Simulation–extrapolation for bias correction with exposure uncertainty in radiation risk analysis utilizing grouped data

A Historical Survey of Key Epidemiological Studies of Ionizing Radiation Exposure

In this article we review the history of key epidemiological studies of populations exposed to ionizing radiation. We highlight historical and recent findings regarding radiation-associated risks for incidence and mortality of cancer and non-cancer outcomes with emphasis on study design and methods of exposure assessment and dose estimation along with brief consideration of sources of bias for a few of the more important studies. We examine the findings from the epidemiological studies of the Japanese atomic bomb survivors, persons exposed to radiation for diagnostic or therapeutic purposes, those exposed to environmental sources including Chornobyl and other reactor accidents, and occupationally exposed cohorts. We also summarize results of pooled studies. These summaries are necessarily brief, but we provide references to more detailed information. We discuss possible future directions of study, to include assessment of susceptible populations, and possible new populations, data sources, study designs and methods of analysis.

Recommendations on statistical approaches to account for dose uncertainties in radiation epidemiologic risk models

PURPOSE

Epidemiological studies of stochastic radiation health effects such as cancer, meant to estimate risks of the adverse effects as a function of radiation dose, depend largely on estimates of the radiation doses received by the exposed group under study. Those estimates are based on dosimetry that always has uncertainty, which often can be quite substantial. Studies that do not incorporate statistical methods to correct for dosimetric uncertainty may produce biased estimates of risk and incorrect confidence bounds on those estimates. This paper reviews commonly used statistical methods to correct radiation risk regressions for dosimetric uncertainty, with emphasis on some newer methods. We begin by describing the types of dose uncertainty that may occur, including those in which an uncertain value is shared by part or all of a cohort, and then demonstrate how these sources of uncertainty arise in radiation dosimetry. We briefly describe the effects of different types of dosimetric uncertainty on risk estimates, followed by a description of each method of adjusting for the uncertainty.

CONCLUSIONS

Each of the method has strengths and weaknesses, and some methods have limited applicability. We describe the types of uncertainty to which each method can be applied and its pros and cons. Finally, we provide summary recommendations and touch briefly on suggestions for further research.

A generalisation of the method of regression calibration and comparison with Bayesian and frequentist model averaging methods

For many cancer sites low-dose risks are not known and must be extrapolated from those observed in groups exposed at much higher levels of dose. Measurement error can substantially alter the dose-response shape and hence the extrapolated risk. Even in studies with direct measurement of low-dose exposures measurement error could be substantial in relation to the size of the dose estimates and thereby distort population risk estimates. Recently, there has been considerable attention paid to methods of dealing with shared errors, which are common in many datasets, and particularly important in occupational and environmental settings. In this paper we test Bayesian model averaging (BMA) and frequentist model averaging (FMA) methods, the first of these similar to the so-called Bayesian two-dimensional Monte Carlo (2DMC) method, and both fairly recently proposed, against a very newly proposed modification of the regression calibration method, the extended regression calibration (ERC) method, which is particularly suited to studies in which there is a substantial amount of shared error, and in which there may also be curvature in the true dose response. The quasi-2DMC with BMA method performs well when a linear model is assumed, but very poorly when a linear-quadratic model is assumed, with coverage probabilities both for the linear and quadratic dose coefficients that are under 5% when the magnitude of shared Berkson error is large (50%). For the linear model the bias is generally under 10%. However, using a linear-quadratic model it produces substantially biased (by a factor of 10) estimates of both the linear and quadratic coefficients, with the linear coefficient overestimated and the quadratic coefficient underestimated. FMA performs as well as quasi-2DMC with BMA when a linear model is assumed, and generally much better with a linear-quadratic model, although the coverage probability for the quadratic coefficient is uniformly too high. However both linear and quadratic coefficients have pronounced upward bias, particularly when Berkson error is large. By comparison ERC yields coverage probabilities that are too low when shared and unshared Berkson errors are both large (50%), although otherwise it performs well, and coverage is generally better than the quasi-2DMC with BMA or FMA methods, particularly for the linear-quadratic model. The bias of the predicted relative risk at a variety of doses is generally smallest for ERC, and largest for the quasi-2DMC with BMA and FMA methods (apart from unadjusted regression), with standard regression calibration and Monte Carlo maximum likelihood exhibiting bias in predicted relative risk generally somewhat intermediate between ERC and the other two methods. In general ERC performs best in the scenarios presented, and should be the method of choice in situations where there may be substantial shared error, or suspected curvature in the dose response.

