Hierarchical regression for epidemiologic analyses of multiple exposures.

Many epidemiologic investigations are designed to study the effects of multiple exposures. Most of these studies are analyzed 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 modeling methods can outperform these conventional approaches. These methods are reviewed and compared to two hierarchical methods, empirical-Bayes regression and a variant here called "semi-Bayes" regression, to full-model maximum likelihood and to model reduction by preliminary testing. The performance of the methods in a problem of predicting neonatal-mortality rates are compared. Based on the literature to date, it is suggested that hierarchical methods should become part of the standard approaches to multiple-exposure studies.