washington 99352

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3 In many epidemiologic studies addressing exposure-response relationships, sources of error that lead to systematic bias in exposure measurements are known to be present, but there is uncertainty in the magnitude and nature of the bias. Two approaches that allow this uncertainty to be reflected in confidence limits and other statistical inferences were developed, and are applicable to both cohort and case-control studies. The first approach is based on a numerical approximation to the likelihood ratio statistic, and the second uses computer simulations based on the score statistic. These approaches were applied to data from a cohort study of workers at the Hanford site ( ) exposed occupationally to external radiation; to combined data on workers exposed at Hanford, Oak Ridge National Laboratory, and Rocky Flats Weapons plant; and to artificial data sets created to examine the effects of varying sample size and the magnitude of the risk estimate. For the worker data, sampling uncertainty dominated and accounting for uncertainty in systematic bias did not greatly modify confidence limits. However, with increased sample size, accounting for these uncertainties became more important, and is recommended when there is interest in comparing or combining results from different studies. iii

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5 CONTENTS SUMMARY INTRODUCTION MATERIALS AND METHODS APPROACHES FOR ACCOUNTING FOR SYSTEMATIC MEASUREMENT ERROR... iii STUDIES OF NUCLEAR WORKERS EXPOSED TO EXTERNAL RADIATION.... RESULTS... DISCUSSION... REFERENCES

6 TABLES Characteristics, of the Hanford Worker Study Population and of the Combined Study Population of Workers at Hanford, ORNL, and Rocky Flats... Number of Deaths in Hanford Worker and Combined Study Popul at i ons by Recorded Cumul a t i ve Dose... Excess Relative Risk (ERR) Estimates (per Sv) with 90% and 95% Confidence Intervals (CI) for All Cancer Except Leukemia and for Leukemia Excluding CLL: Hanford Worker Study and Combined Data on Workers at Hanford, ORNL, and Rocky Flats... Excess Relative Risk (ERR) Estimates (per Sv) with 90% and 95% Confidence Intervals (CI) Based on Several Modifications to the Hanford Worker Study Data... Excess Relative Risk (ERR) Estimates (per Sv) with 90% and 95% Confidence Intervals (CI) for Leukemia Excluding CLL- Based on Combined Data Set Consisting of I) the Actual Hanford Worker Data the Hanford Data Modified so that the Estimated ERR was Equal to Twice the Linear Estimate From High Dose Data vi

7 INTRODUCTION It is well known that results of exposure-response analyses can be distorted in various ways if exposures are measured with error and these errors are not taken into account. Recent research on this problem has emphasized adjusting analyses for random measurement errors with little specific attention given to the generally simpler problem of adjustment for systematic errors (Armstrong 1990, Clayton 1992, Pierce et a , Richardson and Gilks 1993, Thomas et a ). This paper addresses the situation in which potential for systematic bias exists, but the exact nature of the bias is not known with certainty. The studies that motivated this paper were those of nuclear workers exposed occupationally to external radiation (Gilbert et a a, Gilbert et a b, Carpenter et a , Gribbin et a , IARC 1994). A major objective of these studies is to provide a direct assessment of the carcinogenic risk of exposure to ionizing radiation at low doses and dose rates. To accomplish this objective, risk estimates (expressed per unit of dose) and confidence limits are compared with risk estimates that serve as the basis for radiation protection standards, and which have been based on extrapol ation from data on persons exposed at high doses and dose rates (National Academy of Sciences 1990, UNSCEAR 1988). In making these comparisons, it is important to adjust recorded doses for systematic biases and to reflect the uncertainty in these adjustments in confidence limits and other inferences. Dose estimates for workers were obtained from personal dosimeters, and are subject to several sources of error that lead to systematic bias of an uncertain nature. 1.1

