France Mentré
INSERM U194, Dpt de Biostatistiques et Informatique Médicale, CHU Pitié-Salpétrière, 91 Bd de 1'Hôpital, 75013 Paris, France
It is well known in nonlinear regression that the accuracy of the estimator is related to the experimental design. The inverse of the Fisher information matrix is usually used as an estimate of the estimation variance, which is thrue only asymptotically for nonlinear models. Many developments were made for estimation of optimal designs using this matrix and the D-optimality criterion, which lead to the maximization of its determinant, 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, two specific problems arise in designing optimal experiments: designs for population analysis and Bayesian designs.
The first 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 problem is to define the number of subjects, the number of data points per subject and the individual designs to be performed given a maximal cost for the experiment. When a parametric distribution is assumed, a first goal can be defined as increasing the accuracy of the estimation of the population parameters. In population pharmacokinetics (PK) several simulations studies were performed to compare designs using NONMEM for analyzing the data; their results are briefly reviewed. A new approach, using the D-optimality criterion for the mean and variance of a Gaussian distribution is also presented. It is evaluated on a simple PK model using a first-order linearization of the model around the mean; results obtained using several settings are shown. Another goal, however, in finding optimal “population designs” is to increase the predictive ability of the estimated distribution when it is used as prior information for subsequent Bayesian analyses. Example of some evaluations of predictive performances on simulated data are presented and a possible new approach – the evaluation of the predictive distributions – is shown.
A second problem is to estimate optimal “Bayesian designs”. More specifically, assuming that the prior distribution is known and that Bayesian estimation of the parameters is scheduled, the problem is to define the individual design to be performed to increase the accuracy of the posterior estimates. The Bayes D-optimality criterion was defined for that problem but it was evaluated especially for linear models and Gaussian distributions. This criterion is based on an extension of the Fisher information matrix for random effect regression models. Some results using a simple PK model are presented and compared to the standard D-optimal designs. Another approach based on the Lindley information – which is related to the entropy of a distribution – is also presented. It is illustrated on a real example which concerns the kinetics of radioiodine for the treatment of Grave’s disease using a nonparametric discrete prior distribution. Other goals in defining “Bayesian designs” may be derived from utility functions based on the use of the posterior individual distributions for subsequent dosage optimization and not on the accuracy on the parameter’s estimates.
For both problems, some developments for linear models and Gaussian distributions have been performed but only few results in population pharmacokinetics of pharmacodynamics were obtained. Mainly because of the nonlinearity of the model, the proposed criteria have no analytical expression so that specific software must be developed to estimate the involved expectations using stochastic simulation. The presented results on simple examples, however, illustrate that optimal “population designs” or “Bayesian designs” may differ from the standard ones.
Reference: PAGE 2 () Abstr 913 [www.page-meeting.org/?abstract=913]
Poster: oral presentation