Empirical likelihood inference for non-randomized pretest-posttest studies with missing data

Abstract

Pretest-posttest studies are commonly used for assessing the effect of a treatment or an intervention. We propose an empirical likelihood based approach to both testing and estimation of the treatment effect in non-randomized pretest-posttest studies where the posttest outcomes are subject to missingness. The proposed empirical likelihood ratio test and the estimation procedure are multiply robust in the sense that multiple working models are allowed for the propensity score of treatment assignment, the missingness probability and the outcome regression, and the validity of the test and the estimation requires only a certain combination of those multiple working models to be correctly specified. An empirical likelihood ratio confidence interval can be constructed for the treatment effect and has better coverage probabilities than confidence intervals based on the Wald statistic. Simulations are conducted to demonstrate the finite-sample performances of the proposed methods.