Incorporating Correlation in Interindividual Variability for the Optimal Design of Multiresponse Pharmacokinetic Experiments

Abstract

This paper presents a method for optimal design of multiresponse population pharmacokinetic experiments taking into account correlations between interindividual variances. Expressions for the population Fisher information matrix have been defined for uniresponse and multiresponse pharmacokinetic experiments. A major assumption often made is that the variance–covariance matrix of the interindividual variance components has only diagonal elements so that whenever intersubject covariance elements are present, they are ignored during the design of the experiment. Recently expressions that accounted for these off diagonal elements were developed for uniresponse population pharmacokinetic experiments. The work presented here extends these expressions to multiresponse population pharmacokinetic experiments. These were applied to a population pharmacokinetic model, a population pharmacokinetic–pharmacodynamic model, and a parent–metabolite pharmacokinetic model example. The results obtained showed that optimal designs are different with diagonal omega matrix and full omega matrix and ignoring the off diagonal elements can lead to a design that produces more biased and less precise parameter estimates compared to a design that includes the off diagonal elements. The results also showed correlation between residual components of the responses has an effect on the optimal design.

Key Words:

• D-optimality
• Fisher information matrix
• Multiresponse
• Optimal design
• Pharmacodynamics
• Population pharmacokinetics

ACKNOWLEDGMENTS

The corresponding author was supported by Hoffman-La Roche and the research was sponsored by the Centre for Applied Pharmacokinetic Research (CAPKR is supported by the following consortium members; Eli Lilly, GlaxoSmithKline, Novartis, Pfizer and Servier).