Abstract

Covariate-adaptive randomization (CAR) leverages covariates at the

design stage to enhance comparability between treatment groups, but typically

allows only a limited set of covariates to be incorporated. We therefore study

covariate adjustment at the analysis stage to achieve more efficient estimation of

the treatment effect under CAR. Existing work on covariate adjustment under

CAR typically relies on a single, pre-specified model. Although this complies with

regulatory guidance that the adjustment model be specified before the trial, a

single-model approach can be vulnerable to misspecification and may be less efficient when the covariate-outcome relationship is uncertain. To address this issue,

we propose a model averaging framework for covariate adjustment under CAR

that accommodates a collection of pre-specified candidate models. The averaging weights are selected via K-fold cross-validation to minimize the asymptotic

variance of the treatment effect estimator. We establish that the resulting estimator is asymptotically normal and achieves asymptotic variance optimality

within the candidate model class under mild regularity conditions. Simulation

studies demonstrate that the proposed approach yields substantial variance reduction compared with single-model adjustment. Overall, this paper introduces

a theoretically grounded and flexible framework for treatment effect estimation

under CAR that complies with regulatory pre-specification requirements while

effectively handling uncertainty in covariate-outcome relationships.

Key words and phrases: Covariate-adaptive randomization, Covariate adjust- ment, Cross-validation, Model averaging, Machine learning 1

Information

Preprint No.SS-2025-0502
Manuscript IDSS-2025-0502
Complete AuthorsFuyi Tu, Jiahui Xin, Wei Ma
Corresponding AuthorsWei Ma
Emailsmawei@ruc.edu.cn

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Acknowledgments

We thank the Associate Editor and the reviewers for their valuable comments and suggestions.

Wei Ma was supported by the National Natural Science Foundation of China (Grant No. 12571277), the Fundamental

Research Funds for the Central Universities and the Research Funds of

Renmin University of China (Grant No. 202630333). Fuyi Tu was supported by the Doctoral Research Start-up Funding of CQUPT (Grant No.

Supplementary Materials

Detailed proofs of the main theorems, additional technical lemmas, and tables of simulation results are available in the online supplementary material.

Supplementary materials are available for download.