  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.
