Propensity score specification for optimal estimation of average treatment effect with binary response

Propensity score methods are commonly used in statistical analyses of observational data to reduce the impact of confounding bias in estimations of average treatment effect. While the propensity score is defined as the conditional probability of a subject being in the treatment group given that subject's covariates, the most precise estimation of average treatment effect results from specifying the propensity score as a function of true confounders and predictors only. This property has been demonstrated via simulation in multiple prior research articles. However, we have seen no theoretical explanation as to why this should be so. This paper provides that theoretical proof. Furthermore, this paper presents a method for performing the necessary variable selection by means of elastic net regression, and then estimating the propensity scores so as to obtain optimal estimates of average treatment effect. The proposed method is compared against two other recently introduced methods, outcome-adaptive lasso and covariate balancing propensity score. Extensive simulation analyses are employed to determine the circumstances under which each method appears most effective. We applied the proposed methods to examine the effect of pre-cardiac surgery coagulation indicator on mortality based on a linked dataset from a retrospective review of 1390 patient medical records at Jewish Hospital (Louisville, KY) with the Society of Thoracic Surgeons database.