Abstract

For a rare disease, all the patients having the disease constitute a small population, and the standard single-stage hypergeometric test is uniformly most powerful to evaluate the response probability of a specific treatment regimen. Although exact group sequential designs are widely employed in phase II clinical trials for binomial proportions, it is unknown whether or not similar tests can be employed for hypergeometric proportions. In this manuscript, it is proved that, for hypergeometric proportions, there exist exact group sequential designs that achieve the predesignated significance level and power with maximum total sample size bounded above by the sample size for the corresponding standard exact single-stage test. Additionally, two types of optimal two-stage designs are examined for a range of design parameters; one is optimal in the sense that the expected sample size under the null hypothesis is minimized, and the other is optimal in the sense that the maximum sample size is minimized.

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