Y. Merlé and F. Mentré
INSERM U194, GERC, Service d'lnformatique Médicale, CHU Pitié-Salpêtrière, 75013 Paris
Once a parameter distribution of a pharmacokinetic or a pharmacodynamic model has been estimated in a given population a Bayesian approach may then be used to perform the estimation of the parameters for a new individual from only a few measurements. Many therapeutic applications of this approach, have been proposed to individualize dosages of various drug regimens and have been implemented in Bayesian forecasting programs. The accuracy of the parameter estimation for a new patient clearly depends on the design of the experiment (i.e., sampling times, administered doses…). Several approaches to optimizing experimental design for standard individual parameter estimation have been proposed. The principle of these methods is to optimize a criterion with respect to design variates. The most used of these criterions is the D-optimality, namely the determinant of the Fisher information matrix, which depends on the parameter to be estimated for non-linear models.
Bayesian forecasting programs often involve modules for designing experiments. The latter generally compute the D-optimal design for the mean of the prior distribution. This approach is easy to implement but exhibits some deficiencies. Thus, the design obtained from this approach will be optimal only if the individual parameters are equal to the mean of the prior distribution. In addition the D-optimal design criterion has not been developed in a Bayesian estimation context but in a standard one; consequently it is not defined if the number of measurements is lower than the number of parameters to estimate. Furthermore, this approach does not take into account all the characteristics of the parameter distribution.
The determinant of the Bayesian information matrix, also called Bayes D-optimality, has been proposed as a Bayesian design criterion. It incorporates prior knowledge for both estimation and design procedures. Unfortunately, for continuous prior distributions and non-linear models with respect to the parameters the computation of this criterion is rather difficult because it has no analytical expression. Therefore it has rarely be used up to now for planning experiments in the area of pharmacodynamics and pharmacokinetics.
In this work an approach for simplifying the computation of this Bayesian design criterions for non-linear models and continuous prior distributions is firstly proposed. This approach relies on the discretization of the prior distribution. This method is applied to design experiments for estimating the parameters of two models usually encountered in the area of pharmacokinetics and pharmacodynamics: the one compartment open model with bolus intravenous injection-single dose and the Emax model. The prior parameter distribution is supposed to be gaussian and the measurement error either homoscedastic or heteroscedastic. Our attention is restricted to designs with limited number of measurements (one or two), that often occurs in practice when Bayesian estimations are performed. The optimal experiments obtained from the determinant of the Bayesian information matrix for various combinations of the variances of the parameters and of the measurement error were compared to those provided by standard approaches.
Our results show that the Bayesian D-optimal designs may be different from those obtained by the D-optimality for the mean parameters. Particularly, in some cases, the measurements must be repeated. General principles for Bayesian design of experiments can be drawn from this study. The results also show that the discretization procedure considerably simplify the computation of the Bayesian D-optimality criterion. In addition this approach could be employed for the computation of other proposed Bayesian designs criterions. Therefore they should be used for designing experiments and incorporated in packages of Bayesian forecasting programs.
Reference: PAGE 3 (1994) Abstr 871 [www.page-meeting.org/?abstract=871]
Poster: oral presentation