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Joint modelling of longitudinal and repeated time-to-event data using nonlinear mixed-effects models and the stochastic approximation expectation-maximization algorithm

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2015年第8期85卷 1512-1528页

作者： Mbogning, Cyprien Bleakley, Kevin Lavielle, Marc Inria Saclay POPIX Team Saclay France LMO F-91405 Orsay France ENSP LIMSS Yaounde 8390 Cameroon

We propose a nonlinear mixed-effects framework to jointly model longitudinal and repeated time-to-event data. A parametric nonlinear mixed-effects model is used for the longitudinal observations and a parametric mixed-effects hazard model for repeated event times. We show the importance for parameter estimation of properly calculating the conditional density of the observations (given the individual parameters) in the presence of interval and/or right censoring. Parameters are estimated by maximizing the exact joint likelihood with the stochastic approximation expectation-maximization algorithm. This workflow for joint models is now implemented in the Monolix software, and illustrated here on five simulated and two real datasets.

关键词： maximum likelihood mixed-effects models repeated time-to-events joint models saem algorithm

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Mixed-Effects Estimation in Dynamic Models of Plant Growth for the Assessment of Inter-individual Variability

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JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS 2018年第2期23卷 208-232页

作者： Baey, Charlotte Mathieu, Amelie Jullien, Alexandra Trevezas, Samis Cournede, Paul-Henry Univ Lille Lab Paul Painleve F-59655 Villeneuve Dascq France Univ Paris Saclay INRA AgroParis Tech UMRECOSYS F-78850 Thiverval Grignon France Natl & Kapodistrian Univ Athens Sect Stat & Operat Res Dept Math Athens 15784 Greece Univ Paris Saclay Cent Supelec Lab Math Interact Comp Sci MICS F-92290 Chatenay Malabry France

Modeling inter-individual variability in plant populations is a key issue to understand crop heterogeneity and its variations in response to the environment. Being able to describe the interactions among plants and explain the variability observed in the population could provide useful information on how to control it and improve global plant growth. We propose here a method to model plant variability within a field, by extending the so-called GreenLab functional-structural plant model from the individual to the population scale via nonlinear mixed-effects modeling. Parameter estimation of the population model is achieved using the stochastic approximation expectation maximization algorithm, implemented in the platform for plant growth modeling and analysis PyGMAlion. The method is first applied on a set of simulated data and then on a real dataset from a population of 34 winter oilseed rape plants at the rosette stage. Results show that our method allows for a good characterization of the variability in the population with only a limited number of parameters, which is a key point for plant models. Results on simulated data show that parameters associated with a low sensitivity index are inaccurately estimated by the algorithm when considered as random effects, but a good stability of the results can be obtained by considering them as fixed effects. These results open new ways for the analysis of inter-plant variability within a population and the study of plant-plant *** materials accompanying this paper appear online.

关键词： Brassica napus GreenLab model Inter-individual variability MCMC Nonlinear mixed model nlme Population model saem algorithm Winter oilseed rape WOSR

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Estimation in nonlinear mixed-effects models using heavy-tailed distributions

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STATISTICS AND COMPUTING 2012年第1期22卷 121-139页

作者： Meza, Cristian Osorio, Felipe De la Cruz, Rolando Univ Valparaiso CIMFAV Dept Estadist Valparaiso Chile Pontificia Univ Catolica Chile Escuela Med Dept Salud Publ Santiago Chile Pontificia Univ Catolica Chile Fac Matemat Dept Estadist Santiago Chile

Nonlinear mixed-effects models are very useful to analyze repeated measures data and are used in a variety of applications. Normal distributions for random effects and residual errors are usually assumed, but such assumptions make inferences vulnerable to the presence of outliers. In this work, we introduce an extension of a normal nonlinear mixed-effects model considering a subclass of elliptical contoured distributions for both random effects and residual errors. This elliptical subclass, the scale mixtures of normal (SMN) distributions, includes heavy-tailed multivariate distributions, such as Student-t, the contaminated normal and slash, among others, and represents an interesting alternative to outliers accommodation maintaining the elegance and simplicity of the maximum likelihood theory. We propose an exact estimation procedure to obtain the maximum likelihood estimates of the fixed-effects and variance components, using a stochastic approximation of the EM algorithm. We compare the performance of the normal and the SMN models with two real data sets.

关键词： Mixed-effects model Outliers Scale mixtures of normal distributions saem algorithm Random effects

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Parametric inference for mixed models defined by stochastic differential equations

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ESAIM - Probability and Statistics 2008年第1期12卷 196-218页

作者： Donnet, Sophie Samson, Adeline Paris-Sud University Laboratoire de Mathématiques Orsay France UMR CNRS 8145 University Paris 5 Paris France INSERM U738 Paris France University Paris 5 Paris France

Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed. This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxiliary data introduced to complete the diffusion process between each pair of measurement instants. A tuned hybrid Gibbs algorithm based on conditional Brownian bridges simulations of the unobserved process paths is included in this algorithm. The convergence is proved and the error induced on the likelihood by the Euler-Maruyama approximation is bounded as a function of the step size of the approximation. Results of a pharmacokinetic simulation study illustrate the accuracy of this estimation method. The analysis of the Theophyllin real dataset illustrates the relevance of the SDE approach relative to the deterministic approach. © 2008 EDP Sciences SMAI.

