Three-sided hypothesis testing: simultaneous testing of superiority, equivalence and inferiority

Statistics in Medicine
Jelle J GoemanTheo Stijnen

Abstract

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.

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Citations

Sep 22, 2012·Statistics in Medicine·M Hasler, L A Hothorn
Aug 15, 2015·Journal of the American Statistical Association·Samuel D PimentelPaul R Rosenbaum
Sep 15, 2015·Statistics in Biopharmaceutical Research·Kevin S S Henning, Peter H Westfall
Apr 22, 2017·Biometrical Journal. Biometrische Zeitschrift·Aldo Solari
Apr 14, 2018·PloS One·Harlan Campbell, Paul Gustafson
Sep 7, 2018·Biometrical Journal. Biometrische Zeitschrift·Rosa J MeijerJelle J Goeman
May 5, 2012·Anesthesia and Analgesia·Edward J Mascha, Alparslan Turan
Mar 23, 2017·Clinical and Experimental Pharmacology & Physiology·Ricardo Murphy
Jul 13, 2017·Scientific Reports·Han-Yi Shih, Wen-Chung Lee
May 21, 2021·The Journal of Bone and Joint Surgery. American Volume·Anna WallaceJennifer Wood

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