8 2.0 MATERIALS AND METHODS 2.1 APPROACHES FOR ACCOUNTING FOR SYSTEMATIC MEASUREMENT ERROR Methods developed in this paper are applicable to either cohort or case- control studies, although illustrations are based on cohort studies of nuclear workers. Following Moolgavkar and Venzon (1987), the relative risk associated with exposure variable x is denoted by R(x,B); that is, R(x,B) is the incidence rate ratio for exposure x relative to absence of exposure (x=o). Let i index cases of the disease of interest (i=l, 2,... N) with case i occurring at time ti. With a cohort design, let mi denote the number of sub- jects in the risk set for case i, where the risk set consists of subjects at risk of disease at time ti who are similar to case i with respect to specified stratification variables. ber of matched controls for case i. dose of case i, and xij denote the dose of the j t h person in risk set i (j th control). With a case-control design, let mi In the nuclear worker studies, xi has usually been taken to be the dose accumulated by some specified lag period prior to the time the case occurs, and analyses have been stratified on calendar-year period, sex, and other variables thought to affect the baseline risk. Finally, let vi designate various characteristics of the risk (or case-control) sets. cohort study, the partial likelihood is then given by denote the num- For either design, let xio denote the For a For a case-control study, this same expression results, but is referred to as a conditional likelihood. Commonly used forms for the relative risk are the log-linear relative risk model with R(x,B) = exp (m), and the linear relative risk model R(x,B) = 1 + m. Analyses of data on populations exposed to radiation, including worker studies, have been based primarily on the linear model (Gilbert 1989, 2.1

9 Gilbert e t a ). This model is also used for applications in this paper, and B is referred to as the excess relative risk or ERR. Now let z designate an estimate o f the true exposure x, with subscripting for z analogous to that for x. It is assumed that z is subject to systematic error such that xij= h(zjj, vi, e ), and that e, the vector of parameters indicating the magnitude and nature of the systematic error, is not known with certainty, but can be described by a density function g(v, e). When no confusion is likely to result, h(z, e) is substituted for h(zij, vi, e), and g(e) is substituted for g(y, e ). Most results in this paper are based on a simple model, h(z, 8)= 8 z with a lognormal density used for g(8). The partial likelihood function for B based on the estimated doses z can be written as where Lz(/3, zle) is the partial likelihood function for /3 conditional on e. Because knowledge of both z and is equivalent to knowledge of the true doses x, L,(B, Zle) is obtained by substituting x = h(z, e) in the likelihood given in equation 1. For the simple model with x = 8z and the linear relative risk model used for applications in this paper, where Mi is the mean of the zij, j = O, 1,..., mi. Although closed l ~ r expresm sions for the likelihood in equation 2 are rarely available, inferences based on the likelihood ratio statistic can be obtained by approximating the integral in equation 2 by a sum o f the form 2.2

10 where the parameter space for e is partitioned into K categories, and 8, is the value of e at a central point in category k. Because the distributions g have often been obtained subjectively, and are rarely known precisely, the use of a discrete approximation is unlikely to result in any serious loss of information. In some cases, g may be a discrete function to begin with and no approximation is necessary. Calculations in this paper were based on the assumption that log 6 follows a normal distribution with mean 0 and standard deviation u, and intervals were chosen to cover the range from exp(-5o) to exp(+5u) with l o g 8: - log 8,' = 0.5 u, where 6," and 8,' are the upper and lower boundaries of interval k; 8, (see equation 4 ) was taken to be the geometric mean of these boundaries. Intervals with logarithmic length 0.5 u gave nearly identical results to finer intervals of length 0.1 u. Multivariate lognormal distributions were used for situations in which e was multidimensional. The sum in equation 4 can be evaluated for several candidate values of b, and in this way both the value j that maximizes L,(/3, z), and confidence limits /3- that satisfy can be determined, where is the appropriate percentile of the single degree-of-freedom chi-square distribution. Although this is a trial and error approach, it was not unduly difficult to implement for most applications of interest in the nuclear worker studies. However, i s multidimensional, the number of terms in equation 2 may become large, and one may prefer computer simulations in which e is repeatedly sampled from the density g(e). The score statistic based on equation 2 i s not generally tractable, but one can develop a somewhat ad hoc procedure based on the "usual" score statistic that would be used under the assumption of no systematic bias in dose estimates. With uncertainty in systematic bias, the usual asymptotic properties of this score statistic are modified, but computer simulations can be 2.3

