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

TL;DR

This paper develops a new approach for designing optimal experiments in population pharmacokinetics using random effect models with correlated errors, improving efficiency over traditional uncorrelated assumptions.

Contribution

It introduces an asymptotic method to determine optimal design densities accounting for correlation, enhancing design efficiency in nonlinear mixed models.

Findings

Asymptotic designs are highly efficient compared to exact designs.

Correlated error models improve estimation accuracy over uncorrelated assumptions.

Naively chosen designs like equal spacing can be suboptimal.

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.