Propensity scores based methods for estimating average treatment effect and average treatment effect among treated: A comparative study.

Propensity score based statistical methods, such as matching, regression, stratification, inverse probability weighting (IPW), and doubly robust (DR) estimating equations, have become popular in estimating average treatment effect (ATE) and average treatment effect among treated (ATT) in observational studies. Propensity score is the conditional probability receiving a treatment assignment with given covariates, and propensity score is usually estimated by logistic regression. However, a misspecification of the propensity score model may result in biased estimates for ATT and ATE. As an alternative, the generalized boosting method (GBM) has been proposed to estimate the propensity score. GBM uses regression trees as weak predictors and captures nonlinear and interactive effects of the covariate. For GBM-based propensity score, only IPW methods have been investigated in the literature. In this article, we provide a comparative study of the commonly used propensity score based methods for estimating ATT and ATE, and examine their performances when propensity score is estimated by logistic regression and GBM, respectively. Extensive simulation results indicate that the estimators for ATE and ATT may vary greatly due to different methods. We concluded that (i) regression may not be suitable for estimating ATE and ATT regardless of the estimation method of propensity score; (ii) IPW and stratification usually provide reliable estimates of ATT when propensity score model is correctly specified; (iii) the estimators of ATE based on stratification, IPW, and DR are close to the underlying true value of ATE when propensity score is correctly specified by logistic regression or estimated using GBM.