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September 2010 Optimal designs for random effect models with correlated errors with applications in population pharmacokinetics
Holger Dette, Andrey Pepelyshev, Tim Holland-Letz
Ann. Appl. Stat. 4(3): 1430-1450 (September 2010). DOI: 10.1214/09-AOAS324


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.


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Holger Dette. Andrey Pepelyshev. Tim Holland-Letz. "Optimal designs for random effect models with correlated errors with applications in population pharmacokinetics." Ann. Appl. Stat. 4 (3) 1430 - 1450, September 2010.


Published: September 2010
First available in Project Euclid: 18 October 2010

zbMATH: 1202.62101
MathSciNet: MR2758335
Digital Object Identifier: 10.1214/09-AOAS324

Keywords: asymptotic optimal design density , compartmental models , correlated observations , nonlinear least squares estimate , Random effect models

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.4 • No. 3 • September 2010
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