The Annals of Applied Statistics

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

Holger Dette, Andrey Pepelyshev, and Tim Holland-Letz

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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.

Article information

Source
Ann. Appl. Stat., Volume 4, Number 3 (2010), 1430-1450.

Dates
First available in Project Euclid: 18 October 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1287409380

Digital Object Identifier
doi:10.1214/09-AOAS324

Mathematical Reviews number (MathSciNet)
MR2758335

Zentralblatt MATH identifier
1202.62101

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

Citation

Dette, Holger; Pepelyshev, Andrey; Holland-Letz, Tim. Optimal designs for random effect models with correlated errors with applications in population pharmacokinetics. Ann. Appl. Stat. 4 (2010), no. 3, 1430--1450. doi:10.1214/09-AOAS324. https://projecteuclid.org/euclid.aoas/1287409380


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