Marc Lavielle(1) and the Monolix research group(2)
(1) Université Paris-Sud, Bât 425, Equipe de Probabilités, Statistique et Modélisation, 91405 Orsay Cedex, France; (2) http://www.math.u-psud.fr/~lavielle/monolix
Stochastic Approximation EM (SAEM) is a powerful algorithm for maximum likelihood estimation in nonlinear mixed effects models [1-4]. This algorithm estimates the population parameters from pharmacokinetic (PK) or Pharmacodynamic (PD) data without any linearizing technique.
SAEM can handle covariates and nondiagonal covariance matrix for the random effects. The exact observed likelihood is very well estimated using an importance sampling Monte-Carlo scheme. Thus, Likelihood Ratio tests can be performed with accurate error probabilities. Standard errors of the estimated parameters are also computed without linearization.
We have implemented a rather generic version of SAEM in MATLAB. We have successfully used this method to analyze different sets of simulated and real clinical data. SAEM is fast in practice and converge in situations where other reference methods (NONMEM, nlme) do not.
References
[1] Delyon B, Lavielle M and Moulines E. Convergence of a stochastic approximation version of the EM algorithm. Annals of Statistics, 1999; 27:94-128
[2] Kuhn E and Lavielle M. Maximum likelihood estimation in nonlinear mixed-effects models. PAGE 2003 (oral communication)
[3] Kuhn E and Lavielle M. Coupling a stochastic approximation version of EM with an MCMC procedure. ESIAM in Probability and Statistics (to appear)
[4] Samson A, Lavielle M and Mentré F . Stochastic Approximation EM algorithm in nonlinear mixed effects models: an evaluation by simulation. PAGE 2004 (oral communication)
Reference: PAGE 13 (2004) Abstr 544 [www.page-meeting.org/?abstract=544]
Poster: poster