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Primary Submission Category: Bayesian Causal Inference

Bayesian Nonparametrics for Principal Stratification: an Application on Environmental Policies Effects on Health.

Authors: Falco J. Bargagli-Stoffi, Fabrizia Mealli, Francesca Dominici, Antonio Canale, Dafne Zorzetto,

Presenting Author: Falco J. Bargagli-Stoffi*

Regulatory actions have been enacted in the United States to diminish the levels of pollutants in the air and reduce the connected environmental risks for health. Indirect accountability studies -assessing the causal effect of exposure to higher levels of air pollution- and direct accountability studies -assessing the causal impact of interventions aimed at reducing the level of air pollution- have found solid evidence of health benefits. However, the existing literature lacks robust methods that consider two crucial points in health studies: evaluate heterogeneity in the health effects of air pollution regulations across different groups of individuals, and consider the joint relations between direct and indirect effects. In this work, we develop a novel approach combining Bayesian nonparametric (BNP) methods and Principal stratification (PS) framework to deal with post-treatment variables that are potentially affected by the treatment and also affecting the response. We introduce three major innovations: (i) we rely on BNP methodologies for the imputation of missing potential outcomes for the post-treatment and outcome variables; (ii) we introduce new conditional estimands; (iii) we propose a data-driven methodology to discover causal heterogeneity. We illustrate the performance of the method through simulations. In the application we discover and estimate the heterogeneous effects of US national air quality regulations on pollution levels and health outcomes.