Covariate Balance in a Bayesian Propensity Score Analysis of Beta Blocker Therapy in Heart Failure Patients

Regression adjustment for the propensity score is a statistical method that reduces confoundingfrom measured variables in observational data. A Bayesian propensity score analysis extends thisidea by using simultaneous estimation of the propensity scores and the treatment effect. In thisarticle, we conduct an empirical investigation of the performance of Bayesian propensity scores inthe context of an observational study of the effectiveness of beta-blocker therapy in heart failurepatients. We study the balancing properties of the estimated propensity scores. TraditionalFrequentist propensity scores focus attention on balancing covariates that are strongly associatedwith treatment. In contrast, we demonstrate that Bayesian propensity scores can be used tobalance the association between covariates and the outcome. This balancing property has the effectof reducing confounding bias because it reduces the degree to which covariates are outcome riskfactors.