Frequentist model averaging for analysis of dose-response in epidemiologic studies with complex exposure uncertainty

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.