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High-dimensional data can be useful for causal inference by providing manyconfounders that may bolster the plausibility of the ignorability assumption.Propensity score methods are powerful tools for causal inference, are popularin health care research, and are particularly useful for high-dimensional data.Recent interest has surrounded a Bayesian formulation of these methods in orderto flexibly estimate propensity scores and summarize posterior quantities whileincorporating variance from the (potentially high-dimensional) treatment model.We discuss methods for Bayesian propensity score analysis of binary treatments,focusing on modern methods for high-dimensional Bayesian regression and thepropagation of uncertainty from the treatment regression. We introduce a noveland simple estimator for the average treatment effect that capitalizes onconjugancy of the beta and binomial distributions. Through simulations, we showthe utility of horseshoe priors and Bayesian additive regression trees pairedwith our new estimator, while demonstrating the importance of includingvariance from the treatment and outcome models. Cardiac stent data with almost500 confounders and 9000 patients illustrate approaches and compare amongexisting frequentist alternatives.

Bayesian Propensity Scores for High-Dimensional Causal Inference: A Comparison of Drug-Eluting to Bare-Metal Coronary Stents