Stratified doubly robust estimators for the average causal effect.

Suppose we are interested in estimating the average causal effect from an observational study. A doubly robust estimator, which is a hybrid of the outcome regression and propensity score weighting, is more robust than estimators obtained by either of them in the sense that, if at least one of the two models holds, the doubly robust estimator is consistent. However, a doubly robust estimator may still suffer from model misspecification since it is not consistent if neither of them is correctly specified. In this article, we propose an alternative estimator, called the stratified doubly robust estimator, by further combining propensity score stratification with outcome regression and propensity score weighting. This estimator allows two candidate models for the propensity score and is more robust than existing doubly robust estimators in the sense that it is consistent either if the outcome regression holds or if one of the two models for the propensity score holds. Asymptotic properties are examined and finite sample performance of the proposed estimator is investigated by simulation studies. Our proposed method is illustrated with the Tone study, which is a community survey conducted in Japan.