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

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)

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

Estimação e diagnóstico em modelos multivariados para dados censurados

Orientadores: Víctor Hugo Lachos Dávila, Luis Mauricio Castro CeperoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: Em alguns ensaios clínicos da síndrome da imunodeficiência adquirida (AIDS), as medições dos ácidos ribonucleicos do vírus da imunodeficiência humana (HIV-1) são coletadas periodicamente ao longo do tempo e muitas vezes estão sujeitas a limites de detecção inferiores ou superiores, dependendo dos ensaios de quantificação que foram utilizados. Assim, estas respostas podem ser censuradas à esquerda ou à direita. Na prática, dados longitudinais provenientes de estudos de acompanhamento do HIV, podem ser modelados utilizando modelos lineares e não-lineares de efeitos mistos censurados e também modelos de regressão censurados com estruturas de correlação específicas sobre os erros. Uma complicação adicional surge quando duas ou mais variáveis respostas são coletadas de forma irregular e repetidamente em cada sujeito durante um certo período de tempo. Os modelos lineares multivariados de efeitos mistos com respostas censuradas são ferramentas bastante utilizadas para análise conjunta de mais de uma série de respostas de dados longitudinais. Nesta tese desenvolvemos métodos inferenciais para lidar com dados censurados com estrutura longitudinal sob uma perspectiva clássica. Como resultado, conclusões importantes foram obtidas a partir da análise dos modelos propostosAbstract: In some acquired immunodeficiency syndrome (AIDS) clinical trials, the human immunodeficiency virus-1 ribonucleic acid measurements are collected irregularly over time and are often subject to some upper and lower detection limits, depending on the quantification assays. Hence, these responses are either left- or right-censored. In practice, longitudinal data coming from those follow-up studies can be modelled using censored linear and nonlinear mixed-effects models and also censored regression models with a specific correlation structures on the error terms. A complication arises when more than one series of responses are repeatedly collected on each subject at irregularly occasions over a period of time. The multivariate censored linear mixed model is a frequently used tool for a joint analysis of more than one series of longitudinal data. In this thesis we develop a series of essays in which different models and techniques to deal with censored data are applied. As result, we had several works to carry out censored dataDoutoradoEstatisticaDoutora em Estatística2011/22063-9, 2015/05385-3FAPES

Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation–Maximization (SAEM) Algorithm

The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation–maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed

Restricted maximum likelihood estimation in generalized linear mixed models

Restricted maximum likelihood (REML) estimation is a widely accepted and frequently used method for fitting linear mixed models, with its principal advantage being that it produces less biased estimates of the variance components. However, the concept of REML does not immediately generalize to the setting of non-normally distributed responses, and it is not always clear the extent to which, either asymptotically or in finite samples, such generalizations reduce the bias of variance component estimates compared to standard unrestricted maximum likelihood estimation. In this article, we review various attempts that have been made over the past four decades to extend REML estimation in generalized linear mixed models. We establish four major classes of approaches, namely approximate linearization, integrated likelihood, modified profile likelihoods, and direct bias correction of the score function, and show that while these four classes may have differing motivations and derivations, they often arrive at a similar if not the same REML estimate. We compare the finite sample performance of these four classes through a numerical study involving binary and count data, with results demonstrating that they perform similarly well in reducing the finite sample bias of variance components

Particle Gibbs with Ancestor Sampling

Particle Markov chain Monte Carlo (PMCMC) is a systematic way of combining the two main tools used for Monte Carlo statistical inference: sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). We present a novel PMCMC algorithm that we refer to as particle Gibbs with ancestor sampling (PGAS). PGAS provides the data analyst with an off-the-shelf class of Markov kernels that can be used to simulate the typically high-dimensional and highly autocorrelated state trajectory in a state-space model. The ancestor sampling procedure enables fast mixing of the PGAS kernel even when using seemingly few particles in the underlying SMC sampler. This is important as it can significantly reduce the computational burden that is typically associated with using SMC. PGAS is conceptually similar to the existing PG with backward simulation (PGBS) procedure. Instead of using separate forward and backward sweeps as in PGBS, however, we achieve the same effect in a single forward sweep. This makes PGAS well suited for addressing inference problems not only in state-space models, but also in models with more complex dependencies, such as non-Markovian, Bayesian nonparametric, and general probabilistic graphical models

Hybrid training approaches to Hidden Markov Model-based acoustic models for automatic speech recognition

Doctor of Philosoph