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. (doi:10.1198/016214505000001087).

Download

[img]
Preview
Postscript
Download (1719Kb)

Description/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.

Item Type: Article
ISSNs: 0162-1459 (print)
Related URLs:
Keywords: Binary response model; Dose ranging; Dose-response; Dual problem; Link function; Locally compound optimal design; Minimum ellipse
Subjects: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Statistics
ePrint ID: 41816
Date Deposited: 05 Oct 2006
Last Modified: 27 Mar 2014 18:26
URI: http://eprints.soton.ac.uk/id/eprint/41816

Actions (login required)

View Item View Item

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics