Bayesian Nonparametrics for Principal Stratification with Continuous Post-Treatment Variables
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连续处理后变量主层分析的贝叶斯非参数方法
- 研究问题
- 二元处理伴随连续处理后变量时，如何将不可观测的主层划分为可解释的粗化群体，并量化层成员身份与主层效应的不确定性？
- 方法与思路
- 作者提出 CASBAH，通过具有共享原子层级结构的贝叶斯非参数混合模型描述潜在处理后结果，形成数据自适应的粗化主层。
- 材料陈述的贡献
- 摘要称方法可自适应识别粗化主层并量化成员不确定性，模拟中主层刻画和效应估计优于既有方法，并应用于美国空气质量监管。
- 阅读关注点
- 核对连续潜在处理后变量的联合建模与识别限制、粗化规则和主层效应定义，以及先验选择、分类不确定性与比较设计。
- 阅读边界
- 这是 arXiv 预印本，同行评审和期刊接收均未核实；摘要未完整说明因果识别假设，数据自适应分层也不意味着潜在主层可直接观测。
原文摘要
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.