In three-arm studies, there are often multiple hypotheses to be tested among the arms. In this article, we describe a multiple comparisons procedure that controls the familywise error rate in the strong sense. The procedure is appropriate when one of the arms is a control, and both treatment arms will be compared to the control as well as to each other. The procedure is shown to be consistent and the asymptotic relative efficiency (compared to the uniformly most powerful test for the individual comparisons) is close to 1 in many scenarios. Furthermore, the special case where the arms are placebo, active control, and test drug with one goal of showing noninferiority is examined.
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