Section: New Results

Estimation in mixtures of models

Participant : Marc Lavielle.

We have proposed an improved SAEM algorithm for maximum likelihood estimation in mixtures of non linear mixed effects models. This involves a new methodology for maximum likelihood estimation in mixtures of non linear mixed effects models (NLMEM). Such mixtures of models include mixtures of distributions, mixtures of structural models and mixtures of residual error models. Since the individual parameters inside the NLMEM are not observed, we have proposed to combine the EM algorithm usually used for mixtures models when the mixture structure concerns an observed variable, with the Stochastic Approximation EM (SAEM) algorithm, which is known to be suitable for maximum likelihood estimation in NLMEM and also has nice theoretical properties. The main advantage of this hybrid procedure is to avoid a simulation step of unknown group labels required by a “full” version of SAEM. The resulting MSAEM (Mixture SAEM) algorithm is now implemented in the Monolix software. We have also proposed several criteria for classification of subjects and estimation of individual parameters. Our numerical experiments on simulated data have shown that MSAEM performs well in a general framework of mixtures of NLMEM. Indeed, MSAEM provides an estimator close to the maximum likelihood estimator in very few iterations and is robust with regards to initialization. Our application of the method to pharmacokinetic (PK) data demonstrated the potential of the method for practical applications.