  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.
