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# Optimal designs for dose-response models with restricted design spaces

Biedermann, Stefanie, Dette, Holger and Zhu, Wei (2006) Optimal designs for dose-response models with restricted design spaces. Journal of the American Statistical Association, 101 (474), 747-759.

Record type: Article

## Abstract

In dose-response studies, the dose range is often restricted due to concerns over drug toxicity and/or efficacy. We derive optimal designs for estimating the underlying dose-response curve for a restricted or unrestricted dose range with respect to a broad class of optimality criteria. The underlying curve belongs to a diversified set of link functions suitable for the dose response studies and having a common canonical form. These include the fundamental binary response models -- the logit and the probit as well as the skewed versions of these models. Our methodology is based on a new geometric interpretation of optimal designs with respect to Kiefer's $\Phi_p$-criteria in regression models with two parameters, which is of independent interest. It provides an intuitive illustration of the number and locations of the support points of $\Phi_p$-optimal designs. Moreover, the geometric results generalize the classical characterization of $D$-optimal designs by the minimum covering ellipsoid [see Silvey (1972) or Sibson (1972)] to the class of Kiefer's $\Phi_p$-criteria. The results are illustrated through the re-design of a dose ranging trial.

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Published date: 1 June 2006
Keywords: Binary response model, Dose ranging, Dose-response, Dual problem, Link function, Locally compound optimal design, Minimum ellipse
Organisations: Statistics

## Identifiers

Local EPrints ID: 41816
URI: http://eprints.soton.ac.uk/id/eprint/41816
ISSN: 0162-1459
PURE UUID: 6bbb4968-ff38-432c-a621-c1d14f032046
ORCID for Stefanie Biedermann: orcid.org/0000-0001-8900-8268

## Catalogue record

Date deposited: 05 Oct 2006

## Contributors

Author: Holger Dette
Author: Wei Zhu