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- Title
Adaptive designs with arbitrary dependence structure based on Fisher's combination test.
- Authors
Schmidt, René; Faldum, Andreas; Gerß, Joachim
- Abstract
Adaptive designs were originally developed for independent and uniformly distributed $$p$$ -values. However, in general the type I error rate of a given adaptive design depends on the true dependence structure between the stage-wise $$p$$ -values. Since there are settings, where the $$p$$ -values of the stages might be dependent with even unknown dependence structure, it is of interest to consider the most adverse dependence structure maximizing the type I error rate of a given adaptive design (worst case). In this paper, we explicitly study the type I error rate in the worst case for adaptive designs without futility stop based on Fisher's combination test. Potential inflation of the type I error rate is studied if the dependence structure between the $$p$$ -values of the stages is not taken into account adequately. It turns out that considerable inflation of the type I error rate can occur. This emphasizes that the examination of the true dependence structure between the stage-wise $$p$$ -values and an adequate choice of the conditional error function is crucial when adaptive designs are used.
- Subjects
ADAPTIVE computing systems; ERROR analysis in mathematics; MATHEMATICAL functions; SYSTEMS design; MATHEMATICAL models
- Publication
Statistical Methods & Applications, 2015, Vol 24, Issue 3, p427
- ISSN
1618-2510
- Publication type
Article
- DOI
10.1007/s10260-014-0291-6