Subclassification estimation of the weighted average treatment effect

Weighting and subclassification are popular approaches using propensity scores (PSs) for estimation of causal effects. Weighting is appealing in that it gives consistent estimators for various causal estimands if appropriate weights are well defined and the PS model is correctly specified. Subclassification is known to be more robust to model misspecification than weighting, but its application to diverse causal estimands is limited. In this article, we propose generalized stratum weights to implement subclassification estimators for various causal estimands. These weights include stratum weights for the average treatment effect (ATE) of the overall population and those for the ATE of the treated as special cases. For this, we incorporate strata into the expression of the weighted average treatment effect (WATE). Particularly, we identify stratum weights for the ATE for the overlap population (ATO), for which the weighting estimator is known to be most efficient among the class of WATE estimators. We show that the identified stratum weights for ATO are equivalent to the optimal stratum weights, which are the inverse variances of the stratum-specific estimators. Simulation studies demonstrate that the proposed subclassification estimator for ATO is more robust to model misspecification than the weighting estimator for ATO. We also propose augmented subclassification estimators, which are shown to be less biased than the subclassification estimators when only the outcome model is correctly specified. The practical utility of the proposed methods is illustrated in a study of right heart catheterization.