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Shared Dosimetry Error in Epidemiological Dose-Response Analyses

Radiation dose reconstruction systems for large-scale epidemiological studies are sophisticated both in providing estimates of dose and in representing dosimetry uncertainty. For example, a computer program was used by the Hanford Thyroid Disease Study to provide 100 realizations of possible dose to study participants. The variation in realizations reflected the range of possible dose for each cohort member consistent with the data on dose determinates in the cohort. Another example is the Mayak Worker Dosimetry System 2013 which estimates both external and internal exposures and provides multiple realizations of "possible" dose history to workers given dose determinants. This paper takes up the problem of dealing with complex dosimetry systems that provide multiple realizations of dose in an epidemiologic analysis. In this paper we derive expected scores and the information matrix for a model used widely in radiation epidemiology, namely the linear excess relative risk (ERR) model that allows for a linear dose response (risk in relation to radiation) and distinguishes between modifiers of background rates and of the excess risk due to exposure. We show that treating the mean dose for each individual (calculated by averaging over the realizations) as if it was true dose (ignoring both shared and unshared dosimetry errors) gives asymptotically unbiased estimates (i.e. the score has expectation zero) and valid tests of the null hypothesis that the ERR slope β is zero. Although the score is unbiased the information matrix (and hence the standard errors of the estimate of β) is biased for β≠0 when ignoring errors in dose estimates, and we show how to adjust the information matrix to remove this bias, using the multiple realizations of dose. Use of these methods for several studies, including the Mayak Worker Cohort and the U.S. Atomic Veterans Study, is discussed.

epidemiological analysis↗

Correction of confidence intervals in excess relative risk models using Monte Carlo dosimetry systems with shared errors

Introduction: Measurement errors are ubiquitous in epidemiological studies, especially for doses arising from environmental and occupational exposures, which are difficult to assess. Correction methods for independent measurement errors, have been comprehensively described elsewhere, including regression calibration, simulation extrapolation (SIMEX), etc. However, when exposure estimates are constructed using complicated physical and biological models, uncertainties in the dosimetry system can become very complex. In such systems, uncertainties in some parameters may affect a large group of study participants simultaneously, and hence are “shared” as opposed to independent dosimetric uncertainties. Representing the structure of the uncertainty in the dosimetry by providing multiple realizations of possible dose has been described for several studies. The goal of this paper is to implement, and explore the properties of, a generalized estimating equation-based approach to shared uncertainties based on principles described in an earlier paper. Methods: The effects of shared and unshared dosimetry error on parameter estimates and confidence intervals in a generalized excess relative risk model are examined. A post-hoc correction method is implemented that constructs corrected confidence intervals based on an underlying variance structure described in an earlier paper. In this correction method it is assumed that the estimated slope parameter in a linear excess relative risk model is distributed as a mixture of normal and lognormal components. A simulation study of the behavior of this correction was developed based on multiple realizations provided by the Monte Carlo dosimetry system used for the plutonium exposures in the Mayak Worker Cohort and a risk model with close similarity to that used in analyses of lung cancer data in that cohort. Results: In the simulation study we found that shared dose errors severely degraded the coverage probabilities of confidence limits for the slope parameter in the linear excess relative risk model relating uncertain exposure to lung cancer risk. Using our correction method to adjust the confidence intervals provided much improved coverage probabilities for this parameter. A smaller amount of degradation in confidence interval coverage for other parameters (e.g. those in the baseline and dose modification terms) was noted, and the proposed correction method also improved coverage for these parameters as well. Discussion: Compared to other recently described methods our proposed correction method relies on relatively familiar software to fit dose response models. The basic modeling philosophy described here first uses existing Poisson regression methods to estimate parameters in the excess relative risk model; in this first stage mean dose (computed from the multiple realizations) is used as the independent variable in the regression. Once the model is fit we then correct (widen) the standard errors for all parameters using the proposed correction method. The simulation studies indicate that the methods described here are an important contribution to the available tools for dealing with shared measurement errors in complex risk analysis.

61 RADIATION PROTECTION AND DOSIMETRY↗

UNCERTAINTY ANALYSIS FOR THE TECHA RIVER DOSIMETRY SYSTEM

Uncertainties in the doses estimated for the members of the Techa River Cohort (TRC) are being estimated with a two-dimensional Monte Carlo approach. In order to provide more accurate and precise estimates of individual dose (and thus more precise estimates of radiation risk) for the members of the TRC, a new dosimetric calculation system, the Techa River Dosimetry System-2009 (TRDS-2009) has been prepared. The deterministic version of the improved dosimetry system TRDS-2009D was basically completed in April 2009. Recent developments in evaluation of dose-response models in light of uncertain dose have highlighted the importance of different types of uncertainties in the development of individual dose estimates. These include uncertain parameters that may be either shared (common to some or all individuals) or unshared (a unique value for each person whose dose is to be estimated) within the dosimetric cohort. The nature of the type of uncertainty may be aleatory (random variability of true values due to stochastic processes) or epistemic (due to lack of complete knowledge about a unique quantity). Finally, there is a need to identify whether the structure of the errors is either related to measurement (the estimate differs from the true value by an error that is stochastically independent of the true value; frequently called classical uncertainty) or related to grouping (the true value varies from the estimate by an error that is random and is independent of the estimate; frequently called Berkson uncertainty). An approach has been developed that identifies the nature of the various input parameters and calculational methods incorporated in the Techa River Dosimetry System (based on the TRDS-2009D implementation), and a stochastic calculation model has been prepared to estimate the uncertainties in the dose estimates. This article reviews the concepts of uncertainty analysis, the equations, and input parameters, and then identifies the authors’ interpretations of their general nature. It presents the approach selected so that the stochastic, Monte-Carlo, implementation of the dosimetry system - TRDS-2009MC - provides useful information regarding the uncertainties of the doses.

uncertainty analysis, radiation dosimetry, Techa R↗