Gerhard Hommel (University of Mainz, Germany)
Adaptive modifications of hypotheses after an interim analysis
It is investigated how one can modify the hypothesis/es in a study after an interim analysis such that the type I error rate is controlled. If only a global statement is desired, a solution was given by Bauer (1989). If individual statements should be made, the formal application of the closure test may lead to an excessive type I error rate; two proposals for a correction are given. For a general multiple testing problem, by Kieser, Bauer and Lehmacher (1999) and Bauer and Kieser (1999) solutions are given, by means of which the set of hypotheses can be reduced after the interim analysis. If weights for the tests within each of two stages are chosen, the same idea can be applied. Since it is allowed that a hypothesis has weight 0 in the first stage, but a weight > 0 in the second stage, a formal way has been found to include additional hypotheses in the second stage. Nevertheless, the scientific reason of such an inclusion has to be discussed very critically.