A generalisation of the method of regression calibration

There is direct evidence of risks at moderate and high levels of radiation dose for highly radiogenic cancers such as leukaemia and thyroid cancer. For many cancer sites, however, it is necessary to assess risks via extrapolation from groups exposed at moderate and high levels of dose, about which there are substantial uncertainties. Crucial to the resolution of this area of uncertainty is the modelling of the dose-response relationship and the importance of both systematic and random dosimetric errors for analyses in the various exposed groups. It is well recognised that measurement error can alter substantially the shape of this relationship and hence the derived population risk estimates. Particular attention has been devoted to the issue of shared errors, common in many datasets, and particularly important in occupational settings. We propose a modification of the regression calibration method which is particularly suited to studies in which there is a substantial amount of shared error, and in which there may also be curvature in the true dose response. This method can be used in settings where there is a mixture of Berkson and classical error. In fits to synthetic datasets in which there is substantial upward curvature in the true dose response, and varying (and sometimes substantial) amounts of classical and Berkson error, we show that the coverage probabilities of all methods for the linear coefficient [Formula: see text] are near the desired level, irrespective of the magnitudes of assumed Berkson and classical error, whether shared or unshared. However, the coverage probabilities for the quadratic coefficient [Formula: see text] are generally too low for the unadjusted and regression calibration methods, particularly for larger magnitudes of the Berkson error, whether this is shared or unshared. In contrast Monte Carlo maximum likelihood yields coverage probabilities for [Formula: see text] that are uniformly too high. The extended regression calibration method yields coverage probabilities that are too low when shared and unshared Berkson errors are both large, although otherwise it performs well, and coverage is generally better than these other three methods. A notable feature is that for all methods apart from extended regression calibration the estimates of the quadratic coefficient [Formula: see text] are substantially upwardly biased.

A generalisation of the method of regression calibration

There is direct evidence of risks at moderate and high levels of radiation dose for highly radiogenic cancers such as leukaemia and thyroid cancer. For many cancer sites, however, it is necessary to assess risks via extrapolation from groups exposed at moderate and high levels of dose, about which there are substantial uncertainties. Crucial to the resolution of this area of uncertainty is the modelling of the dose-response relationship and the importance of both systematic and random dosimetric errors for analyses in the various exposed groups. It is well recognised that measurement error can alter substantially the shape of this relationship and hence the derived population risk estimates. Particular attention has been devoted to the issue of shared errors, common in many datasets, and particularly important in occupational settings. We propose a modification of the regression calibration method which is particularly suited to studies in which there is a substantial amount of shared error, and in which there may also be curvature in the true dose response. This method can be used in settings where there is a mixture of Berkson and classical error. In fits to synthetic datasets in which there is substantial upward curvature in the true dose response, and varying (and sometimes substantial) amounts of classical and Berkson error, we show that the coverage probabilities of all methods for the linear coefficient \(\alpha\) are near the desired level, irrespective of the magnitudes of assumed Berkson and classical error, whether shared or unshared. However, the coverage probabilities for the quadratic coefficient \(\beta\) are generally too low for the unadjusted and regression calibration methods, particularly for larger magnitudes of the Berkson error, whether this is shared or unshared. In contrast Monte Carlo maximum likelihood yields coverage probabilities for \(\beta\) that are uniformly too high. The extended regression calibration method yields coverage probabilities that are too low when shared and unshared Berkson errors are both large, although otherwise it performs well, and coverage is generally better than these other three methods. A notable feature is that for all methods apart from extended regression calibration the estimates of the quadratic coefficient \(\beta\) are substantially upwardly biased.

Simulation extrapolation method for measurement error: A review

Measurement error is pervasive in statistics due to the non-availability of authentic data. The reasons for measurement error mainly relate to cost, convenience, and human error. Measurement error can result in non-negligible bias due to attenuated estimates, reduced power of statistical tests, and lower coverage probabilities of the coefficient estimators in a regression model. Several methods have been proposed to correct for measurement error, all of which can be grouped into two broad categories based on the underlying model-functional and structural. Functional models provide flexibility and robustness to estimators by placing minimal or no assumptions on the distribution of the mismeasured covariate or by treating them as a fixed entity, as opposed to a structural model which treats the underlying mismeasured covariates as random with a specified structure. The simulation extrapolation method is one method that is used for the partial correction of measurement error in both structural and functional models. Reviews of measurement error correction techniques are available in the literature. However, none of the previously conducted reviews has exclusively focused on simulation extrapolation and its application in continuous measurement error models, despite its widespread use and ease of application. We attempt to close this gap in the literature by highlighting its development over the past two and a half decades.

