WITHDRAWN: Causal BART Mixture Model for Estimating Heterogeneous Treatment Effects

• Activity Number: 290 - Advanced Bayesian Topics (Part 3)
• Type: Contributed
• Date/Time: Wednesday, August 11, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Omar Chavez and Sinead Williamson and Michael J. Daniels
• Companies: University of Texas at Austin, Department of Statistics and Data Sciences and University of Texas at Austin, Department of Statistics and Data Sciences and University of Florida
• Keywords: Causal Inference; Transformed Response; Bayesian Additive Regression Trees; BART; Heterogeneous Effects; Treatment Effects

Abstract

We propose a flexible Bayesian semi-parametric approach for estimating heterogeneous treatment effects from observational data. Specifically, we model the Transformed Response Variable (TRV) proposed by Dudik et al. (2011) and Beygelzimer and Langford (2009) as the conditional average treatment effect (CATE) with Bayesian Additive Regression Trees (BART) plus a residual which is a mixture of two Gaussian distributions resulting from the response under treatment and response under control. We therefore flexibly adapt to effect heterogeneity by simultaneously accounting for the response independent of treatment status. Importantly, our method allows us to estimate the treatment effect directly without the need to model two response surfaces for the groups assigned to treatment and control. Moreover, due to the improved model specification in our method, we are able to substantially reduce the error in the CATE relative to competing methods using the TRV while simultaneously reducing the variance of our estimators.