The SAEM algorithm and its implementation in MONOLIX 2.1
M. Lavielle (1,2), H. Mesa (3,2), F. Mentrť (4,5)
(1) INRIA Futurs, Paris, France; (2) University Paris 5, Paris, France. (3) University of La Habana, Cuba. (4) INSERM, U738, Paris, France ; (5) Universitť Paris 7, Paris, France ; AP-HP, HŰpital Bichat, Paris, France.
Introduction: The statistical model for most population PK/PD analyses is the nonlinear-mixed effects model (NLMEM). As opposed to linear models, there are statistical issues to express the optimisation criteria for these nonlinear models so that first approximation methods (FO and FOCE) based on linearization of the model were proposed. It is well known that these methods have several methodological and theoretical drawbacks. They are also very sensitive to initial estimates which make lot's of run to failed to converge with a waste of time for the modeller. Population analyses are now used not only to provide mean estimates but also to make model selection, hypothesis testing, simulations and predictions based on all the estimated components: better estimation methods are therefore needed.
The SAEM (Stochastic Approximation EM) algorithm avoids any linearization and is based on recent statistical algorithms. This algorithm is a powerful tool for Maximum Likelihood Estimation (MLE) for very general incomplete data models. The convergence of this algorithm to the MLE and its good statistical properties have been proven. The SAEM algorithm is implemented in the free MONOLIX software that can be downloaded at http://www.monolix.org. It is possible to download the full Matlab version of MONOLIX 2.1 and/or only a compiled version of the software that does not require Matlab.
Objectives: 1) To present the new release of MONOLIX (version 2.1); 2) To illustrate the estimation capabilities of the algorithm on some difficult examples; 3) To discuss how MONOLIX could be extended to other incomplete data problems
1) Version 2.1 of MONOLIX has major improvement compare to the previous one: a) a library of PK and PD models, some defined with differential equations, b) ability to deal with data below limit of quantification, c) lot's of interactive graphical outputs...
2) This version of MONOLX was tested on several data sets. For some of which it was difficult to get the FOCE algorithm to converge (models with Michaelis-Menten elimination and multiple doses, models with lag time, etc...). Results and demonstrations will be presented.
3) The SAEM algorithm can handle very general non linear mixed effect models:
- left-censored data,
- models defined by stochastic differential equations,
- multi-responses models,
- mixtures of distributions,
- inter-occasion variability,
- missing covariates,
- time to event data,
- count data,
Indeed, all these models are statistical models that include a set of observations and a set of non observed data. SAEM requires the computation of the conditional distribution of these non observed data and their simulation at each iteration. Some of these models are already implemented in version 2.1 of the MONOLIX software and other extensions will be discussed.
Acknowledgements: Version 2.1 of MONOLIX was developed with the financial support of Johnson & Johnson Pharmaceutical Research & Development, a Division of Janssen Pharmaceutica N.V.