Estimating Heterogeneous Exposure Effects in the Case-Crossover Design using BART.

Epidemiological approaches for examining human health responses to environmental exposures in observational studies often control for confounding by implementing clever matching schemes and using statistical methods based on conditional likelihood. Nonparametric regression models have surged in popularity in recent years as a tool for estimating individual-level heterogeneous effects, which provide a more detailed picture of the exposure-response relationship but can also be aggregated to obtain improved marginal estimates at the population level. In this work we incorporate Bayesian additive regression trees (BART) into the conditional logistic regression model to identify heterogeneous exposure effects in a case-crossover design. Conditional logistic BART (CL-BART) utilizes reversible jump Markov chain Monte Carlo to bypass the conditional conjugacy requirement of the original BART algorithm. Our work is motivated by the growing interest in identifying subpopulations more vulnerable to environmental exposures. We apply CL-BART to a study of the impact of heat waves on people with Alzheimer's disease in California and effect modification by other chronic conditions. Through this application, we also describe strategies to examine heterogeneous odds ratios through variable importance, partial dependence, and lower-dimensional summaries.