HIERARCHICAL REGRESSION-ANALYSIS APPLIED TO A STUDY OF MULTIPLE DIETARY EXPOSURES AND BREAST-CANCER

Hierarchical regression attempts to improve standard regression estima tes 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 ri sk estimates for dietary items by using a second-stage model to pull e stimates reward each other when the corresponding variables have simil ar levels of nutrients. Unlike classical Bayesian analysis, however, n o use is made of previous studies on nutrient effects. Compared with r esults obtained with one-stage conditional maximum-likelihood logistic regression, our hierarchical regression model gives more stable and p lausible estimates. In particular, certain effects with implausible ma ximum likelihood estimates have more reasonable semi-Bayes estimates.