11 conducted t o e v a l u a t e i t s d i s t r i b u t i o n under the assumption t h a t these uncer- t a i n t i e s f o l l o w the d e n s i t y g ( e ). Previous a n a l y s e s o f worker d a t a have used computer s i m u l a t i o n s t o a d d r e s s the inadequacy o f asymptotic methods ( G i l b e r t e t a a, G i l b e r t e t a b, IARC 1994) and t h i s approach has been described i n d e t a i l by G i l b e r t (1989). For c a l c u l a t i o n s i n this paper, this approach has been extended by randomly s e l e c t i n g a value o f i n the s i m u l a t i o n process. from g(@) f o r each sample s e l e c t e d Grouped exposure d a t a were used f o r these simulations. Another simple s o l u t i o n may be a p p r o p r i a t e i n some s i t u a t i o n s. simple model, h(2, 6) t i o n of be, the = W i t h the 6 Z, i t may be reasonable t o assume t h a t the d i s t r i b u - maximum l i k e l i h o o d e s t i m a t e o f /3 c o n d i t i o n a l on 6, i s lognormal w i t h the s t a n d a r d d e v i a t i o n o f l o g be given by us, and t h a t g ( 8 ) i s a l s o lognormal with the standard d e v i a t i o n of l o g 8 given by u. In this case, b, the unconditional e s t i m a t e o f B, follows a lognormal d i s t r i b u t i o n such t h a t the v a r i a n c e o f l o g i s ut + $. However, f o r a p p l i c a t i o n t o t h e worker d a t a, where confidence limits f o r /3 f r e q u e n t l y i n c l u d e n e g a t i v e values, the assumption o f a lognormal d i s t r i b u t i o n f o r 2.2 & did not seem a p p r o p r i a t e. STUDIES OF NUCLEAR WORKERS EXPOSED TO EXTERNAL RADIATION Data from a study of workers a t the Hanford s i t e and, t o a lesser extent, d a t a from a pooled a n a l y s e s o f workers a t Hanford, Oak Ridge National Laboratory (ORNL), and Rocky F l a t s are used t o i l l u s t r a t e the methods were d e s c r i b e d above. Except where noted otherwise, the s t a t i s t i c a l methods i n this paper are the same as t h o s e i n previous a n a l y s e s, and d e t a i l s (such a s t h e d e f i n i t i o n and c h o i c e o f s t r a t i f i c a t i o n v a r i a b l e s ) can be found i n G i l b e r t e t a 7. (1993a, 1993b). Tables 2.1 and 2.2 show b a s i c c h a r a c t e r i s t i c s o f the Hanford worker d a t a, and o f the combined d a t a including workers a t Hanford, ORNL, and Rocky F l a t s. Hanford i s by f a r the l a r g e s t population both i n terms o f the number o f workers and the t o t a l exposure. 2.4

12 TABLE 2.1. Doses of the Hanford Worker Study Population and of the Combined Study Population of Workers at Hanford, ORNL, and Rocky Number of workers Combined Hanford, Hanford ORNL, and Rocky Flats 31,763 44,086 Total recorded person-sv 702 1,085 Average recorded dose (msv) (a) Excludes 857 Hanford workers who had confirmed internal depositions of radionuclides or who received a substantial portion of their dose from neutrons or from low-energy photons (A00 kev) (Gilbert and Fix 1995). TABLE 2.2. Number of Deaths in Hanford Worker and Combined Study Popul at i ons by Recorded Cumul ati ve Dose(a) Cumul at i ve Dose (msv) All Cancer Except Leukemia Leukemia Excl udi ng CLL All Cancer Except Leukemi a Leukemia Excl udi ng CLL Total , , , (a) Excl udes 857 Hanford workers who had conf i rmed internal depositions of radionuclides or who received a substantial portion of their dose from neutrons or from low-energy photons (SI00 kev) (Gilbert and Fix 1995). 2.5

