Multiply robust estimation of the average treatment effect with missing outcomes

Abstract

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.

Keywords:

• Average treatment effect
• empirical likelihood
• missing data
• multiple robustness
• propensity score

Acknowledgments

The authors gratefully acknowledge Dr. Steven N. Blair of the University of South Carolina for providing the ACLS data. We thank the Cooper Clinic physicians and technicians for collecting the baseline data, staff at the Cooper Institute for data entry and data management. We would like to thank the Editor and referee for their insightful and constructive comments and suggestions, which led to substantial improvements of the paper.

Disclosure statement

The authors have declared no conflict of interest.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant number 82173612] .