A Bayesian Approach for Achieving Double Robustness in Treatment Effect Estimation

Oregon Convention Center 

Combining propensity and prognostic scores enhances the efficiency of matching methods in estimating average treatment effect in observational studies. This paper aims to provide a Bayesian approach of double score estimation as well as a theoretical support of the consistency of the Bayesian estimator. Specifically, we explore the performance of a semiparametric Bayesian model, utilizing Gaussian process priors and addressing potential model mis-specification. We derive asymptotic results to validate the consistency of Bayesian estimators as the sample size increases. Particularly noteworthy is the demonstrated superiority of double-score Bayesian estimators in estimating both the population and conditional average treatment effects. In the simulation study, we analyze the performance of these models under various scenarios with a finite sample size. The results generated by the MCMC algorithm indicate doubly robust estimation under specific conditions. We also apply our proposed single/double score model to a real-world dataset, yielding results that align with existing studies utilizing matching methods.

Bayesian Semiparametric

Gaussian Process

Propensity and Prognostic Scores Matching

Bayesian Casual Inference

Markov chain Monte Carlo

Heterogeneous Treatment Effect Estimation 

Section on Statistics in Epidemiology