Double score matching estimators of average and quantile treatment effects

Propensity score matching has a long tradition for handling confounding in causal inference. In this article, we propose double score matching estimators of the average treatment effects and the quantile treatment effects utilizing two balancing scores including the propensity score and the prognostic score. We show that the de-biasing double score matching estimators achieve the double robustness property in that they are consistent for the true causal estimands if either the propensity score model or the prognostic score model is correctly specified, not necessarily both.} We characterize the asymptotic distributions for the doubly score matching estimators when either one of the score model is correctly specified based on the martingale representations of the matching estimators and theory for local normal experiments. We also provide a two-stage replication method for variance estimation and therefore doubly robust inference. R package is available online.