Abstract

Modern medical research, such as dose-finding studies, seamless trials, and shared control

designs, often involves comparing multiple treatments simultaneously. Despite its wide applications,

most research focuses on continuous endpoints, leaving the inference for general outcome types in high

demand. In this article, we propose a new inference method for conducting multiple-treatment comparisons involving endpoints within the generalized linear model (GLM) framework under covariate-

adaptive randomization (CAR). First, we investigate the asymptotic properties of the standard Wald

z-statistics (z-scores) in multi-arm trials, highlighting issues when the working model is misspecified,

particularly through omitted covariates.

Our theoretical findings reveal that these z-scores do not

consistently converge to a standard multivariate normal distribution, leading to either conservative

or inflated Type I error rates, depending on the specific GLM endpoint.

Second, based on these

theoretical results, we develop adjusted test statistics to correct the distributional problems. To appropriately control the family-wise Type I error rate inherent in multi-arm comparisons, we incorporate

our adjusted statistics with Simes-type multiple-testing procedures. This robust inference method can

effectively control Type I error while potentially improving power. Extensive simulation studies and a

real-world application to a metastatic breast cancer trial confirm the effectiveness and practicality of

our approach.

Key words and phrases: Clinical trials, Covariate-adaptive randomization, Generalized linear models, Multi-arm trials, Shared control, Type I error 1

Information

Preprint No.SS-2025-0243
Manuscript IDSS-2025-0243
Complete AuthorsGuannan Zhai, Feifang Hu
Corresponding AuthorsFeifang Hu
Emailsfeifang@gwu.edu

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Supplementary Materials

Additional technical details are provided in the Supplementary Materials.

They include

the formal definitions of the imbalance measures under multi-arm CAR, auxiliary lemmas,

proofs of the main theorems in Section 3, and derivations of the working variance term under

different GLMs.

Supplementary materials are available for download.