Robust Estimation of Propensity Score Weights via Subclassification

The propensity score plays a central role in inferring causal effects from observational studies. In particular, weighting and subclassification are two principal approaches to estimate the average causal effect based on estimated propensity scores. Unlike the conventional version of the propensity score subclassification estimator, if the propensity score model is correctly specified, the weighting methods offer consistent and possibly efficient estimation of the average causal effect. However, this theoretical appeal may be diminished in practice by sensitivity to misspecification of the propensity score model. In contrast, subclassification methods are usually more robust to model misspecification. We hence propose to use subclassification for robust estimation of propensity score weights. Our approach is based on the intuition that the inverse probability weighting estimator can be seen as the limit of subclassification estimators as the number of subclasses goes to infinity. By formalizing this intuition, we propose novel propensity score weighting estimators that are both consistent and robust to model misspecification. Empirical studies show that the proposed estimators perform favorably compared to existing methods.