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 two 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.

翻译：主分层分析评估了处理对主要结局的因果效应如何根据单位在某个中间量上的处理效应而定义的层间变化。当中间变量是连续尺度且存在无限多的基本主分层时，这一任务面临巨大挑战。我们采用贝叶斯非参数方法，灵活地评估跨过灵活建模的主分层的处理效应。该方法使用贝叶斯因果森林（BCF）同时指定两个贝叶斯加法回归树模型：一个用于主分层成员关系，另一个用于以主分层为条件的结果。我们展示了BCF捕捉处理效应异质性的能力如何特别适用于评估处理效应如何沿连续尺度主分层定义的表面变化，此外还有与目标选择和正则化诱导混淆相关的其他优势。通过模拟研究展示了所提方法的能力，并将该方法应用于研究电厂排放控制技术对环境颗粒物污染的因果效应如何随技术对二氧化硫排放的影响而变化。