  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 double score matching(DSM) for general causal
estimands utilizing two balancing scores including 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
for the true causal estimand if any model of the propensity score or prognostic
score is correct.
