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：主层分析为存在后处理变量时的处理效应研究提供了因果推断框架。主层通过识别在所有处理水平下潜在后处理变量取值相同或相似的单元组，在刻画处理效应中发挥关键作用。现有文献主要关注二值后处理变量，仅少数研究涉及连续后处理变量。当存在连续后处理变量时，如何识别并表征能够产生可解释主因果效应的潜在主层的有意义粗化是一个挑战。本文提出了混淆因子感知共享原子贝叶斯混合模型（CASBAH），这是一种针对二值处理变量与连续后处理变量的新型主层分析方法。CASBAH通过创新分层结构对潜在后处理结果施加贝叶斯非参数先验，克服了先前研究的部分局限性。具体而言，我们方法的创新特性允许：(i)通过数据自适应方法识别粗化主层，(ii)全面量化层成员归属的不确定性。通过蒙特卡洛模拟，我们证明所提方法在刻画主层和估计处理主效应方面优于现有方法。最后，我们将CASBAH应用于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的案例研究。