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Three‐sided hypothesis testing: Simultaneous testing of superiority, equivalence and inferiority
Author(s) -
Goeman Jelle J.,
Solari Aldo,
Stijnen Theo
Publication year - 2010
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4002
Subject(s) - statistical hypothesis testing , equivalence (formal languages) , alternative hypothesis , null hypothesis , multiple comparisons problem , inference , confidence interval
We propose three‐sided testing , a testing framework for simultaneous testing of inferiority, equivalence and superiority in clinical trials, controlling for multiple testing using the partitioning principle. Like the usual two‐sided testing approach, this approach is completely symmetric in the two treatments compared. Still, because the hypotheses of inferiority and superiority are tested with one‐sided tests, the proposed approach has more power than the two‐sided approach to infer non‐inferiority or non‐superiority. Applied to the classical point null hypothesis of equivalence, the three‐sided testing approach shows that it is sometimes possible to make an inference on the sign of the parameter of interest, even when the null hypothesis itself could not be rejected. Relationships with confidence intervals are explored, and the effectiveness of the three‐sided testing approach is demonstrated in a number of recent clinical trials. Copyright © 2010 John Wiley & Sons, Ltd.