The New England Journal of Statistics in Data Science

Analyzing health effects associated with exposure to environmental chemical mixtures is a challenging problem in epidemiology, toxicology, and exposure science. In particular, when there are a large number of chemicals under consideration it is difficult to estimate the interactive effects without incorporating reasonable prior information. Based on substantive considerations, researchers believe that true interactions between chemicals need to incorporate their corresponding main effects. In this paper, we use this prior knowledge through a shrinkage prior that a priori assumes an interaction term can only occur when the corresponding main effects exist. Our initial development is for logistic regression with linear chemical effects. We extend this formulation to include non-linear exposure effects and to account for exposure subject to detection limit. We develop an MCMC algorithm using a shrinkage prior that shrinks the interaction terms closer to zero as the main effects get closer to zero. We examine the performance of our methodology through simulation studies and illustrate an analysis of chemical interactions in a case-control study in cancer.