Methods for epidemiologic analyses of multiple exposures: A review and comparative study of maximum‐likelihood, preliminary‐testing, and empirical‐bayes regression

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Abstract
Many epidemiologic investigations are designed to study the effects of multiple exposures. Most of these studies are analysed either by fitting a risk‐regression model with all exposures forced in the model, or by using a preliminary‐testing algorithm, such as stepwise regression, to produce a smaller model. Research indicates that hierarchical modelling methods can outperform these conventional approaches. I here review these methods and compare two hierarchical methods, empirical‐Bayes regression and a variant I call ‘semi‐Bayes’ regression, to full‐model maximum likelihood and to model reduction by preliminary testing. I then present a simulation study of logistic‐regression analysis of weak exposure effects to illustrate the type of accuracy gains one may expect from hierarchical methods. Finally, I compare the performance of the methods in a problem of predicting neonatal mortality rates. Based on the literature to date, I suggest that hierarchical methods should become part of the standard approaches to multiple‐exposure studies.

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