Doubly robust estimation in causal inference with missing outcomes: With an application to the Aerobics Center Longitudinal Study

Estimation of the average treatment effect (ATE) and the average treatment effect on the treated (ATT) are two important topics of causal inference. However, when using the observational data for causal inference, two main problems including unbalanced covariates and missing outcomes should be tackled. In order to handle these two challenges and provide protection against model misspecification, the doubly robust estimators are developed, which remain consistent when the propensity score model and the selection probability model are correctly specified concurrently, or the outcome regression model is correctly specified. Under regularity conditions, the asymptotic normality of the estimators is established. Simulation studies confirm the desirable finite-sample performance of the proposed methods. Based on the Aerobics Center Longitudinal Study, the significant positive causal effect of physical activity levels on health status is discovered.