A Baseline Covariate Adjusted Chi-Square Test for Binary and Categorical Data

We propose a test of comparison of treatment groups adjusted based on information brought by a baseline covariate in a randomized clinical trial for which the main efficacy endpoint is a binary or a categorical criterion. This test is linked to the statistical information notions of Kullback-Leibler information and I-projection and leads to a lest statistic that must be compared to the chi-square distribution with the same degrees of freedom as the Pearson chi-square test. With some simulations, the nonasymptotic properties of this test have been investigated: it is shown that in some cases the power of this adjusted test is superior to the Pearson chi-square test whereas the type I error is less sensitive to the large baseline empirical differences of the prognostic covariate.