A semi‐bayes approach to the analysis of correlated multiple associations, with an application to an occupational cancer‐mortality study

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Abstract
Thomas et al.1 presented the application of empirical-Bayes methods to the problem of multiple inference in epidemiologic studies. One limitation of their approach, which they noted, was the need to assume exchangeable log relative-risk parameters, and independent relative-risk estimates. Numerical integration was also required. Here I generalize their approach to allow for non-exchangeable parameters and non-independent estimates. The resulting method is Bayesian in so far as some feature of the prior distribution are specified from prior information, but is empirical Bayes in so far as some explicit parameters in the prior distribution are estimated from the data. Estimation is based on approximations to the posterior distribution; this allows one to implement the approach with standard software packages for matrix algebra. The method is illustrated in an occupational mortality study of 84 exposure-cancer associations.

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