Bayesian nonparametric trees for principal causal effects.

Principal stratification analysis evaluates how causal effects of a treatment on a primary outcome vary across strata of units defined by their treatment effect on some intermediate quantity. This endeavor is substantially challenged when the intermediate variable is continuously scaled and there are infinitely many basic principal strata. We employ a Bayesian nonparametric approach to flexibly evaluate treatment effects across flexibly modeled principal strata. The approach uses Bayesian Causal Forests (BCF) to simultaneously specify 2 Bayesian Additive Regression Tree models; one for the principal stratum membership and one for the outcome, conditional on principal strata. We show how the capability of BCF for capturing treatment effect heterogeneity is particularly relevant for assessing how treatment effects vary across the surface defined by continuously scaled principal strata, in addition to other benefits relating to targeted selection and regularization-induced confounding. The capabilities of the proposed approach are illustrated with a simulation study, and the methodology is deployed to investigate how causal effects of power plant emissions control technologies on ambient particulate pollution vary as a function of the technologies' impact on sulfur dioxide emissions.