Testing Hypotheses of Covariate-Adaptive Randomized Clinical Trials

However, the theoretical properties of conventional testing hypotheses are usually unknown under covariate-adaptive randomized clinical trials. In the literature, most studies are based on simulations.

In this article, we provide theoretical foundation of hypothesis testing under covariate-adaptive designs based on linear models. We derive the asymptotic distributions of the test statistics of testing both treatment effects and the significance of covariates under null and alternative hypotheses. Under a large class of covariate-adaptive designs, (i) the hypothesis testing to compare treatment effects is usually conservative in terms of small Type I error; (ii) the hypothesis testing to compare treatment effects is usually more powerful than complete randomization; and (iii) the hypothesis testing for significance of covariates is still valid.