# 2002

Paris, France

**Optimisation Of Individual And Population Pharmacokinetic Designs Using S-Plus**

Sylvie Retout, France Mentré

Dpt de Biostatistiques et d'Epidemiologie, INSERM U436, CHU Bichat, Paris, France

An approach based on the Fisher information matrix for non linear mixed effects models, implemented in a generic Splus function PFIM (Population Fisher Information Matrix), is now available to evaluate the expected standard errors of estimation and to compare directly designs in the context of population PK or PD studies [1-2]. Population designs are defined as a set of elementary designs to be performed in a number of subjects, each one composed of several sampling times. The usefulness of this approach compared to extensive simulations was shown [3]. We now address the problem of designs optimisation using Splus.First, we developed an Splus function IFIM (Individual Fisher Information Matrix): this function evaluates and optimises individual designs in nonlinear regression, using either a Simplex algorithm, as in the ADAPT software [4], or ‘nlmin’, a minimisation function of Splus based on the quasi-Newton algorithm. Comparison to the results provided by ADAPT shows the relevance of IFIM either for an homoscedastic or an heteroscedastic variance error model. Second, we extended PFIM for optimisation of population designs. We tested the performance of the Simplex and the ‘nlmin’ function, using the example of a one compartment model, with three parameters: volume, rate constant of absorption and rate constant of elimination. The random effects are modelled exponentially and the variance error model is homoscedastic. Different designs, all with a total number of 180 samples, are optimised: first, a design with the same elementary design with three sampling times, to be repeated in 90 subjects; second, a population design composed of three elementary designs each with two sampling times to be repeated in 30 subjects; third the same previous design including in addition the optimisation of the proportion of subjects to be allocated to each elementary design. For each case, the designs optimised with the Simplex algorithm are similar to those optimised using the ‘nlmin’ function. Relevance of the optimisation is shown by comparison to a grid research computed for this example on the first optimised population design. This study confirms that the inclusion of a Simplex algorithm or of the ‘nlmin’ function in IFIM / PFIM gives new efficient Splus tools to the pharmacologist to optimise individual or population designs.

[1] Retout S, Duffull S, Mentré F. Development and implementation of the population Fisher information matrix for evaluation of population pharmacokinetics designs. Comput Meth Prog Biomed, 2001, 65:141-51.

[2] http://hermes.biomath.jussieu.fr/pfim.htm

[3] Retout S, Bruno R, Mentré F. Fisher information matrix for non linear mixed- effects models: evaluation and application for optimal design of enoxaparin population pharmacokinetics. Stat Med, 2002, in press.

[4] D’Argenio DZ, Schumitzky A. ADAPT II User’s Guide: Pharmacokinetic / Pharmacodynamic Systems Analysis Software. Biomedical Simulations Resource, Los Angeles, 1997.