Geometric construction of optimal designs for dose-responsemodels with two parameters

Holger Dette, Stefanie Biedermann and Wei Zhu

No 2005,08, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

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 [Omega]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 [Omega]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 [Omega]p-criteria. The results are illustrated through the re-design of a dose ranging trial.

Keywords: Binary response model; Dose ranging; Dose-response; Dual problem; Link function; Locally compound optimal design; Minimum ellipse (search for similar items in EconPapers)
Date: 2005
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