13 Dose estimates for workers at these.facilities were obtained from personal dosimeters worn by workers, and are subject to both systematic and random uncertainty. Sources of systematic uncertainty, of concern for this paper, include bias resulting from the fact that dosimeters were limited in their ability t o respond accurately to all radiation energies to which workers were exposed or to radiation coming from all directions. They also include bias resulting from the fact that modern dosimetry programs are usually designed to estimate "deep dose" (defined as the energy absorbed at a depth of 1 cm in tissue) rather than the organ doses needed for epidemiologic purposes, particularly for comparing risk estimates with those based on studies of populations exposed at high doses. In general, the magnitude of the.bias depends strongly on both the radiation energy and the geometry (direction from which the radiation was received). Because the distributions of energies and geometries in worker exposure environments are not known with certainty, uncertainty in the magnitude of the bias results. Additional uncertainty results because historical documentation, especially for early periods of plant operation, is not always adequate to allow precise evaluation of the magnitude of bias from some sources. Extensive efforts have been made to document the dosimetry systems used at Hanford (Wilson e t a ) and, very recently, Gilbert et a l. (1996) made a specific effort to quantify biases and their associated uncertainties. For estimating lung dose, where bias would be expected to be similar to that in estimating doses to many other internal organs, overall bias factors, defined as the ratios of the recorded dose to the lung dose, were estimated to be 1.3, 1.1, 1.2, and 1.1 for the respective time periods , , , and when different dosimetry practices were in use. For estimating bone marrow dose, relevant for analyses of leukemia mortality, the respective factors were estimated to be 1.8, 1.4, 1.6, and 1.4. Gilbert e t a l. also evaluated random errors, but these are not considered in the present paper. Gilbert e t a7. (1994) use lognormal distributions to quantify uncertainties, which are expressed as 95% uncertainty factors K determined so that the 2.6

14 intervals obtained by respectively dividing and multiplying by them include 95% of all observations. Estimates of these uncertainty factors were based on judgments of the authors regarding how well bias factors from various sources were known. For both lung dose and bone marrow dose, the estimated factors reflecting uncertainty in the systematic bias factors were estimated to be about 1.5 for doses received 1957 and later, and about 1.7 for earlier doses. Although these uncertainty factors give a sense of how well the bias factors are known, they cannot be considered to provide a fully rigorous characterization of uncertainties. For this reason, in the adjustments made bel ow, several uncertainty val ues are eval uated. The evaluation of bias and uncertainty summarized above was intended to apply only to dose received from external exposure to high energy photons. For this reason, analyses in this paper have excluded 857 Hanford workers who had confirmed internal depositions of radionuclides or who received a substantial portion of their dose from neutrons or from low-energy photons (400 kev). These workers were identified as described by Gilbert and Fix (1995). An evaluation of bias and uncertainty in dose estimates of the type conducted for Hanford (Gilbert et a ) has not been conducted for ORNL and Rocky Flats workers. For this reason, some analyses have allowed the uncertainty in systematic bias to be greater for ORNL and Rocky Flats workers than for Hanford workers. In addition, because many Rocky Flats workers were exposed to neutrons and to internal sources of radiation, some analyses have allowed for greater uncertainty for Rocky Flats than for ORNL. In analyses including these workers, correction factors similar to those for Hanford were used; specifically, the recorded doses of ORNL and Rocky Flats were divided by 1.1 and 1.5 to obtain respective estimates of lung and bone marrow doses. 2.7

