**Optimization of sampling times for PK/PD models: approximation of elemental Fisher information matrix**

Valerii V. Fedorov, Sergei L. Leonov

GlaxoSmithKline, Collegeville, U.S.A.

**Introduction:** Optimal design of population PK and PD studies has seen an increasing interest over the last decade. In 2006, an annual Population Optimum Design of Experiments (PODE) workshop was initiated on the theory of optimal experimental design for nonlinear mixed effects models and its applications in drug development; see http://www.maths.qmul.ac.uk/~bb/PODE/PODE.html. A special session was organized at PODE 2007 to present different software tools for population PK/PD optimal designs. Presentations at this session were summarized at PAGE 2007 meeting, see Mentré et al. [3]; and a discussion of software tools continued at PODE 2009.

**Methods and Objectives:** The key component for constructing model-based optimal designs is the Fisher information matrix of a properly defined single observational unit; see Fedorov and Hackl [1]. In the context of PK/PD studies the elemental information matrix corresponds to a sequence of sampling times for an individual subject; e.g., see Gagnon and Leonov [2], Retout and Mentré [4]. In our presentation, we focus on certain options of calculating/approximating the information matrix which include different ways of modeling population variability; different orders of approximation of the mean response; regular scale of measurements vs log-scale for PK data.

**Results:** We present several examples, including (a) rather simple ones, where closed-form expressions may be obtained and, therefore, the comparison of different options becomes quite transparent, and (b) more complex models which are used in practice and which require Monte Carlo simulations to validate the results.

**References:**

[1] Fedorov VV, Hackl P. (1997), *Model-Oriented Design of Experiments*. Springer, NY.

[2] Gagnon R, Leonov S (2005). Optimal population designs for PK models with serial sampling, *J. Biopharm. Statist*., **15**(1), 143-163.

[3] Mentré F, Duffull S, Gueorguieva I, Hooker A, Leonov S, Ogungbenro K, Retout S (2007). Software for optimal design in population pharmacokinetics and pharmacodynamics: a comparison In: *Abstracts of the Annual Meeting of the Population Approach Group in Europe (PAGE)*. ISSN 1871-6032, http://www.page-meeting.org/?abstract=1179

[4] Retout S, Mentré F (2003). Further developments of the Fisher information matrix in nonlinear mixed effects models with evaluation in population pharmacokinetics, *J. Biopharm. Statist*., **13**(2), 209-227.