Journées MAS et Journée en l'honneur de Jacques Neveu

31 août - 3 septembre 2010 à Bordeaux

Marc Lavielle (INRIA Saclay)

The SAEM algorithm: a powerful stochastic algorithm for population pharmacology modeling transparents

In order to evaluate a drug's impact, trial researchers must confront the need to model biological phenomena that evolve over time and present a high level of inter-individual variability. These highly variable systems are depicted by so called non-linear mixed effect models, often defined by systems of differential equations and for which it is particularly hard to estimate their numerous parameters. For 30 years now, pharmacologists wanting to interpret their clinical trials in preparation for market release applications have been using software programs that employ model linearization. This solution, however, raises major practical problems.

The SAEM algorithm is a stochastic approximation version of the EM algorithm for maximum likelihood estimation in the context of incomplete data models. During the last years, this stochastic algorithm has demonstrated very good practical properties for many complex applications in the framework of non-linear mixed effect models: pharmacokinetics-pharmacodynamics, viral dynamics, glucose-insulin, epilepsy. SAEM combined with MCMC and Simulated Annealing is few sensitive to the initial guess and it is fast.

SAEM was first implemented in the MONOLIX software (http://software.monolix.org). Having started out initially just as a modest piece of code, MONOLIX has developed significantly over the years and is now widely used both by people in academic research as well as those in the industry itself. Furthermore, SAEM now becomes a reference algorithm in the field of population pharmacology modeling. This stochastic algorithm is now available in NONMEM (the gold standard in this field) and was recently implemented in Matlab.

I will present in this talk several extensions of the SAEM algorithm for complex models: mixed models defined with ordinary or stochastic
differential equations, mixed hidden Markov models.