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Group sequential procedures which are truly closed are developed for situations in which the probability of success for Treatment 1 is pi, that for Treatment 2 is P2, and the experimental objective is to test the hypothesis that pi = P2. The experiment then consists of a specified maximum number of groups or stages each containing an equal number of subjects on each treatment. The test statistic is the difference between the numbers of successes with Treatment 1 and with Treatment 2. This is equivalent to forming incidental pairs and scoring these as 1 if (success, failure) occurs, 0 if (failure, failure) or (success, success) occurs, and -1 if (failure, success) occurs. At the end of each stage the cumulative score is compared with the decision rules for the test plan to determine if the experiment terminates or continues. General iterative formulas, based on the trinomial distribution, are developed which directly yield the operating characteristics and average sample number for these plans.
Elfring et al. (1973) studied this question.
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