15 3.0 RESULTS Table 3.1 shows estimates of the ERR with both 90% and 95% confidence limits based on data on Hanford workers, and on the combined data. are shown for all cancer except leukemia, and for leukemia excluding chronic lymphatic leukemia (CLL), interest in radiation risk assessment. the two disease categories that have been of major For comparison, the Hanford estimates based on recorded doses without adjustment were per Sv (90% CI = <0-1.0) for all cancer except leukemia, and -1.1 per Sv (90% CI = <0-2.1) for leukemia excluding CLL (Gilbert and Fix 1995). For the combined data, the comparable estimates were 0.0 per Sv (90% CI = (0-0.8) and -1.0 per Sv (9O%CI = <0-2.2), respectively (Gilbert et a b). Results Analyses of the combined data were based on the assumption that uncer- tainty was perfectly correlated for the three studies. tion is not likely to be realistic, it can be considered a "worst case" situa- tion in that with less than perfect correlation, some "cancelling" out of bias may occur. uncertainties were independent in the three populations led to the same or slightly smaller upper confidence limits. Although this assump- Repeats of the leukemia simulations based on the assumption that Results in Table 3.1 indicate that the absolute values of the maximum 1 i kel i hood estimates decreased sl ightly as the uncertainty factor increased, but that the upper confidence limits did not change greatly with allowance for modest uncertainty (95% uncertainty factor of 2 or less). allowing for uncertainty was greater for leukemia excluding CLL than for all cancer except leukemia, and slightly greater for the combined analyses than for analyses based only on Hanford. The effect of Allowing greater uncertainty for ORNL and Rocky Flats than for Hanford did not greatly modify results over those obtained with a 1.5 uncertainty factor for all three studies; probably because the sample sizes for ORNL and Rocky Flats were much smaller than that for Hanford. 3.1

16 TABLE 3.1. Excess R e l a t i v e Risk (ERR) Estimates ( p e r Sv) w i t h 90% and 95% Confidence I n t e r v a l s (CI) f o r A l l Cancer Except Leukemia and f o r Leukemia Excluding CLL(a): Hanford Worker Study and Combined Data on Workers a t Hanford, ORNL, and Rocky F l a t s All Cancer fbfept Leukemia 95% Uncertainty Factor(s) A ERR - 90% CI 0.20 <O-1.5 Hanford Workers <O < < % CI ERR <O-1.8 so-1.9 <o-2.0 <O-2.4 Leukemia x luding CLLfC7 Leukemia Excl udi ng CLL (b) % CI 95% CI 90% CI 95% CI <O-4.3 <O-6.1 <O-3.6 <O-5.0 <O-4.4 <O-4.5 <O-4.8 ~ <0-6.6 < Combined Data on Hanford, ORNL. and Rocky Flats Workers , 2.0, 3.0 (d) 1.5, 3.0(e)* 0.17 eo-1.1 <O-1.3 <o-1.2 co-1. 5 < <O-3.7 <O-5.1 <O-3.6 <0-3.7 <0-5.0 co-5. 1 <0-3.a <0-5.6 <0-4.1 co-5.5 <O-4.3 co-5.9 <O <0-3.7 <0-5.3 <0-4.2 <O <0-4.1 co-6. 1 <O-4.6 < <I?-3.8 ~ ~ <O <0-1.2 <O co-3.7 co-5.3 <0-4.2 co <o-1.2 co co-3.7 <O-5.3 <O-4.3 <O-5.7 (a) Based on estimated lung dose for all cancers except leukemia and on estimated bone marrow dose for 1 eukemi a excl udi ng CLL. (b) Confidence intervals based on approximation to the likelihood ratio statistic using ungrouped doses. (c) Confidence intervals based on computer simulations using the score statistic and grouped doses: (d) The 95% uncertainty factor was 1.5 for Hanford. 2.0 for the ORNL, and 3.0 for Rocky Flats with uncertainties assumed to be perfectly correlated for the three studies. (e) The 95% uncertainty factor was 1.5 for Hanford. 3.0 for ORNL and Rocky Flats with uncertainties assumed to be perfectly correlated for the three studies. Analyses based on the simulated s c o r e s t a t i s t i c y i e l d e d d i f f e r e n t upper limits than the l i k e l i h o o d r a t i o procedure, and this may be p a r t i a l l y due t o inadequacies w i t h the asymptotic approximation since the number o f leukemia d e a t h s was small and the dose d i s t r i b u t i o n s highly skewed. Also, the sim- u l a t e d results were based on grouped exposure d a t a while the results using the l i k e l i h o o d r a t i o approach were based on ungrouped exposure d a t a. 3.2

