Primary Submission Category: Bayesian Causal Inference
Bayesian Nonparametrics for Heterogeneity in Treatment Effect.
Authors: Dafne Zorzetto, Falco Joannes Bargagli-Stoffi, Antonio Canale, Francesca Dominici,
Presenting Author: Dafne Zorzetto*
In causal inference studies, some observed characteristics play a key role in the identification of heterogeneity in the treatment effect. In this work, we propose a Bayesian nonparametric (BNP) approach that incorporates the information carried by the observed characteristics, for imputing the missing potential outcomes and data-driven discovering the heterogeneity in the causal effects. The literature for BNP framework applied to causal inference for heterogeneity in treatment effect is quite recent and has mostly focused on reworks of Bayesian Additive Regression Tree (BART) (Chipman et al., 2010), — as the works of Hill (2011) and Hahn et al. (2020) — and Dependent Dirichlet Process (DDP) (MacEachern, 2000; Quintana et al., 2020) mixture models — e.g., the works of Roy et al. (2018) and Oganisian et al. (2020). Exploiting the flexibility of the DDP, we propose a Dependent Probit Stick-breaking Process (Rodriguez and Dunson, 2011) mixture model to retrieve the conditional marginal potential outcome distributions, that allow us to: (i) estimate the individual treatment effects; (ii) identify the subgroups defined by similar conditional treatment effects, and (iii) characterize the heterogeneity in the effects in a precise and interpretable manner. We illustrate the performance of the method through simulations. We apply our method to assess the causal effect heterogeneity of long-term fine exposure to PM2.5 on mortality.