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

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