17 TABLE 3.2. Excess Relative Risk (ERR) Estimates (per Sv) with 90% and 95% Confidence Intervals (CI) Based on Several Modifications to the Hanford Worker Study Data(a) All Cancer Except Leukemia Leukemia Excluding CLL 95% Uncertainty Factor ERR 90% CI 95% CI - ERR 90% CI 95% CI A. Estimated ERR Equal to Linear Estimates From High Dose Data (b) <0-1.6 <o <O-18 < <O-1.6 <o <o-19 < <O-1.7 <o <o-20 < <O-1.8 <O <O-23 <0-32 B. Estimated ERR Equal to Ten Times Linear Estimate From High Dose Data. 1.o C. As in Table 3.1A With Number of Deaths Increased by Factor of Ten <O-0.58 <O <o, < <O <O, <O <O-0.65 <O CO-0.02 <O <O-0.74 <O CO-0.09 <O As in A (Above) With Number of Deaths Increased by Factor of Ten <O-0.62 cd <O-0.65 <O < < O <O-O. 83 < E. As in B (Above) With Number of Deaths Increased by Factor of Ten (a) (b) Confidence intervals based on approximation to the likelihood ratio statistic using ungrouped doses. These estimates were 0.24 per Sv for all cancers except leukemia, and 3.7 per Sv for 1 eukemi a excl udi ng CLL. 3.3

18 To investigate the e f f e c t of uncertainty in other situations t h a t might occur, the Hanford data were modified in various ways with r e s u l t s shown in For 3.2A, the Hanford d a t a were adjusted t o achieve an ERR e s t i mate equal t o the l i n e a r estimate from analyses of d a t a on male atomic bomb survivors exposed as adults (UNSCEAR 1988); these estimates were 0.24 per Sv Table 3.2. f o r a l l cancers except leukemia, and 3.7 per Sv f o r leukemia excluding CLL. For 3.2B, the data were adjusted t o achieve ERR estimates t h a t were ten times the atomic bomb survivor linear estimates. These adjustments were made by multiplying the doses of workers dying of the cause of i n t e r e s t by an approp r i a t e factor. In general, the e f f e c t of accounting f o r systematic uncer- t a i n t y became greater as the magnitude of the estimate increased. One of the reasons t h a t allowing f o r systematic uncertainty in dose estimates did n o t greatly affect r e s u l t s discussed t h u s f a r was t h a t s t a t i s t i cal uncertainty resulting from sampling error was very large and dominated results. To investigate how r e s u l t s might be modified i f sampling uncertainty were smaller, analyses shown in Table 3.1A, 3.2A, and 3.28 were repeated with the numbers of deaths increased by a factor of ten; r e s u l t s are shown in Table 3.2C, 3.2D, and 3.2E. As expected, the e f f e c t of accounting f o r uncer- t a i n t y in systematic bias became much more important w i t h the increased sample size. Also, i n one case (leukemia analyses 3.2C), the assumption of uncer- t a i n t y factors of 2 or 3 yielded confidence limits t h a t included zero, whereas the analyses not accounting f o r uncertainty had excluded zero. With the Hanford data, Gilbert e t a 7. (1996) judged t h a t uncertainty i n doses received before 1957 was larger than t h a t f o r doses received l a t e r. For t h i s reason, the analyses shown in Tables 3.1A and 3.2C were repeated using larger uncertainty factors for the e a r l i e r period. Specifically, analyses were conducted analyses with a 95% uncertainty factor of 1.5 f o r the period 1957 and l a t e r, and a 95% uncertainty factor of 3 f o r the period Uncertainties f o r the two time periods were assumed t o be independent or, alternatively, t o be perfectly correlated. 3.4 Because most of the dose was

