Eliminating residual confounding in the stratified estimator via smoothing along with the propensity score

The stratified estimator by the propensity score is one of the most popular estimator for the average causal effect in the presence of confounding. Despite of its advantages of robustness and simplicity, it has a serious shortcoming of residual confounding even with the correctly specified propensity score. On the other hand, the inverse probability weighting estimator by the propensity score is free from residual confounding and many corresponding variants have been proposed. Wang et al. (2021, Robust estimation of propensity score weights via subclassification) pointed it out that the stratified estimator can be regarded as a special case of the inverse probability weighting estimator with piecewise constant propensity score and proposed a method eliminating residual confounding in the stratified estimator. In this paper, we provide an alternative interpretation of the stratified estimator as the outcome regression with a piecewise constant function over the propensity score. By considering kernel smoothing, an estimator free from residual confounding is proposed based on the stratified estimator, which preserves the robustness of the stratified estimator. We also propose a doubly robust estimator, which does not rely on the inverse probability weighting.