An Empirical Likelihood Approach to Nonparametric Covariate Adjustment in Randomized Clinical Trials

TL;DR

This paper introduces a nonparametric empirical likelihood method for covariate adjustment in randomized trials, improving efficiency and bias reduction without relying on regression models.

Contribution

It proposes a model-free covariate adjustment approach using empirical likelihood, achieving optimal covariate utilization and semiparametric efficiency.

Findings

The method is asymptotically most powerful.

It achieves the semiparametric efficiency bound.

Validated through simulations and application to GUSTO-I trial.

Abstract

Covariate adjustment is an important tool in the analysis of randomized clinical trials and observational studies. It can be used to increase efficiency and thus power, and to reduce possible bias. While most statistical tests in randomized clinical trials are nonparametric in nature, approaches for covariate adjustment typically rely on specific regression models, such as the linear model for a continuous outcome, the logistic regression model for a dichotomous outcome and the Cox model for survival time. Several recent efforts have focused on model-free covariate adjustment. This paper makes use of the empirical likelihood method and proposes a nonparametric approach to covariate adjustment. A major advantage of the new approach is that it automatically utilizes covariate information in an optimal way without fitting nonparametric regression. The usual asymptotic properties, including the Wilks-type result of convergence to a chi-square distribution for the empirical likelihood ratio based test, and asymptotic normality for the corresponding maximum empirical likelihood estimator, are established. It is also shown that the resulting test is asymptotically most powerful and that the estimator for the treatment effect achieves the semiparametric efficiency bound. The new method is applied to the Global Use of Strategies to Open Occluded Coronary Arteries (GUSTO)-I trial. Extensive simulations are conducted, validating the theoretical findings.