Optimal Design for Multivariate Response Pharmacokinetic Models

We address the problem of designing pharmacokinetic experiments in multivariate response situations. Criteria, based on the Fisher information matrix, whose inverse according to the Rao–Cramer inequality is the lower bound of the variance–covariance matrix of any unbiased estimator of the parameters, have previously been developed for univariate response for an individual and a population. We extend these criteria to design individual and population studies where more than one response is measured, for example, when both parent drug and metabolites are measured in plasma, multi-compartment models, where measurements are taken at more than one site, or when drug concentration and pharmacodynamic data are collected simultaneously. We assume that measurements made at distinct times are independent, but measurements made of each concentration are correlated with a response variance–covariance matrix. We investigated a number of optimisation algorithms, namely simplex, exchange, adaptive random search, simulated annealing and a hybrid, to maximise the determinant of the Fisher information matrix as required by the D-optimality criterion. The multiresponse optimal design methodology developed was applied in two case studies, where the aim was to suggest optimal sampling times. The first was a restrospective iv infusion experiment aimed to characterise the disposition kinetics of tolcapone and its two metabolites in healthy volunteers. The second was a prospective iv bolus experiment designed to estimate the tissue disposition kinetics of eight beta-blockers in rat.