Testing for Treatment Effect in Covariate-Adaptive Randomized Clinical Trials with Generalized Linear Models and Omitted Covariates

TL;DR

This paper investigates the validity of unadjusted treatment effect tests in covariate-adaptive randomized clinical trials using generalized linear models, providing asymptotic distributions, conditions for validity, and an adjustment method to ensure correct test size.

Contribution

It derives the asymptotic distribution of unadjusted tests under covariate-adaptive randomization and proposes an adjustment method to maintain valid inference across various generalized linear models.

Findings

Unadjusted tests can be conservative, valid, or anti-conservative depending on conditions.

The proposed adjustment method effectively corrects test size.

Numerical studies support the theoretical results.

Abstract

Concerns have been expressed over the validity of statistical inference under covariate-adaptive randomization despite the extensive use in clinical trials. In the literature, the inferential properties under covariate-adaptive randomization have been mainly studied for continuous responses; in particular, it is well known that the usual two sample t-test for treatment effect is typically conservative, in the sense that the actual test size is smaller than the nominal level. This phenomenon of invalid tests has also been found for generalized linear models without adjusting for the covariates and are sometimes more worrisome due to inflated Type I error. The purpose of this study is to examine the unadjusted test for treatment effect under generalized linear models and covariate-adaptive randomization. For a large class of covariate-adaptive randomization methods, we obtain the asymptotic distribution of the test statistic under the null hypothesis and derive the conditions under which the test is conservative, valid, or anti-conservative. Several commonly used generalized linear models, such as logistic regression and Poisson regression, are discussed in detail. An adjustment method is also proposed to achieve a valid size based on the asymptotic results. Numerical studies confirm the theoretical findings and demonstrate the effectiveness of the proposed adjustment method.