The Annals of Statistics

Optimal designs for dose response curves with common parameters

Chrystel Feller, Kirsten Schorning, Holger Dette, Georgina Bermann, and Björn Bornkamp

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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.

Article information

Ann. Statist., Volume 45, Number 5 (2017), 2102-2132.

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K05: Optimal designs
Secondary: 62F03: Hypothesis testing

Admissible design different treatment groups $D$-optimal design Loewner ordering nonlinear regression


Feller, Chrystel; Schorning, Kirsten; Dette, Holger; Bermann, Georgina; Bornkamp, Björn. Optimal designs for dose response curves with common parameters. Ann. Statist. 45 (2017), no. 5, 2102--2132. doi:10.1214/16-AOS1520.

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Supplemental materials

  • Supplement to “Optimal designs for dose response curves with common parameters”. This supplement file contains the additional proofs omitted in the main paper and some additional comments on the derivation of the candidate models considered in Section 5.