Efficiency Properties of Bias-Corrected Matching Estimators: The Impact of Differing Covariate Roles

Thomas M. Menino Convention & Exhibition Center 

Matching estimators are widely used to estimate the Average Treatment Effect on the Treated (ATT). However, their precision depends on the choice of covariates. In particular the role of prognostic covariates (Xp) is less well studied relative to confounders (Xc). In this study, we consider a setting where variables Xc satisfy the unconfoundedness assumption, while variables Xp provide additional prognostic information. We compare several designs including in which outcome relationships are modeled using : (1)Xc only, and (2)both Xc and Xp. Drawing on Hahn's (1998, 2004) semiparametric efficiency bounds, we study the restricted propensity score and demonstrate the potential efficiency gains of the second design. We further examine how a bias-corrected matching estimator performs in finite samples using these designs. This approach decouples assignment sufficiency from prediction sufficiency, allowing prognostic information to reduce variance without introducing propensity-score noise. Simulations confirm that bias correction is essential and that incorporating Xp leads to significant variance reduction. Finally we aim to illustrate this method through a tobacco initiation analysis.

Causal inference

Average Treatment Effect (ATT)

Matching

Semiparametric Efficiency

Bias correction

Prognostic covariates and confounders 

Section on Statistics in Epidemiology