19 received in l a t e r y e a r s, t h i s approach modified r e s u l t s very l i t t l e over those in which the 95% u n c e r t a i n t y f a c t o r was assumed t o be 1.5 f o r a l l the d a t a. To f u r t h e r i n v e s t i g a t e t h e use of d i f f e r e n t u n c e r t a i n t i e s for d i f f e r e n t parts of t h e d a t a, analyses of a combined leukemia d a t a set comprised of the actual Hanford d a t a and of Hanford d a t a adjusted t o y i e l d an ERR e s t i m a t e t h a t was twice the l i n e a r e s t i m a t e obtained from male A-bomb s u r v i v o r s exposed i n adulthood ( 7. 4 per Sv) were conducted. Results of these analyses a r e shown i n Table With t h e actual sample s i z e (3.3A), the assumption o f d i f f e r e n t u n c e r t a i n t y f a c t o r s did n o t g r e a t l y modify r e s u l t s over those obtained w i t h t h e assumption of t h e same uncertainty f a c t o r. However, when t h e sample s i z e was increased by a f a c t o r of ten, both the ERR e s t i m a t e s and t h e confidence l i m i t s depended on which p a r t of t h e d a t a was assumed t o be more uncertain ( l a s t two l i n e s o f Table 3. 3 B ). Of course, in a r e a l s i t u a t i o n, the appropria t e n e s s of combining d i s p a r a t e e s t i m a t e s from d i f f e r e n t segments of t h e d a t a would need t o be considered. 3.5

20 TABLE 3.3. Excess R e l a t i v e Risk ERR Estimates (per SV) w i t h 90% and 95% Confidence I n t e r v a l s(a\ (21) f o r Leukemia Excluding CLL-Based on Combined Data Set C o n s i s t i n g o f I ) t h e Actual Hanford Worker Data t h e Hanford Data M o d i f i e d so t h a t t h e Estimated ERR was Equal t o Twice t h e L i n e a r Estimate From High Dose Data ( 7. 4 p e r Sv) 90% Uncert i ty Factorsbf I I1 1.0, , , 1.5, 3.0, 1.5, 3.0, Uncertainty From Two Parts of Data, Independent ERR 90% CI 95% CI A. Actual Sample Size (86 Deaths) - Uncertainty From Two Parts of Data, Perfectly Correlated ERR 90% CI 95% CI 1.9 co-8.0 co <O co-8.2 co eo-8.3 CO co <O co <o-9.9 co co Number of Deaths Increased by a Factor of Ten CO-9.8 CO-10 co-13 eo-9.9 co (a) Confidence intervals based on approximation t o the likelihood ratio statistic using ungrouped doses. (b) The first factor was applied t o the component consisting of the actual Hanford data ( I ) ; the second factor was applied t o the component consisting of the modi fi ed Hanford data ( I I ). 3.6

21 4.0 DISCUSSION An approach for accounting for uncertainty in systematic bias has been described and applied to data on workers exposed occupationally to external radiation. For Hanford workers, an extensive evaluation of bias and uncertainties in dose estimates had recently been completed, and the analyses presented in this paper were the first to apply adjustment factors to recorded doses (to obtain estimates of lung and bone marrow dose), and to allow for uncertainty in the magnitude of the adjustment factors. For all cancer except leukemia, where the estimated adjustment factors were only slightly greater than one, these modifications did not alter results greatly. For leukemia excluding CLL, the application of the adjustment factors increased the absolute values of estimates and confidence limits by a factor of about 1.5, a difference that is important in comparing worker-based estimates and confidence limits with those obtained from data on populations exposed at high doses, which serve as the basis for current radiation protection standards. For both all cancer except leukemia and leukemia excluding CLL, sampling uncertainty was large, and, thus, allowing for modest uncertainty in the adjustment factor did not greatly modify results over those with no such a1 1 owance. Results of analyses of combined data from Hanford, ORNL, and Rocky Flats were also presented, but must be regarded as preliminary since a detailed evaluation of bias in dose estimates used in these studies has not been conducted. However, even with a 95% uncertainty factor of 3.0 for these studies (but smaller uncertainty for Hanford), results were not greatly different from those with no allowance for uncertainty. In addition to the U.S. nuclear worker studies evaluated in this paper, studies have also been carried out in the United Kingdom (Carpenter et a]. 1994) and Canada (Gribbin et a ) and combined analyses of data from the three countries conducted (IARC 1994). Also, a collaborative study including workers in several additional countries is currently underway. As indicated 4.1

