Impact of uncertainties in exposure assessment on thyroid cancer risk among cleanup workers in Ukraine exposed due to the Chornobyl accident

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 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. Recently, there has been considerable attention paid to methods of dealing with shared errors, which are 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. The quasi-2DMC+BMA method performs well when a linear model is assumed, but poorly when a linear-quadratic model is assumed. FMA performs as well as quasi-2DMC+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. 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+BMA or FMA methods, particularly for the linear-quadratic model. The bias of predicted relative risk at a variety of doses is generally smallest for ERC, and largest for quasi-2DMC+BMA and FMA, 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 and comparison with the Bayesian 2-dimensional Monte Carlo method

For many cancer sites it is necessary to assess risks from low-dose exposures via extrapolation from groups exposed at moderate and high levels of dose. Measurement error can substantially alter the shape of this relationship and hence the derived population risk estimates. 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, much attention has been devoted to the issue of shared errors, common in many datasets, and particularly important in occupational settings. In this paper we test a Bayesian model averaging method, the so-called Bayesian two-dimensional Monte Carlo (2DMC) method, that has been fairly recently proposed against a very newly proposed 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. We also compared both methods against standard regression calibration and Monte Carlo maximum likelihood. The Bayesian 2DMC method performs poorly, with coverage probabilities both for the linear and quadratic dose coefficients that are under 5%, particularly when the magnitudes of classical and Berkson error are both moderate to large (20%-50%). The method also 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. By comparison the extended regression calibration method 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 Bayesian 2DMC and all other methods. The bias of the predicted relative risk at a variety of doses is generally smallest for extended regression calibration, and largest for the Bayesian 2DMC method (apart from unadjusted regression), with standard regression calibration and Monte Carlo maximum likelihood exhibiting bias in predicted relative risk generally somewhat intermediate between the other two methods.

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.