Multiply robust estimation of the average treatment effect with missing outcomes

When using the observational data to estimate the average treatment effect, unbalanced covariates may induce confounding bias and missing outcomes may induce selection bias. In order to correct these two types of bias and offer protection against model mis-specification, a multiply robust estimator is proposed, which allows multiple candidate models to be taken account into estimation. The proposed estimator is consistent when any pair of models for propensity score and selection probability is correctly specified, or any model for outcome regression is correctly specified. Under regularity conditions, asymptotic normality of the estimator is obtained. Moreover, the proposed estimator achieves the semiparametric efficiency bound when the correct models for propensity score, selection probability and outcome regression are included in the candidate models simultaneously. Finite-sample performance of the proposed method is evaluated via simulations and an empirical study.