Optimal designs for random effect models with correlated errors with applications in population pharmacokinetics

Dette, Holger, Pepelyshev, Andrey ORCID: https://orcid.org/0000-0001-5634-5559 and Holland-Letz, Tim 2010. Optimal designs for random effect models with correlated errors with applications in population pharmacokinetics. The Annals of Applied Statistics 4 (3) , pp. 1430-1450. 10.1214/09-AOAS324

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Abstract

We consider the problem of constructing optimal designs for population pharmacokinetics which use random effect models. It is common practice in the design of experiments in such studies to assume uncorrelated errors for each subject. In the present paper a new approach is introduced to determine efficient designs for nonlinear least squares estimation which addresses the problem of correlation between observations corresponding to the same subject. We use asymptotic arguments to derive optimal design densities, and the designs for finite sample sizes are constructed from the quantiles of the corresponding optimal distribution function. It is demonstrated that compared to the optimal exact designs, whose determination is a hard numerical problem, these designs are very efficient. Alternatively, the designs derived from asymptotic theory could be used as starting designs for the numerical computation of exact optimal designs. Several examples of linear and nonlinear models are presented in order to illustrate the methodology. In particular, it is demonstrated that naively chosen equally spaced designs may lead to less accurate estimation.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Random effect models; nonlinear least squares estimate; correlated observations; compartmental models; asymptotic optimal design density
Additional Information:	Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/1932-6157/ (accessed 28/02/2014).
Publisher:	Institute of Mathematical Statistics
ISSN:	1932-6157
Date of First Compliant Deposit:	30 March 2016
Last Modified:	11 May 2023 05:55
URI:	https://orca.cardiff.ac.uk/id/eprint/49047

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