22 in some of the hypothetical results shown in Tables 3.2 and 3.3, uncertainty in systematic bias becomes more important as sample size increases. For this reason, it is important to allow for this uncertainty in future international combined analyses. It is hoped that further work to evaluate bias and uncertainty in dose estimates used in nuclear worker studies throughout the world will be undertaken. Ideally dose-response analyses should take account of all errors in dose estimates including both random and systematic components. Several papers have addressed methods for a more general error structure with particular attention to random errors, but tractable solutions are not always readily available (Armstrong 1990, Clayton 1992, Pierce et a , Richardson and Gilks 1993, Thomas et a ). Although it is hoped that methods for adjusting for all types of exposure measurement errors will continue to be explored, the approach described and illustrated in this paper provides a relatively simple procedure for accounting for one potentially important source of uncertainty. The need to account for uncertainty in systematic bias is not of course limited to studies of nuclear workers. Attention to such bias is likely to be especially important in studies where sampling uncertainty is relatively small, and where some subjects are clearly subject to greater uncertainties than others. For example, in the atomic bomb survivor studies, the sampling uncertainty is much smaller than in the worker studies (National Academy of Sciences 1990, UNSCEAR 1988, Shimizu et a ). In addition, the estimated yield of the Hiroshima bomb is estimated to be much less certain than that for the Nagasaki bomb (Kaul 1984), and thus the potential for systematic bias in dose estimates of Hiroshima subjects is much greater than for Nagasaki subjects. Another example is the large number of lung cancer case-control studies of the effects of exposure to residential radon, where sampling uncertainty may become small if analyses of combined data including several thousand cases are eventually conducted (Samet et a ). Like the worker studies, risk estimates and confidence limits from the residential studies are 4.2

23 compared with those obtained from studies at higher exposure levels (in this case, from studies of underground miners) (Lubin 1994). To apply the methods of this paper, systematic bias and its uncertainty must be specified. Although in some cases, relevant data may be available to provide an objective basis for determining the uncertainty distributions in most cases, subjective judgments of experts are likely to be required. In these cases, it is desirable to perform analyses based on more than one set of assumptions regarding the magnitude of the bias, as has been done with the nuclear workers. With the workers, even allowing fairly large uncertainty did not greatly affect results, and these calculations thus allow one to be more confident that allowance for systematic uncertainty does not greatly modify conclusions. For the worker studies, the assumption that g(t3) was lognormal was judged appropriate. However, the general approach could be applied to other distributions in other situations. The general approach described in this paper could also be applied to uncertainty in systematic bias resulting from factors other than exposure measurement, for example, bias resulting from confounding. To do this, it would be necessary to specify distributions describing the uncertainty, and this would also involve subjective judgments. 4.3

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26 DISTRIBUTION PNL UC-605 No. of CoDies OFFSITE FOREIGN D. Cragle, Director Center for Epidemiologic Res ear c h Oak Ridge Institute of Science and Educat i on P.O. Box 117 Oak Ridge, TN R. Hornung National Institute for Occupational Safety and Heal t h 4676 Columbia Parkway, MS R-44 Cincinnati, OH W. E. Murray National Institute for Occupational Safety and Health 4676 Columbia Parkway, MS R-44 Cincinnati, OH E. Cardis, Head Programme on Radiation and Cancer International Agency for Research on Cancer 150, Cour Albert-Thomas Lyon Cedex 08 FRANCE No. of Copies ONS ITE Lucy Carpenter, Ph. D. Department of Pub1 ic Health and Primary Care Gibson Bldg. Radcl iffe Infirmary Oxford OX2 6HE UNITED KINGDOM Colin R. Muirhead, Ph.D. National Radiological Protection Board Chilton, Didcot, Oxon OX11 ORQ UNITED KINGDOM L. Salmon 8 Upton Close Abi ngdon, Oxonl4 2A1 UNITED KINGDOM G. Cowper 4 Cartier Circle Deep River, Ontario KOJlPO CANADA (19) Paci f i c Northwest Nat i onal Laboratory J. A. Buchanan K3-54 J. J. Fix P7-02 E. S. Gilbert (15) K3-54 PNNL Information Release (7) Di str. 1