Abstract

Longitudinal outcomes are often involved in covariate-adaptive ran

domized (CAR) trials. However, most existing studies disregard the longitudinal structure and focus on a cross-sectional analysis. In this article, we utilize

generalized estimating equations (GEE) to conduct inference for the marginal

treatment effect following CAR. In addition, we introduce an additional stratification variable to allow for the analysis with unbalanced longitudinal data. We

show that the treatment estimate is consistent under the null hypothesis, even

when omitted covariates are involved in the analysis. This enables us to construct tests that preserve the Type I error rate even when the working model

used for analysis is misspecified. By deriving the asymptotic normality of the

treatment effect estimator, we show that the robust property of GEE still holds

under CAR designs, but the balance of covariates used in design and the additional stratification affects the classical Wald tests, yielding reduced Type I error.

To remedy this issue, we propose an adjustment procedure and show that the

adjustment recovers the nominal significance level of the test for most commonly

used CAR procedures. Extensive simulation studies corroborate our theoretical

findings and highlight the practical advantages of the proposed methods in terms

of both estimation efficiency and inferential validity.

Key words and phrases: Covariate-adaptive randomization; longitudinal data; generalized estimating equations; conservative tests; bootstrap adjustment 1

Information

Preprint No.SS-2025-0428
Manuscript IDSS-2025-0428
Complete AuthorsRuichen Fu, Yang Liu
Corresponding AuthorsYang Liu
Emailsyangliu2022@ruc.edu.cn

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Acknowledgments

The authors would like to thank the editor and AE. and the two reviewers for the insightful comments that lead to a much improved version of

the paper. Liu’s research was supported by the National Natural Science

Foundation of China grant no. 12301324, and the Fundametal Research

Funds for the Central Universities and the Research Funds of University of

China [grant no. 202630333]. This research was also supported by Public

Computing Cloud, Renmin University of China.

Supplementary Materials

contain the proofs of theoretical results and the

additional simulation results.

Supplementary materials are available for download.