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 ef-

fects and the asymptotic selection bias. Our results reveal that under covariateadaptive randomization: (i) hypothesis tests generally lose power when covari-

ates 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.

Key words and phrases: Balancing covariates, clinical trial, loss of power, selec- tion bias, Pocock and Simon’s procedure 1

Information

Preprint No.SS-2025-0290
Manuscript IDSS-2025-0290
Complete AuthorsLi-Xin Zhang
Corresponding AuthorsLi-Xin Zhang
Emailsstazlx@mail.zjgsu.edu.cn

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Acknowledgments

The authors thank the Associate Editor and the two anonymous referees for

many helpful comments and suggestions. The research was partly supported

by grants from NSF of China (No. U23A2064), National Key R&D Program

of China (No. 2024YFA1013502) and the Summit Advancement Disciplines

of Zhejiang Province (Zhejiang Gongshang University - Statistics).

Supplementary Materials

The online supplementary material contains the theoretical proof of all the

theorems, and the simulation study of the new CAR with a specific allocation function g in (4.8).

Supplementary materials are available for download.