Hierarchical Regression Analysis Applied to a Study of Multiple Dietary Exposures and Breast Cancer

Hierarchical regression attempts to improve standard regression estimates by adding a second-stage "prior" regression to an ordinary model. Here, we use hierarchical regression 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 the corresponding variables 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.