Geometric construction of optimal design for dose-response models with two parameters
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Date
2005
Journal Title
Journal ISSN
Volume Title
Publisher
Universität Dortmund
Abstract
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 Φ_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 Φ_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 Φ_p-criteria. The results are illustrated through the re-design of a dose ranging trial.
AMS Classification: 62K05, 62J12
Description
Table of contents
Keywords
binary response model, dose ranging, dose-response, dual problem, link function, locally compound optimal design, minimum ellipse