Empirical Likelihood Weighted Estimation of Average Treatment Effects

Abstract: There has been growing attention on how to effectively and objectively use covariate information when the primary goal is to estimate the average treatment effect (ATE) in randomized clinical trials (RCTs). In this paper, we propose an effective weighting approach to extract covariate information based on the empirical likelihood (EL) method. The resulting two-sample empirical likelihood weighted (ELW) estimator includes two classes of weights, which are obtained from a constrained empirical likelihood estimation procedure, where the covariate information is effectively incorporated into the form of general estimating equations. Furthermore, this ELW approach separates the estimation of ATE from the analysis of the covariate-outcome relationship, which implies that our approach maintains objectivity. In theory, we show that the proposed ELW estimator is semiparametric efficient. We extend our estimator to tackle the scenarios where the outcomes are missing at random (MAR), and prove the double robustness and multiple robustness properties of our estimator. Furthermore, we derive the semiparametric efficiency bound of all regular and asymptotically linear semiparametric ATE estimators under MAR mechanism and prove that our proposed estimator attains this bound. We conduct simulations to make comparisons with other existing estimators, which confirm the efficiency and multiple robustness property of our proposed ELW estimator. An application to the AIDS Clinical Trials Group Protocol 175 (ACTG 175) data is conducted.