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October 2017 Optimal designs for dose response curves with common parameters
Chrystel Feller, Kirsten Schorning, Holger Dette, Georgina Bermann, Björn Bornkamp
Ann. Statist. 45(5): 2102-2132 (October 2017). DOI: 10.1214/16-AOS1520


A common problem in Phase II clinical trials is the comparison of dose response curves corresponding to different treatment groups. If the effect of the dose level is described by parametric regression models and the treatments differ in the administration frequency (but not in the sort of drug), a reasonable assumption is that the regression models for the different treatments share common parameters.

This paper develops optimal design theory for the comparison of different regression models with common parameters. We derive upper bounds on the number of support points of admissible designs, and explicit expressions for $D$-optimal designs are derived for frequently used dose response models with a common location parameter. If the location and scale parameter in the different models coincide, minimally supported designs are determined and sufficient conditions for their optimality in the class of all designs derived. The results are illustrated in a dose-finding study comparing monthly and weekly administration.


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Chrystel Feller. Kirsten Schorning. Holger Dette. Georgina Bermann. Björn Bornkamp. "Optimal designs for dose response curves with common parameters." Ann. Statist. 45 (5) 2102 - 2132, October 2017.


Received: 1 March 2016; Revised: 1 August 2016; Published: October 2017
First available in Project Euclid: 31 October 2017

zbMATH: 06821120
MathSciNet: MR3718163
Digital Object Identifier: 10.1214/16-AOS1520

Primary: 62K05
Secondary: 62F03

Keywords: $D$-optimal design , admissible design , different treatment groups , Loewner ordering , Nonlinear regression

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 5 • October 2017
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