Lifetime Mortality Risk from Cancer and Circulatory Disease Predicted from the Japanese Atomic Bomb Survivor Life Span Study Data Taking Account of Dose Measurement Error

Dosimetric measurement error is known to potentially bias the magnitude of the dose response, and can also affect the shape of dose response. In this report, generalized relative and absolute rate models are fitted to the latest Japanese atomic bomb survivor solid cancer, leukemia and circulatory disease mortality data (followed from 1950 through 2003), with the latest (DS02R1) dosimetry, using Bayesian techniques to adjust for errors in dose estimates and assessing other model uncertainties. Linear-quadratic models are fitted and used to assess lifetime mortality risks for contemporary UK, USA, French, Russian, Japanese and Chinese populations. For a test dose of 0.1 Gy absorbed dose weighted by neutron relative biological effectiveness, solid cancer, leukemia and circulatory disease mortality risks for a UK population using a generalized linear-quadratic relative rate model were estimated to be 3.88% Gy-1 [95% Bayesian credible interval (BCI): 1.17, 6.97], 0.35% Gy-1 (95% BCI: -0.03, 0.78) and 2.24% Gy-1 (95% BCI: -0.17, 13.76), respectively. Using a generalized absolute rate linear-quadratic model at 0.1 Gy, the lifetime risks for these three end points were estimated to be 3.56% Gy-1 (95% BCI: 0.54, 6.78), 0.41% Gy-1 (95% BCI: 0.01, 0.86) and 1.56% Gy-1 (95% BCI: -1.10, 7.21), respectively. There was substantial evidence of curvature for solid cancer (in particular, the group of solid cancers excluding lung, breast and stomach cancers) and leukemia, so that for solid cancer and leukemia, estimates of excess risk per unit dose were nearly doubled by increasing the dose from 0.01 to 1.0 Gy, with most of the increase occurring in the interval from 0.1 to 1.0 Gy. For circulatory disease, the dose-response curvature was inverse, so that risk per unit dose was nearly halved by going from 0.01 t o 1.0 Gy weighted absorbed dose, although there were substantial uncertainties. In general, there were higher radiation risks for females compared to males. This was true for solid cancer and circulatory disease overall, as well as for lung, breast, stomach and the group of other solid cancers, and was the case whether relative or absolute rate projection models were employed; however, for leukemia this pattern was reversed. Risk estimates varied somewhat between populations, with lower cancer risks in aggregate for China and Russia, but higher circulatory disease risks for Russia, particularly using the relative rate model. There was more pronounced variation for certain cancer sites and certain types of projection models, so that breast cancer risk was markedly lower in China and Japan using a relative rate model, but the opposite was the case for stomach cancer. There was less variation between countries using the absolute rate models for stomach cancer and breast cancer, but this was not the case for lung cancer and the group of other solid cancers, or for circulatory disease.

Effect of Heterogeneity in Background Incidence on Inference about the Solid-Cancer Radiation Dose Response in Atomic Bomb Survivors

A recent analysis of solid cancer incidence in the Life Span Study of atomic bomb survivors (Hiroshima and Nagasaki, Japan) found evidence of a nonlinear, upwardly curving radiation dose response among males but not among females. Further analysis of this new and unexpected finding was necessary. We used two approaches to investigate this finding. In one approach, we excluded individual cancer sites or groups of sites from all solid cancers. In the other approach, we used joint analysis to allow for heterogeneity in background-rate parameters across groups of cancers with dissimilar trends in background rates. Exclusion of a few sites led to the disappearance of curvature among males in the remaining collection of solid cancers; some of these influential sites have unique features in their background age-specific incidence that are not captured by a background-rate model fit to all solid cancers combined. Exclusion of a few sites also led to an appearance of curvature among females. Misspecification of background rates can cause bias in inference about the shape of the dose response, so heterogeneity of background rates might explain at least part of the all solid cancer dose-response difference in curvature between males and females. We conclude that analysis based on all solid cancers as a single outcome is not the optimal method to assess radiation risk for solid cancer in the Life Span Study; joint analysis with suitable choices of cancer groups might be preferable by allowing for background-rate heterogeneity across sites while providing greater power to assess radiation risk than analyses of individual sites.