M. Tod
Dpt of Pharmacotoxicology, Avicenne Hospital, Bobigny, France
The design of a population pharmacokinetics study can be optimized to improve the accuracy and the precision of hyperparameter (y) estimates. To date, the simulation approach has been used for this purpose. However, approaches based on the Fisher information matrix for y (PF matrix), analagous to the D-optimality criterion, are attractive, since PF-1 is the lower bound of the covariance matrix of any unbiased estimator of y.
The expectation of the determinant of PF-1 (EID criterion) is proposed to evaluate and optimize designs for the estimation of population pharmacokinetic parameters. Given a pharmacokinetic model, a measurement error model, a parametric distribution of the parameters and a prior distribution representing the belief about the hyperparameters to be estimated, the EID criterion is minimized in order to find the optimal population design. In this approach, a group is defined as a number of subjects to whom the same sampling schedule (i.e., the number of samples and their timing) is applied. The constraints, which are defined a priori, are the number of groups, the size of each group and the number of samples per subject in each group. The goal of the optimization is to determine the optimal sampling times in each group.
As an exemple, this criterion has been applied to a one-compartment open model with first-order absorption. The error model is either homoscedastic or heteroscedastic with constant coefficient of variation. Individual parameter are assumed to arise from a lognormal distribution with mean vector M and covariance matrix C. Uncertainties about the M and C are accounted for by a prior distribution which is normal for M and Wishart for C. Sampling times are optimized by using a stochastic gradient algorithm. Influence of the number of different sampling schemes, the number of subjects per sampling schedule, the number of samples per subject in each sampling scheme, the uncertainties on M and C and the assumption about the error model and the dose have been investigated.
Finally, some general conclusions regarding the properties of individual and population D- or EID-optimal times will be discussed, as well as the potential benefit of design optimization with respect to the ultimate goals of a population analysis.
Reference: PAGE 8 (1999) Abstr 138 [www.page-meeting.org/?abstract=138]
Poster: oral presentation