关键词： Brownian bridge diffusion process Euler-Maruyama approximation Gibbs algorithm incomplete data model maximum likelihood estimation non-linear mixed effects model saem algorithm

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Heavy-tailed longitudinal regression models for censored data: a robust parametric approach

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TEST 2019年第3期28卷 844-878页

作者： Matos, Larissa A. Lachos, Victor H. Lin, Tsung-I Castro, Luis M. Univ Estadual Campinas Dept Stat Campinas SP Brazil Univ Connecticut Dept Stat Storrs CT 06269 USA Natl Chung Hsing Univ Inst Stat Taichung 402 Taiwan China Med Univ Dept Publ Hlth Taichung 404 Taiwan Pontificia Univ Catolica Chile Dept Stat Santiago Chile

Longitudinal HIV-1 RNA viral load measures are often subject to censoring due to upper and lower detection limits depending on the quantification assays. A complication arises when these continuous measures present a heavy-tailed behavior because inference can be seriously affected by the misspecification of their parametric distribution. For such data structures, we propose a robust nonlinear censored regression model based on the scale mixtures of normal distributions. By taking into account the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is considered. A stochastic approximation of the EM algorithm is developed to obtain the maximum likelihood estimates of the model parameters. The main advantage of this new procedure os to allow estimating the parameters of interest and evaluating the log-likelihood function easily and quickly. Furthermore, the standard errors of the fixed effects and predictions of unobservable values of the response can be obtained as a byproduct. The practical utility of the proposed method is exemplified using both simulated and real data.

关键词： HIV viral load Longitudinal data Nonlinear models saem algorithm Outliers

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Selection of nonlinear mixed models for growth curves of dairy buffaloes (Bubalus bubalis)

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JOURNAL OF AGRICULTURAL SCIENCE 2020年第3期158卷 218-224页

作者： Araujo Neto, F. R. Oliveira, D. P. Aspilcueta-Borquis, R. R. Vieira, D. A. Guimaraes, K. C. Oliveira, H. N. Tonhati, H. IF Goiano Inst Fed Educ Ciencia & Tecnol Goiano Campus Rio Verde BR-75901970 Rio Verde Go Brazil Univ Estadual Paulista UNESP Campus Jaboticabal BR-14884900 Jaboticabal SP Brazil Fundacao Univ Fed Grande Dourados BR-79825070 Dourados MS Brazil

The determination of livestock growth patterns is important for meat or milk production systems, and nonlinear models are used to summarize and interpret the information. The aim of this study was to more accurately estimate growth curve parameters in buffalo cows by evaluating and selecting nonlinear mixed models that employ different types of residuals and include or not contemporary groups (CG) as a covariate. Weight records from 720 animals obtained over a period of 60 months were used. The growth curves were fit using nonlinear mixed-effects models. The Bertalanffy, Gompertz and Logistic models were evaluated. Modelling residuals using four structures (constant, combined, exponential and proportional) and the inclusion or not of CG in the models were also evaluated. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) were used to select the model. In addition to estimating the parameters of the nonlinear growth models and their correlations, the instantaneous growth rate and inflection point were obtained. The Bertalanffy model with a combined residual structure and CG exhibited the lowest AIC and BIC values. Asymptotic weight (A) estimates ranged from 621.8 to 742.1 kg, and the maturity rate (k) ranged from 0.068 to 0.115 kg/month. The correlation betweenAandkranged from -0.32 to -0.82 among the models evaluated. The selection criteria indicated that the Bertalanffy model was the most suitable for growth curve analysis in buffaloes.

关键词： Model comparison random effect saem algorithm

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Flexible longitudinal linear mixed models for multiple censored responses data

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STATISTICS IN MEDICINE 2019年第6期38卷 1074-1102页

作者： Lachos, Victor H. Matos, Larissa A. Castro, Luis M. Chen, Ming-Hui Univ Connecticut Dept Stat 215 Glenbrook RdU-4120 Storrs CT 06269 USA Univ Estadual Campinas Dept Estat Campinas SP Brazil Pontificia Univ Catolica Chile Dept Estadist Santiago Chile

In biomedical studies and clinical trials, repeated measures are often subject to some upper and/or lower limits of detection. Hence, the responses are either left or right censored. A complication arises when more than one series of responses is repeatedly collected on each subject at irregular intervals over a period of time and the data exhibit tails heavier than the normal distribution. The multivariate censored linear mixed effect (MLMEC) model is a frequently used tool for a joint analysis of more than one series of longitudinal data. In this context, we develop a robust generalization of the MLMEC based on the scale mixtures of normal distributions. To take into account the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is considered. For this complex longitudinal structure, we propose an exact estimation procedure to obtain the maximum-likelihood estimates of the fixed effects and variance components using a stochastic approximation of the EM algorithm. This approach allows us to estimate the parameters of interest easily and quickly as well as to obtain the standard errors of the fixed effects, the predictions of unobservable values of the responses, and the log-likelihood function as a byproduct. The proposed method is applied to analyze a set of AIDS data and is examined via a simulation study.

