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

In epidemiologic studies, association estimates of an exposure with disease outcomes are often biased when the uncertainties of exposure are ignored. Consequently, corresponding confidence intervals (CIs) will not have correct coverage. This issue is particularly problematic when exposures must be reconstructed from physical measurements, for example, for environmental or occupational radiation doses that were received by a study population for which radiation doses cannot be measured directly. To incorporate complex uncertainties in reconstructed exposures, the two-dimensional Monte Carlo (2DMC) dose estimation method has been proposed and used in various dose reconstruction efforts. The 2DMC method generates multiple exposure realizations from dosimetry models that incorporate various sources of errors to reflect the uncertainty of the dose distribution as well as the uncertainties in individual doses in the exposed population. Traditional measurement-error model approaches, typically based on using mean doses in the dose-exposure analysis, do not fully account exposure uncertainties. A recently developed statistical approach that overcomes many of these limitations by analyzing multiple exposure realizations in relation to disease risk is Bayesian model averaging (BMA). The analytic advantage of the BMA is its ability to better accommodate complex exposure uncertainty in the risk estimation, but a practical. Drawback is its significant computational complexity. In this present paper, we propose a novel frequentist model averaging (FMA) approach which has all the analytical advantages of the BMA method but is much simpler to implement and computationally faster. We show in simulations that, like BMA, FMA yields 95% confidence intervals for association parameters that close to 95% coverage rate. In simulations, the FMA has shorter length of CIs than those of another frequentist approach, the corrected information matrix (CIM) method. We illustrate the similarities in performance of BMA and FMA from a study of exposures from radioactive fallout in Kazakhstan.