Optimal Design In Population Pharmacokinetics
France Mentre, Alain Mallet
INSERM U436, Dpt de Biostatistiques et Informatique Medicale,CHU Pitie-Salpetriere, 91 Bd de l'Hopital, 75013 Paris, France
The accuracy of the estimator of pharmacokinetic parameters using standard nonlinear regression is related to the experimental design. Many developments were made for estimation of optimal designs in nonlinear regression using the inverse of the Fisher information matrix as an estimate of the estimation variance. The D-optimality criterion which leads to maximization of the determinant of the information matrix has been mainly used.
When random effect models are studied, that is to say when the parameters of the regression model are assumed to be random in the population, the problem is to design an experiment for estimating the distribution of the parameters, from a set of individual measurements in a sample of subjects. The îpopulation design" is defined by individual designs (number and date of samples within an individual) to be performed in group of subjects. For a given maximal cost for the experiment, one should find the optimal population design.
When a parametric distribution is assumed, the optimality criteria for the population design should be associated with increasing the accuracy of the estimation of the population parameters. In population pharmacokinetics several simulations studies were performed to compare designs using NONMEM for analyzing the data; their results are briefly reviewed.
We have proposed an approach using the D-optimality criteria on the Fisher information matrix of the population characteristics. We have developed this criteria for the mean and variance of a gaussian distribution using a first-order linearization of the model around the mean. An optimisation method has also been proposed to find the optimal population design given a set of sampling times and a maximal cost for the experiment (often the total number of samples). Constraints on the individual designs can be taken into account.
Therefore it is now possible to compare several population designs and/or to find optimal population design without using extensive simulations. Several examples from real pharmacokinetic data in different settings are presented. The obtained results on these examples illustrated that optimal population designs may differ from standard intuitive ones but are often based on standard D-optimal sampling times. Several statistical developments of this method are presently ongoing.