Principal stratification provides a causal inference framework for investigating treatment effects in the presence of a post-treatment variable. Principal strata play a key role in characterizing the treatment effect by identifying groups of units with the same or similar values for the potential post-treatment variable at all treatment levels. The literature has focused mainly on binary post-treatment variables. Few papers considered continuous post-treatment variables. In the presence of a continuous post-treatment, a challenge is how to identify and characterize meaningful coarsening of the latent principal strata that lead to interpretable principal causal effects. This paper introduces the Confounders-Aware SHared atoms BAyesian mixture (CASBAH), a novel approach for principal stratification with binary treatment and continuous post-treatment variables. CASBAH leverages Bayesian nonparametric priors with an innovative hierarchical structure for the potential post-treatment outcomes that overcomes some of the limitations of previous works. Specifically, the novel features of our method allow for (i) identifying coarsened principal strata through a data-adaptive approach and (ii) providing a comprehensive quantification of the uncertainty surrounding stratum membership. Through Monte Carlo simulations, we show that the proposed methodology performs better than existing methods in characterizing the principal strata and estimating principal effects of the treatment. Finally, CASBAH is applied to a case study in which we estimate the causal effects of US national air quality regulations on pollution levels and health outcomes.

翻译：主分层为在存在后处理变量的情况下研究处理效应提供了一个因果推断框架。主分层通过识别在所有处理水平上潜在后处理变量具有相同或相似值的单元组，在刻画处理效应中起着关键作用。现有文献主要关注二元后处理变量，鲜有论文考虑连续后处理变量。在存在连续后处理变量的情况下，一个挑战是如何识别并刻画潜在主分层的有意义粗化，从而得到可解释的主因果效应。本文提出了混淆因子感知的共享原子贝叶斯混合模型（CASBAH），这是一种针对二元处理和连续后处理变量的主分层新方法。CASBAH利用贝叶斯非参数先验，为潜在后处理结果构建了创新的层次结构，克服了先前研究的一些局限性。具体而言，我们方法的新特性允许：（i）通过数据自适应方法识别粗化的主分层；（ii）对分层成员关系的不确定性进行全面量化。通过蒙特卡洛模拟，我们表明所提出的方法在刻画主分层和估计处理的主效应方面优于现有方法。最后，将CASBAH应用于一项案例研究，评估美国国家空气质量法规对污染水平和健康结果的因果效应。