Performance in population models for count data, part II: a new SAEM algorithm.

International audienceAnalysis of count data from clinical trials using mixed effect analysis has recently become widely used. However, algorithms available for the parameter estimation, including LAPLACE and Gaussian quadrature (GQ), are associated with certain limitations, including bias in parameter estimates and the long analysis runtime. The stochastic approximation expectation maximization (SAEM) algorithm has proven to be a very efficient and powerful tool in the analysis of continuous data. The aim of this study was to implement and investigate the performance of a new SAEM algorithm for application to count data. A new SAEM algorithm was implemented in MATLAB for estimation of both, parameters and the Fisher information matrix. Stochastic Monte Carlo simulations followed by re-estimation were performed according to scenarios used in previous studies (part I) to investigate properties of alternative algorithms (Plan et al., 2008, Abstr 1372 [ http://wwwpage-meetingorg/?abstract=1372 ]). A single scenario was used to explore six probability distribution models. For parameter estimation, the relative bias was less than 0.92% and 4.13% for fixed and random effects, for all models studied including ones accounting for over- or under-dispersion. Empirical and estimated relative standard errors were similar, with distance between them being <1.7% for all explored scenarios. The longest CPU time was 95 s for parameter estimation and 56 s for SE estimation. The SAEM algorithm was extended for analysis of count data. It provides accurate estimates of both, parameters and standard errors. The estimation is significantly faster compared to LAPLACE and GQ. The algorithm is implemented in Monolix 3.1, (beta-version available in July 2009)

A statistical approach for array CGH data analysis

BACKGROUND: Microarray-CGH experiments are used to detect and map chromosomal imbalances, by hybridizing targets of genomic DNA from a test and a reference sample to sequences immobilized on a slide. These probes are genomic DNA sequences (BACs) that are mapped on the genome. The signal has a spatial coherence that can be handled by specific statistical tools. Segmentation methods seem to be a natural framework for this purpose. A CGH profile can be viewed as a succession of segments that represent homogeneous regions in the genome whose BACs share the same relative copy number on average. We model a CGH profile by a random Gaussian process whose distribution parameters are affected by abrupt changes at unknown coordinates. Two major problems arise : to determine which parameters are affected by the abrupt changes (the mean and the variance, or the mean only), and the selection of the number of segments in the profile. RESULTS: We demonstrate that existing methods for estimating the number of segments are not well adapted in the case of array CGH data, and we propose an adaptive criterion that detects previously mapped chromosomal aberrations. The performances of this method are discussed based on simulations and publicly available data sets. Then we discuss the choice of modeling for array CGH data and show that the model with a homogeneous variance is adapted to this context. CONCLUSIONS: Array CGH data analysis is an emerging field that needs appropriate statistical tools. Process segmentation and model selection provide a theoretical framework that allows precise biological interpretations. Adaptive methods for model selection give promising results concerning the estimation of the number of altered regions on the genome

Rôle et limites de la statistique dans l'évaluation des risques sanitaires liés aux OGM

International audienceLes plantes génétiquement modifiées (PGM) sont des variétés de plantes modifiées génétiquement par l'ajout d'un gène leur conférant, par exemple, une résistance à des insectes nuisibles comme la pyrale du maïs, où une résistance à un herbicide comme le glyphosate. La culture et l'importation des OGM font l'objet d'un cadre réglementaire européen. Toute demande d'autorisation de mise sur le marché qu'un industriel soumet doit être accompagnée d'éléments scientifiques permettant de caractériser le produit et de prouver qu'il répond aux exigences de la réglementation européenne, souveraine en la matière. Plus précisément, le pétitionnaire doit produire différentes études afin de démontrer que son nouveau produit présente des propriétés semblables à une plante non génétiquement modifiée, en termes de composition, de propriétés agronomiques, d'alimentarité, de toxicité, d'allergénicité ou encore de risque environnemental. Depuis 2003, l'Autorité européenne de sécurité des aliments (EFSA) chargée de ce dossier, offre la possibilité aux Etats membres d'évaluer les dossiers. En France, l'Agence nationale de sécurité sanitaire de l'alimentation, de l'environnement et du travail (Anses) et le Haut Conseil des Biotechnologies (HCB) interviennent dans ce cadre. L'Anses se prononce essentiellement sur les aspects de sécurité sanitaire des OGM tandis que le HCB émet principalement des avis sur les aspects environnementaux et de composition des OGM

Between-Subject and Within-Subject Model Mixtures for Classifying HIV Treatment Response

We present a method for using longitudinal data  to classify individuals into clinically-relevant population subgroups. This is achieved by treating ``subgroup'' as a categorical covariate whose value is unknown for each individual, and predicting its value using mixtures of models that represent ``typical'' longitudinal data from each subgroup.  Under a nonlinear mixed effects model framework, two types of model mixtures are presented, both of which have their advantages. Following illustrative simulations, longitudinal viral load data for HIV-positive patients is used to predict whether they are responding -- completely, partially or not at all -- to a new drug treatment

Using penalized contrasts for the change-point problem

A methodology for model selection based on a penalized contrast is developed. This methodology is applied to the change-point problem, for estimating the number of change points and their location. We aim to complete previous asymptotic results by constructing algorithms that can be used in diverse practical situations. First, we propose an adaptive choice of the penalty function for automatically estimating the dimension of the model, that is, the number of change points. In a Bayesian framework, we define the posterior distribution of the change-point sequence as a function of the penalized contrast. MCMC procedures are available for sampling this posterior distribution. The parameters of this distribution are estimated with a stochastic version of EM algorithm (SAEM). An application to EEG analysis and some Monte-Carlo experiments illustrate these algorithms

Genetic analysis of growth curves using the SAEM algorithm

The analysis of nonlinear function-valued characters is very important in genetic studies, especially for growth traits of agricultural and laboratory species. Inference in nonlinear mixed effects models is, however, quite complex and is usually based on likelihood approximations or Bayesian methods. The aim of this paper was to present an efficient stochastic EM procedure, namely the SAEM algorithm, which is much faster to converge than the classical Monte Carlo EM algorithm and Bayesian estimation procedures, does not require specification of prior distributions and is quite robust to the choice of starting values. The key idea is to recycle the simulated values from one iteration to the next in the EM algorithm, which considerably accelerates the convergence. A simulation study is presented which confirms the advantages of this estimation procedure in the case of a genetic analysis. The SAEM algorithm was applied to real data sets on growth measurements in beef cattle and in chickens. The proposed estimation procedure, as the classical Monte Carlo EM algorithm, provides significance tests on the parameters and likelihood based model comparison criteria to compare the nonlinear models with other longitudinal methods

An improved SAEM algorithm for maximum likelihood estimation in mixtures of non linear mixed effects models

International audienceWe propose 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 propose 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. Several criteria for classification of subjects and estimation of individual parameters are also proposed. Numerical experiments on simulated data show 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 regard to initialization. An application to pharmacokinetic (PK) data demonstrates the potential of the method for practical applications