title: Design and analysis of three-arm trials with negative binomially distributed endpoints.
abstract: A three-arm clinical trial design with an experimental treatment, an active control, and a placebo control, commonly referred to as the gold standard design, enables testing of non-inferiority or superiority of the experimental treatment compared with the active control. In this paper, we propose methods for designing and analyzing three-arm trials with negative binomially distributed endpoints. In particular, we develop a Wald-type test with a restricted maximum-likelihood variance estimator for testing non-inferiority or superiority. For this test, sample size and power formulas as well as optimal sample size allocations will be derived. The performance of the proposed test will be assessed in an extensive simulation study with regard to type I error rate, power, sample size, and sample size allocation. For the purpose of comparison, Wald-type statistics with a sample variance estimator and an unrestricted maximum-likelihood estimator are included in the simulation study. We found that the proposed Wald-type test with a restricted variance estimator performed well across the considered scenarios and is therefore recommended for application in clinical trials. The methods proposed are motivated and illustrated by a recent clinical trial in multiple sclerosis. The R package ThreeArmedTrials, which implements the methods discussed in this paper, is available on CRAN.
authors.affiliation: GlaxoSmithKline, 7030 Kit Creek Road, Morrisville, NC 27560, U.S.A.|Institut für Medizinische Statistik, Universitätsmedizin Göttingen, Humboldtallee 32, Göttingen, 37073, Germany.
authors.forename: Tobias
authors.initials: T
authors.lastname: Mütze
authors.affiliation: Institut für Mathematische Stochastik, Georg-August-Universität Göttingen, Goldschmitdstrasse 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: Institut für Medizinische Statistik, Universitätsmedizin Göttingen, Humboldtallee 32, Göttingen, 37073, Germany.
authors.forename: Tim
authors.identifier: http://orcid.org/0000-0001-5347-7441
authors.initials: T
authors.lastname: Friede
mesh_terms: D002986:Clinical Trials as Topic; D003198:Computer Simulation; D000069462:Dimethyl Fumarate / Q000627:therapeutic use; D023381:Endpoint Determination; D006801:Humans; D007166:Immunosuppressive Agents / Q000627:therapeutic use; D008279:Magnetic Resonance Imaging; D015233:Models, Statistical; D009010:Monte Carlo Method; D009103:Multiple Sclerosis / Q000188:drug therapy / Q000473:pathology; D010919:Placebos; D012107:Research Design; D018401:Sample Size
chemical_list: D007166:Immunosuppressive Agents; D010919:Placebos; D000069462:Dimethyl Fumarate
keywords: negative binomial distribution; non-inferiority; restricted maximum likelihood; superiority; three-arm trial