A Baseline Covariate Adjusted Chi-Square Test for Binary and Categorical Data
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Drug Informution Journal, Vol. 35, pp. 145-151, 2001
Printed in the USA. All rights reserved.
A BASELINE COVARIATE ADJUSTED CHI-SQUARE TEST FOR BINARY AND CATEGORICAL DATA BERNARD SEBASTIEN, PHD Biostatistics, Sanofi-Synthelabo, Chilly-Mazarin, France
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 efJicacy 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 test 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. Key Words: Response criterion; Kullback-Leibler information; I-projection; Baseline imbalances
INTRODUCTION RANDOMIZATION IS ESSENTIAL in clinical trials since it ensures that any difference observed between the treatment groups is due to the treatments only, since the populations of these treatment groups are the same as they are sampled from the same population. Nevertheless, despite randomization, it may happen that, between the treatment groups, major imbalances in the distribution of important prognostic variables occur by chance or due to sampling variability. On average, the risk of possible imbalances is taken into account in the evaluation of the probability of type I or type I1 errors but the occurrence of severe imbalances between treatment groups observed before random-
Reprint address: Bernard Sebastien, Sanofi-Synthelabo, 1 avenue Pierre Brossolette, 91385 Chilly-Mazarin CEDEX, France. E-mail: BemardSEBASTWQsanofisynthelabo.com.
ization may make the interpretation of the results of a particular experiment difficult. When the result of the experiment is summarized in a continuous variable, say Y, whose mean is of primary interest and if a key covariate is available, say X, then the analysis of the covariance model followed by the calculation of adjusted means is a useful method to adjust the results to possible imbalances with respect to X. This analysis provides estimates in the form of the adjusted means (or LSMEANS) that have the same interpretation as the raw means. When the result of the experiment is summarized in a categorical variable Y, for example, Y = 1 is a success and Y = 0 is a failure, then the comparisons of the treatment groups are most often conducted using the Pearson chi-square test. When a severe imbalance between the treatment groups with respect to a key covariate X is observed then, most often, either this is ignored in the analysis or a parametric model taking into account the covariate is fitted (very often a logistic regres-
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