Convergence of a stochastic approximation version of the EM algorithm

Delyon, Bernard; Lavielle, Marc; Moulines, Éric

doi:10.1214/aos/1018031103

Cited by 574 publications

(435 citation statements)

References 31 publications

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“…Recently, the stochastic approximation expectation-maximization algorithm (SAEM) has been developed and implemented in the MONOLIX software [9, 10]. It uses a stochastic approximation version of the standard expectation-maximization (EM) algorithm [11,12]. The convergence and the consistence of the estimates have been proved by the authors.…”

Section: Introductionmentioning

confidence: 99%

Fisher information matrix for nonlinear mixed effects multiple response models: Evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model

Bazzoli

Retout

2009

Statistics in Medicine

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information matrix for nonlinear mixed effects multiple response models: evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model.. Statistics in Medicine, Wiley-Blackwell, 2009, 28 (14), pp.1940 It also emphasizes the use of this computing tool for designing population multiple response studies, as for instance in PKPD studies or in PK studies including the modelling of the PK of a drug and its active metabolite.

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Section: Introductionmentioning

confidence: 99%

Fisher information matrix for nonlinear mixed effects multiple response models: Evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model

Bazzoli

Retout

2009

Statistics in Medicine

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“…Other methods of estimation could be investigated like the stochastic approximation expectation maximisation algorithm [23]. The MCMC method of estimation for the random intercept model has not been used in this work due to the difficulties of checking the convergence of the algorithm in an automated way, which would have been suitable for a large number of simulated datasets.…”

Section: Discussionmentioning

confidence: 99%

Binomial outcomes in dataset with some clusters of size two: can the dependence of twins be accounted for? A simulation study comparing the reliability of statistical methods based on a dataset of preterm infants

Sauzet

Peacock

2017

BMC Med Res Methodol

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BackgroundThe analysis of perinatal outcomes often involves datasets with some multiple births. These are datasets mostly formed of independent observations and a limited number of clusters of size two (twins) and maybe of size three or more. This non-independence needs to be accounted for in the statistical analysis. Using simulated data based on a dataset of preterm infants we have previously investigated the performance of several approaches to the analysis of continuous outcomes in the presence of some clusters of size two. Mixed models have been developed for binomial outcomes but very little is known about their reliability when only a limited number of small clusters are present.MethodsUsing simulated data based on a dataset of preterm infants we investigated the performance of several approaches to the analysis of binomial outcomes in the presence of some clusters of size two. Logistic models, several methods of estimation for the logistic random intercept models and generalised estimating equations were compared.ResultsThe presence of even a small percentage of twins means that a logistic regression model will underestimate all parameters but a logistic random intercept model fails to estimate the correlation between siblings if the percentage of twins is too small and will provide similar estimates to logistic regression. The method which seems to provide the best balance between estimation of the standard error and the parameter for any percentage of twins is the generalised estimating equations.ConclusionsThis study has shown that the number of covariates or the level two variance do not necessarily affect the performance of the various methods used to analyse datasets containing twins but when the percentage of small clusters is too small, mixed models cannot capture the dependence between siblings.

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“…In a NLMEM framework, the Stochastic Approximation Expectation-Maximization (SAEM) algorithm [18] implemented in Monolix (www.lixoft.eu) provides unbiased estimates for both longitudinal and survival parameters [8, 9]. As in other EM algorithms, this algorithm is an iterative process where each iteration is divided into a step where the complete likelihood conditional on observations is calculated (E-step), and a step where the complete likelihood is maximized (M-step).…”

Section: Methodsmentioning

confidence: 99%

Nonlinear joint models for individual dynamic prediction of risk of death using Hamiltonian Monte Carlo: application to metastatic prostate cancer

Desmée

Veyrat‐Follet

Sébastien³

et al. 2017

BMC Med Res Methodol

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BackgroundJoint models of longitudinal and time-to-event data are increasingly used to perform individual dynamic prediction of a risk of event. However the difficulty to perform inference in nonlinear models and to calculate the distribution of individual parameters has long limited this approach to linear mixed-effect models for the longitudinal part. Here we use a Bayesian algorithm and a nonlinear joint model to calculate individual dynamic predictions. We apply this approach to predict the risk of death in metastatic castration-resistant prostate cancer (mCRPC) patients with frequent Prostate-Specific Antigen (PSA) measurements.MethodsA joint model is built using a large population of 400 mCRPC patients where PSA kinetics is described by a biexponential function and the hazard function is a PSA-dependent function. Using Hamiltonian Monte Carlo algorithm implemented in Stan software and the estimated population parameters in this population as priors, the a posteriori distribution of the hazard function is computed for a new patient knowing his PSA measurements until a given landmark time. Time-dependent area under the ROC curve (AUC) and Brier score are derived to assess discrimination and calibration of the model predictions, first on 200 simulated patients and then on 196 real patients that are not included to build the model.ResultsSatisfying coverage probabilities of Monte Carlo prediction intervals are obtained for longitudinal and hazard functions. Individual dynamic predictions provide good predictive performances for landmark times larger than 12 months and horizon time of up to 18 months for both simulated and real data.ConclusionsAs nonlinear joint models can characterize the kinetics of biomarkers and their link with a time-to-event, this approach could be useful to improve patient’s follow-up and the early detection of most at risk patients.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-017-0382-9) contains supplementary material, which is available to authorized users.

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Convergence of a stochastic approximation version of the EM algorithm

Cited by 574 publications

References 31 publications

Fisher information matrix for nonlinear mixed effects multiple response models: Evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model

Fisher information matrix for nonlinear mixed effects multiple response models: Evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model

Binomial outcomes in dataset with some clusters of size two: can the dependence of twins be accounted for? A simulation study comparing the reliability of statistical methods based on a dataset of preterm infants

Nonlinear joint models for individual dynamic prediction of risk of death using Hamiltonian Monte Carlo: application to metastatic prostate cancer

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