  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.
