Abstract
We propose a new method to uniformly improve cutoff tests (as, e.g., the Bonferroni test) by replacing them with a sequential testing procedure. The proposed procedure provides a uniform improvement—that is, it rejects the null hypothesis at least in all cases where the original procedure does, has level α, and never requires a sample size larger than that of the original procedure. Information on the often-unknown joint distribution of the test statistics across the hypotheses is not required. We discuss the applications to one- and two-sided tests for the intersection of multiple hypotheses, as well as to tests of elementary hypotheses. For the wide class of asymptotically linear test statistics and under unknown nuisance parameters, we propose an asymptotic approximation to our improved procedure and show that it exhausts the nominal type I error rate asymptotically. We present an application in a clinical study with multiple endpoints where the null hypothesis of no effect is tested against the alternative that at least one endpoint shows an effect, and give a real data example.
Published Version
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