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Abstract:
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In confirmatory clinical trials with the limited sample size (for example, in rare diseases), challenges arise because the asymptotic theory may lose accuracy to approximate the distribution of test statistics. Often, non-parametric exact tests are applied instead. However, the distribution of these statistics is usually discrete and they may be overly conservative with the Type I error rate below the nominal. To overcome this drawback, we propose an optimal multiple testing procedure for multiple binary endpoints to compare a treatment versus a control. The proposed procedure explores the joint distribution of the test statistics for multiple Fisher's exact tests. The optimal rejection region is then derived under the constrained optimization framework using the linear integer programming technique. The procedure and its properties are discussed using a clinical trial in a rare disease.
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