Hierarchical regression in epidemiologic studies of multiple exposures, with an application to diet and breast cance

Hierarchical regression attempts to improve standard regression estimates by adding a second-stage "prior" regression to an ordinary model. In addition, this approach offers a solution to problems of multiple inference. Nevertheless, hierarchical regression techniques have seen limited epidemiologic application. Here I investigate the use of hierarchical regression in studies with multiple correlated continuous exposures. First I develop a two-stage regression model to analyze case-control data on diet and breast cancer. This regression yields semi-Bayes relative risk estimates for dietary items by using a second-stage model to pull estimates toward each other when they have similar levels of nutrients. Unlike classical Bayesian analysis, however, no use is made of previous studies on nutrient effects. Compared with results obtained with one-stage conditional maximum likelihood logistic regression, our hierarchical regression model gives more stable and plausible estimates. In particular, certain effects with implausible maximum-likelihood estimates have more reasonable semi-Bayes estimates. Next I present a simulation study of hierarchical regression based on the diet and breast cancer data. This simulation evaluates the second-stage model required to improve the conventional logistic estimates with hierarchical regression. Simulation results indicate that in general, the hierarchical estimator improves on the ordinary one-stage maximum likelihood estimator. More specifically, provided that any simplification of the second-stage model was conservative, the semi-Bayes estimates were better than ordinary maximum-likelihood estimates. Finally, I briefly discuss the diet and breast cancer study results. In this study, most dietary items high in fat, antioxidants, or fiber do not appear to be associated with premenopausal bilateral breast cancer risk. These findings suggest that genetic or hormonal factors may dominate variations in risk of this rare form of breast cancer.