M. Tod(1) and Jean-Marie Rocchisani(2)
Department de pharmatoxicologie, Hopital Avicenne, Bobigny cedex, France(1)
Service de medicine nucleaire, Hopital Avicenne, Bobigny cedex, France(2)
The most common approach to optimize the sampling schedule in parameter estimation experiments is the D-optimaly criterion, which consists in maximizing the determinant of the Fischer information matrix (max det F). In order to incorporate prior parameter uncertainty in the optimal design, other criteria have been proposed: The ED = max E (det F), EID = min E (1/detF) and API = max E (Log det F) criteria, where the expectation is with respect to the given prior distribution of the parameters. However, respective merits of these criteria and application to real data have not been evaluated. We implemented an algorithm based on random search RS followed by stochastic gradient SG to determine optimal sampling times for parameter estimation in varied pharmacokinetic models. Prior distributions are allowed to be uniform, normal or lognormal. This algorithm combines the robustness of ARS and the speediness of SG (convergence is obtained in a few minutes on a microcomputer). The algorithm has been validated by comparison to the results described by D'Argenio on one compartment model with first-order absorption. Also, the CPU time needed by the SG algorithm and the adaptive RS algorithm used by D'Argenio were compared and the former proved to be much faster. Then, is has been applied to a five parameters stochastic model with zero-order absorption rate and Weibull-distributed residence times which was shown to describe adequately the kinetics of metacycline in humans. Population pharmacokinetic parameters of metacycline were estimateds from a 6 subjects pilot study, by the iterative two-stage method, using ADAPT II repeatedly. Optimal sampling times were determined with each criterion (ED, EID, API) with a multivariate normal prior parameter distribution. Six to seven distinct sampling times could be estimated. Higher numbers of samples revealed coalescing of design points.
Key words: Optimal design - Adaptive random search - Stochastic gradient - ED, EID, API criteria - Population pharmacokinetics.