Principal stratification provides a causal inference framework that allows adjustment for confounded post-treatment variables when comparing treatments. Although the literature has focused mainly on binary post-treatment variables, there is a growing interest in principal stratification involving continuous post-treatment variables. However, characterizing the latent principal strata with a continuous post-treatment presents a significant challenge, which is further complicated in observational studies where the treatment is not randomized. In this paper, we introduce the Confounders-Aware SHared atoms BAyesian mixture (CASBAH), a novel approach for principal stratification with continuous post-treatment variables that can be directly applied to observational studies. CASBAH leverages a dependent Dirichlet process, utilizing shared atoms across treatment levels, to effectively control for measured confounders and facilitate information sharing between treatment groups in the identification of principal strata membership. CASBAH also offers a comprehensive quantification of uncertainty surrounding the membership of the principal strata. Through Monte Carlo simulations, we show that the proposed methodology has excellent performance in characterizing the latent principal strata and estimating the effects of treatment on post-treatment variables and outcomes. 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：主分层提供了一个因果推断框架，允许在比较处理效应时对混杂的后处理变量进行调整。尽管现有文献主要关注二元后处理变量，但涉及连续后处理变量的主分层方法正受到日益增长的关注。然而，当后处理变量为连续型时，潜在主分层的表征面临重大挑战，这一问题在治疗非随机分配的观察性研究中会进一步复杂化。本文提出一种面向混杂因素的共享原子贝叶斯混合模型（CASBAH），这是一种可直接应用于观察性研究的连续后处理变量主分层新方法。CASBAH利用依赖型狄利克雷过程，通过跨处理水平的共享原子结构，有效控制已测量的混杂因素，并促进处理组间在主分层归属识别中的信息共享。该方法还能对主分层归属的不确定性进行全面量化。通过蒙特卡洛模拟，我们证明所提方法在表征潜在主分层、估计处理对后处理变量及结果变量的效应方面具有优异性能。最后，我们将CASBAH应用于案例研究，评估美国国家空气质量法规对污染水平与健康结果的因果效应。