Shared Dosimetry Error in Epidemiological Dose-Response Analyses

<div><p>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. The use of these methods in the context of several studies including, the Mayak Worker Cohort, and the U.S. Atomic Veterans Study, is discussed.</p></div

Noncentrality and Power.

<p>Points indicate effects assuming no sharing of errors, dashes include the shared error effects. For reference the dotted lines show noncentrality parameters and power assuming that true dose rather than estimated dose was available for the study. Results are particular to the AVS data described herein.</p

Effect of accounting for shared dosimetry errors on the length of standard errors in the high-sided calculations performed for the AVS study.

<p>The two dashed lines are based on ordinary least squares calculations and show the upper and lower bounds of a "naïve" confidence interval for slope parameter <i>b</i> (normalized by residual standard deviation, <i>σ</i>) ignoring inhomogeneous or shared errors. The solid lines show the effect of accounting for both inhomogeneous and shared error in expanding the confidence limits. The dot-dash lines between the dashed and solid lines shows the effect of adjusting for inhomogeneous errors but where there are no shared errors (off diagonals of matrix K are zero).</p

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

<div><p>In epidemiological studies, exposures of interest are often measured with uncertainties, which may be independent or correlated. Independent errors can often be characterized relatively easily while correlated measurement errors have shared and hierarchical components that complicate the description of their structure. For some important studies, Monte Carlo dosimetry systems that provide multiple realizations of exposure estimates have been used to represent such complex error structures. While the effects of independent measurement errors on parameter estimation and methods to correct these effects have been studied comprehensively in the epidemiological literature, the literature on the effects of correlated errors, and associated correction methods is much more sparse. In this paper, we implement a novel method that calculates corrected confidence intervals based on the approximate asymptotic distribution of parameter estimates in linear excess relative risk (ERR) models. These models are widely used in survival analysis, particularly in radiation epidemiology. Specifically, for the dose effect estimate of interest (increase in relative risk per unit dose), a mixture distribution consisting of a normal and a lognormal component is applied. This choice of asymptotic approximation guarantees that corrected confidence intervals will always be bounded, a result which does not hold under a normal approximation. A simulation study was conducted to evaluate the proposed method in survival analysis using a realistic ERR model. We used both simulated Monte Carlo dosimetry systems (MCDS) and actual dose histories from the Mayak Worker Dosimetry System 2013, a MCDS for plutonium exposures in the Mayak Worker Cohort. Results show our proposed methods provide much improved coverage probabilities for the dose effect parameter, and noticeable improvements for other model parameters.</p></div

Description of variables in the hazard model.

<p>Description of variables in the hazard model.</p

Comparison of naïve CI, score-type CI and <i>bL</i>+<i>N</i> CI.

<p>Confidence intervals (CI’s) in one simulation with the moderate model with MWDS-2013 are shown. In the plot, the <i>p</i>-values of <i>b</i>₁ at different points are evaluated using the distributions underlying each method and transformed into <i>χ</i>² test statistics.</p

Simulation settings for parameters other than <i>a</i>₀ and <i>b</i>₁.

<p>Simulation settings for parameters other than <i>a</i>₀ and <i>b</i>₁.</p

Confidence interval coverage of different methods for <i>b</i>₁ in moderate and strong model.

<p>Confidence interval coverage of different methods for <i>b</i>₁ in moderate and strong model.</p

Simulation settings for <i>a</i>₀ and <i>b</i>₁.

<p>Simulation settings for <i>a</i>₀ and <i>b</i>₁.</p

Confidence interval coverage for model parameters with MWDS-2013 in moderate and strong models.

<p>Confidence interval coverage for model parameters with MWDS-2013 in moderate and strong models.</p