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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 debiasing 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. [ABSTRACT FROM AUTHOR]

Unlike in randomized clinical trials (RCTs), confounding control is critical for estimating the causal effects from observational studies due to the lack of treatment randomization. Under the unconfoundedness assumption, matching methods are popular because they can be used to emulate an RCT that is hidden in the observational study. To ensure the key assumption hold, the effort is often made to collect a large number of possible confounders, rendering dimension reduction imperative in matching. Three matching schemes based on the propensity score (PSM), prognostic score (PGM), and double score (DSM, ie, the collection of the first two scores) have been proposed in the literature. However, a comprehensive comparison is lacking among the three matching schemes and has not made inroads into the best practices including variable selection, choice of caliper, and replacement. In this article, we explore the statistical and numerical properties of PSM, PGM, and DSM via extensive simulations. Our study supports that DSM performs favorably with, if not better than, the two single score matching in terms of bias and variance. In particular, DSM is doubly robust in the sense that the matching estimator is consistent requiring either the propensity score model or the prognostic score model is correctly specified. Variable selection on the propensity score model and matching with replacement is suggested for DSM, and we illustrate the recommendations with comprehensive simulation studies. An R package is available at https://github.com/Yunshu7/dsmatch. [ABSTRACT FROM AUTHOR]

For ordinal outcomes, the average treatment effect is often ill‐defined and hard to interpret. Echoing Agresti and Kateri, we argue that the relative treatment effect can be a useful measure, especially for ordinal outcomes, which is defined as γ=pr{Yi(1)>Yi(0)}−pr{Yi(1)