Simulation Study of Hierarchical Regression

Hierarchical regression - which attempts to improve standard regression estimates by adding a second-stage 'prior' regression to an ordinary model - provides a practical approach to evaluating multiple exposures. We present here a simulation study of logistic regression in which we compare hierarchical regression fitted by a two-stage procedure to ordinary maximum likelihood. The simulations were based on case-control data on diet and breast cancer, where the hierarchical model uses a second-stage regression to pull conventional dietary-item estimates toward each other when they have similar levels of food constituents. Our results indicate that hierarchical modelling of continuous covariates offers worthwhile improvement over ordinary maximum-likelihood, provided one does not underspecify the second-stage standard deviations.