  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.
