Abstract:
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Exact inference for independent binomial outcomes in small samples is complicated by the presence of a mean-variance relationship that depends on nuisance parameters, discreteness of the outcome space, and departures from normality. To address the various issues, Barnard introduced the concept of unconditional exact tests that use exact distributions of a test statistic evaluated over all possible values of the nuisance parameter. It has been found that unconditional exact tests are preferred to conditional exact tests in fixed sample settings. In this presentation we examine the behavior of unconditional exact tests using Wald, score, likelihood ratio, and Fisher's exact test statistics in the group sequential setting. We suggest three methods of using critical values derived from adjusted fixed sample tests in order to minimize the conservativeness of the actual type 1 error at: the final analysis only; each analysis after 50% accrual of the maximal sample size; and every analysis. Owing to its tendency to behave well across a wide variety of settings, we recommend implementation of the unconditional exact test using the adjusted Fisher's exact test statistic at every analysis.
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