**Analysing population PK/PD data with the MONOLIX software**

Lavielle, Marc (1,2,3) Hector Mesa (1) Julie Bertand (4) Adeline Samson (4) France Mentré (4) and the Monolix group

(1) University Paris 5, (2) University Paris 11, (3) INRIA Futurs, (4) INSERM U738

The software MONOLIX implements an algorithm for maximum likelihood estimation in nonlinear mixed effects models without linearization. This algorithm combines the SAEM (stochastic approximation version of EM) algorithm with a Markov Chain Monte Carlo procedure. The convergence of this algorithm and its good statistical properties have been proven and published in the best statistical journals [1,2]. The algorithm is fast and efficient in practice. It converges in situations where other reference methods (NONMEM, nlme,…) do not. Several blinded comparisons of the performances of different algorithms showed the very good properties of the SAEM algorithm [3].

The MONOLIX software was shown to be also useful for building the covariate model for the fixed effects and the covariance model for the random effects.

A first Matlab version of this software is available at http://www.math.u-psud.fr/~lavielle/monolix/logiciels.

We are now working on several extensions of the MONOLIX software within a research collaboration supported by *Johnson & Johnson Pharmaceutical R&D*. The aim of this scientific collaboration is

- to generate a library of PK and PK-PD models to make
*MONOLIX*more easy to apply - to extend the algorithm implemented in the
*MONOLIX*software for more complex models: models defined by differential equations (often in PD); correct handling of left-censored data, i.e. observations below the limit of quantification; modelling inter-occasion variability.

**References:**

[1] Kuhn E and Lavielle M. Maximum likelihood estimation in nonlinear mixed effects model, *Computational Statistics and Data Analysis*. 49 (2005), 1020--1038 [2] Delyon B, Lavielle M and Moulines E. Convergence of a stochastic approximation version of the EM algorithm. *Annals of Statistics*. 27 (1999), 94- 128.

[3] Girard P. A comparison of estimation methods in nonlinear mixed effects models using a blind analysis. *Fourteenth PAGE meeting.* (2005) Pamplona.