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

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.