Efficient Covariate-Adaptive Randomization with Smallest Selection Bias in Clinical Trials

Abstract

The power of conventional hypothesis tests and the selection bias in covariate-adaptive randomized clinical trials are typically investigated through simulation studies. In this article, we develop a theoretical framework for analyzing both the asymptotic power of linear-model-based tests for treatment effects and the asymptotic selection bias. Our results reveal that under covariate-adaptive randomization: (i) hypothesis tests generally lose power when covariates are not sufficiently balanced; in particular, the more covariates included in the testing model that are not accounted for in the randomization procedure, the greater the loss of power; (ii) the hypothesis test is usually more powerful than that under complete randomization; and (iii) compared with complete randomization, many popular covariate-adaptive randomization procedures in the literature such as Pocock and Simon's marginal procedure, the stratified permuted block design, and Taves's minimization method-are generally efficient in terms of power but yield non-negligible selection bias. To address this trade-off, we propose a new family of covariate-adaptive randomization procedures that simultaneously account for both power and selection bias. Under these procedures, covariate imbalances are kept sufficiently small to achieve asymptotically maximal power for testing treatment effects, while the selection bias remains asymptotically negligible. These theoretical results provide a comprehensive picture of how the power of hypothesis testing, covariate imbalance, and selection bias interact with one another.