Multiply robust matching estimators of average and quantile treatment effects.

Propensity score matching has been a long-standing tradition for handling confounding in causal inference, however requiring stringent model assumptions. In this article, we propose novel double score matching (DSM) utilizing both the propensity score and prognostic score. To gain the protection of possible model misspecification, we posit multiple candidate models for each score. We show that the de-biasing DSM estimator achieves the multiple robustness property in that it is consistent if any one of the score models is correctly specified. We characterize the asymptotic distribution for the DSM estimator requiring only one correct model specification 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 extend DSM for quantile estimation. Simulation demonstrates DSM outperforms single score matching and prevailing multiply robust weighting estimators in the presence of extreme propensity scores.