title: Dose response signal detection under model uncertainty.
abstract: We investigate likelihood ratio contrast tests for dose response signal detection under model uncertainty, when several competing regression models are available to describe the dose response relationship. The proposed approach uses the complete structure of the regression models, but does not require knowledge of the parameters of the competing models. Standard likelihood ratio test theory is applicable in linear models as well as in nonlinear regression models with identifiable parameters. However, for many commonly used nonlinear dose response models the regression parameters are not identifiable under the null hypothesis of no dose response and standard arguments cannot be used to obtain critical values. We thus derive the asymptotic distribution of likelihood ratio contrast tests in regression models with a lack of identifiability and use this result to simulate the quantiles based on Gaussian processes. The new method is illustrated with a real data example and compared to existing procedures using theoretical investigations as well as simulations.
authors.affiliation: Ruhr-Universität Bochum, Fakultät für Mathematik, 44780, Bochum, Germany.
authors.forename: Holger
authors.initials: H
authors.lastname: Dette
authors.affiliation: Continentale Krankenversicherung a.G. Ruhrallee 92, 44139, Dortmund, Germany.
authors.forename: Stefanie
authors.initials: S
authors.lastname: Titoff
authors.affiliation: Ruhr-Universität Bochum, Fakultät für Mathematik, 44780, Bochum, Germany.
authors.forename: Stanislav
authors.initials: S
authors.lastname: Volgushev
authors.affiliation: Novartis Pharma AG, Lichtstrasse 35, 4002 Basel, Switzerland and Shanghai University of Finance and Economics, People's Republic of China.
authors.forename: Frank
authors.initials: F
authors.lastname: Bretz
mesh_terms: D001699:Biometry / Q000379:methods; D017322:Clinical Trials, Phase II as Topic / Q000706:statistics & numerical data; D004305:Dose-Response Relationship, Drug; D055808:Drug Discovery / Q000706:statistics & numerical data; D006801:Humans; D043183:Irritable Bowel Syndrome / Q000188:drug therapy; D016013:Likelihood Functions; D016014:Linear Models; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D012044:Regression Analysis; D035501:Uncertainty
keywords: Contrast tests; Dose response studies; Likelihood ratio test; Model identification; Nonlinear regression