关键词： censored data HIV viral load multiple longitudinal responses saem algorithm outliers

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Influence diagnostics for censored regression models with autoregressive errors

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AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS 2018年第2期60卷 209-229页

作者： Schumacher, Fernanda L. Lachos, Victor H. Vilca-Labra, Filidor E. Castro, Luis M. IBGE Pesquisas Brasilia DF Brazil Univ Connecticut Dept Stat Storrs CT 06269 USA Univ Estadual Campinas Dept Estat Campinas SP Brazil Pontificia Univ Catolica Chile Dept Estadist Santiago Chile

Observations collected over time are often autocorrelated rather than independent, and sometimes include observations below or above detection limits (i.e. censored values reported as less or more than a level of detection) and/or missing data. Practitioners commonly disregard censored data cases or replace these observations with some function of the limit of detection, which often results in biased estimates. Moreover, parameter estimation can be greatly affected by the presence of influential observations in the data. In this paper we derive local influence diagnostic measures for censored regression models with autoregressive errors of order p (hereafter, AR(p)-CR models) on the basis of the Q-function under three useful perturbation schemes. In order to account for censoring in a likelihood-based estimation procedure for AR(p)-CR models, we used a stochastic approximation version of the expectation-maximisation algorithm. The accuracy of the local influence diagnostic measure in detecting influential observations is explored through the analysis of empirical studies. The proposed methods are illustrated using data, from a study of total phosphorus concentration, that contain left-censored observations. These methods are implemented in the R package ARCensReg.

关键词： Autoregressive AR(p) models censored data influential observations limit of detection saem algorithm

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Quantile regression for nonlinear mixed effects models: a likelihood based perspective

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STATISTICAL PAPERS 2020年第3期61卷 1281-1307页

作者： Galarza, Christian E. Castro, Luis M. Louzada, Francisco Lachos, Victor H. Escuela Super Politecn Litoral ESPOL Dept Matemat Guayaquil Ecuador Univ Estadual Campinas Dept Stat Sao Paulo Brazil Pontificia Univ Catolica Chile Dept Stat Casilla 306Correo 22 Santiago Chile Univ Sao Paulo Dept Appl Math & Stat Sao Carlos Brazil Univ Connecticut Dept Stat Storrs CT 06269 USA

Longitudinal data are frequently analyzed using normal mixed effects models. Moreover, the traditional estimation methods are based on mean regression, which leads to non-robust parameter estimation under non-normal error distribution. However, at least in principle, quantile regression (QR) is more robust in the presence of outliers/influential observations and misspecification of the error distributions when compared to the conventional mean regression approach. In this context, this paper develops a likelihood-based approach for estimating QR models with correlated continuous longitudinal data using the asymmetric Laplace distribution. Our approach relies on the stochastic approximation of the EM algorithm (saem algorithm), obtaining maximum likelihood estimates of the fixed effects and variance components in the case of nonlinear mixed effects (NLME) models. We evaluate the finite sample performance of the saem algorithm and asymptotic properties of the ML estimates through simulation experiments. Moreover, two real life datasets are used to illustrate our proposed method using the qrNLMM package from R.

关键词： Asymmetric Laplace distribution Nonlinear mixed effects models Quantile regression saem algorithm

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Likelihood-based inference for censored linear regression models with scale mixtures of skew-normal distributions

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JOURNAL OF APPLIED STATISTICS 2018年第11期45卷 2039-2066页

作者： Mattos, Thalita do Bem Garay, Aldo M. Lachos, Victor H. Univ Estadual Campinas Dept Stat Campinas SP Brazil Univ Fed Pernambuco Dept Stat Recife PE Brazil Univ Connecticut Dept Stat Storrs CT 06269 USA

In many studies, the data collected are subject to some upper and lower detection limits. Hence, the responses are either left or right censored. A complication arises when these continuous measures present heavy tails and asymmetrical behavior;simultaneously. For such data structures, we propose a robust-censored linear model based on the scale mixtures of skew-normal (SMSN) distributions. The SMSN is an attractive class of asymmetrical heavy-tailed densities that includes the skew-normal, skew-t, skew-slash, skew-contaminated normal and the entire family of scale mixtures of normal (SMN) distributions as special cases. We propose a fast estimation procedure to obtain the maximum likelihood (ML) estimates of the parameters, using a stochastic approximation of the EM (saem) algorithm. This approach allows us to estimate the parameters of interest easily and quickly, obtaining as a byproducts the standard errors, predictions of unobservable values of the response and the log-likelihood function. The proposed methods are illustrated through real data applications and several simulation studies.

关键词： Censored regression models heavy tails saem algorithm scale mixtures of skew-normal distributions

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