Empirical likelihood inference in randomized clinical trials

Abstract

In individually randomized controlled trials, in addition to the primary outcome, information is often available on a number of covariates prior to randomization. This information is frequently utilized to undertake adjustment for baseline characteristics in order to increase precision of the estimation of average treatment effects; such adjustment is usually performed via covariate adjustment in outcome regression models. Although the use of covariate adjustment is widely seen as desirable for making treatment effect estimates more precise and the corresponding hypothesis tests more powerful, there are considerable concerns that objective inference in randomized clinical trials can potentially be compromised. In this paper, we study an empirical likelihood approach to covariate adjustment and propose two unbiased estimating functions that automatically decouple evaluation of average treatment effects from regression modeling of covariate–outcome relationships. The resulting empirical likelihood estimator of the average treatment effect is as efficient as the existing efficient adjusted estimators¹ when separate treatment-specific working regression models are correctly specified, yet are at least as efficient as the existing efficient adjusted estimators¹ for any given treatment-specific working regression models whether or not they coincide with the true treatment-specific covariate–outcome relationships. We present a simulation study to compare the finite sample performance of various methods along with some results on analysis of a data set from an HIV clinical trial. The simulation results indicate that the proposed empirical likelihood approach is more efficient and powerful than its competitors when the working covariate–outcome relationships by treatment status are misspecified.