France Mentré
INSERM U194, Dpt de Biostatistiques et Informatique Médicale, CHU Pitié-Salpétrière, 91 Bd de 1'Hôpital, 75013 Paris, France
Introduction
- General considerations on the accuracy of estimators in nonlinear regression, on the Fisher information matrix and D-optimality.
- Extension to optimization of population designs or Bayesian designs
- Optimal design for population analysis
Description of the problem: choice of the number of subjects, number of data points per subject, and individual designs for estimation of the distribution of the parameters.
First goal: increase the accuracy of the estimation, that is to say for parametric distributions, increase the accuracy of the estimates of means and variances
- examples of simulation in population pharmacokinetics
- some results in linear random effect model
- a new approach (which used the NPML algorithm) for linearized models and gaussian distributions, with simulation for simple PK or PD models
Other goal: increase the predictive ability of the distribution as prior information for subsequent Bayesian analysis
- example of some evaluation of predictive performance
- a possible new approach: the evaluation of the predictive distributions for several designs
Bayesian design
Description of the problem: when the prior distribution is known and Bayesian estimation is scheduled, what individual design should be performed to increase the accuracy of the posterior estimates ?
- limitations of D-optimality for that problem
- Bayes-D optimality for linear models and gaussian distributions
- extension of the Fisher information matrix for nonlinear random effect models
- some simulated examples for simple PK, PD models
- another approach: the Lindley information – related to the entropy of a distribution
- illustration on a real example of the kinetics of radioiodine for treatment of Grave’s disease
Future: use utility functions based on the use of the posterior distribution for subsequent dosage optimization and not on the accuracy on the parameter’s estimates.
Conclusion
- Some works for linear models and Gaussian distribution
- Few applications in pop PK/PD
- Most of the time no analytical solutions : specific software to be proposed
Reference: PAGE 2 (1993) Abstr 914 [www.page-meeting.org/?abstract=914]
Poster: oral presentation