title: A studentized permutation test for three-arm trials in the 'gold standard' design.
abstract: The 'gold standard' design for three-arm trials refers to trials with an active control and a placebo control in addition to the experimental treatment group. This trial design is recommended when being ethically justifiable and it allows the simultaneous comparison of experimental treatment, active control, and placebo. Parametric testing methods have been studied plentifully over the past years. However, these methods often tend to be liberal or conservative when distributional assumptions are not met particularly with small sample sizes. In this article, we introduce a studentized permutation test for testing non-inferiority and superiority of the experimental treatment compared with the active control in three-arm trials in the 'gold standard' design. The performance of the studentized permutation test for finite sample sizes is assessed in a Monte Carlo simulation study under various parameter constellations. Emphasis is put on whether the studentized permutation test meets the target significance level. For comparison purposes, commonly used Wald-type tests, which do not make any distributional assumptions, are included in the simulation study. The simulation study shows that the presented studentized permutation test for assessing non-inferiority in three-arm trials in the 'gold standard' design outperforms its competitors, for instance the test based on a quasi-Poisson model, for count data. The methods discussed in this paper are implemented in the R package ThreeArmedTrials which is available on the comprehensive R archive network (CRAN). Copyright © 2016 John Wiley & Sons, Ltd.
authors.affiliation: Department of Medical Statistics, University Medical Center Göttingen, Humboldtallee 32, Göttingen, 37073, Germany.
authors.forename: Tobias
authors.identifier: 0000-0002-4111-1941
authors.initials: T
authors.lastname: Mütze
authors.affiliation: Department of Medical Statistics, University Medical Center Göttingen, Humboldtallee 32, Göttingen, 37073, Germany.|Department of Mathematical Sciences, University of Texas at Dallas, Richardson, 75080, TX, U.S.A.
authors.forename: Frank
authors.initials: F
authors.lastname: Konietschke
authors.affiliation: Institute for Mathematical Stochastics, Georg-August-University of Göttingen, Goldschmidtstraße 7, Göttingen, 37077, Germany.|Max Planck Institute for Biophysical Chemistry, Am Faßberg 11, Göttingen, 37077, Germany.
authors.forename: Axel
authors.initials: A
authors.lastname: Munk
authors.affiliation: Department of Medical Statistics, University Medical Center Göttingen, Humboldtallee 32, Göttingen, 37073, Germany.
authors.forename: Tim
authors.identifier: 0000-0001-5347-7441
authors.initials: T
authors.lastname: Friede
mesh_terms: D002986:Clinical Trials as Topic / Q000379:methods* / Q000592:standards; D000074099:Equivalence Trials as Topic; D006801:Humans; D009010:Monte Carlo Method; D016012:Poisson Distribution; D018401:Sample Size; D016008:Statistical Distributions; D013223:Statistics as Topic
keywords: Wald-type test; gold standard design; non-inferiority; permutation test; three-arm trial