REML Estimation of Variance Parameters in Nonlinear Mixed Effects Models Using the SAEM Algorithm

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.

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“…Extensions of this work to the case of REML estimation can be easily adapted following the approach developed in Meza et al (2007).…”

Section: Discussionmentioning

confidence: 99%

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

2010

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“…Indeed, several efforts have been made to get confidence intervals for this PK parameter [6,7,[17][18][19][20]. For the other parameters, obtaining uncertainty measures is still an issue.…”

Section: Traditional Methodsmentioning

confidence: 99%

Pharmacokinetic parameters estimation using adaptive Bayesian P‐splines models

Jullion

Lambert

Beck³

et al. 2008

Pharmaceutical Statistics

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In preclinical and clinical experiments, pharmacokinetic (PK) studies are designed to analyse the evolution of drug concentration in plasma over time i.e. the PK profile. Some PK parameters are estimated in order to summarize the complete drug's kinetic profile: area under the curve (AUC), maximal concentration (C(max)), time at which the maximal concentration occurs (t(max)) and half-life time (t(1/2)).Several methods have been proposed to estimate these PK parameters. A first method relies on interpolating between observed concentrations. The interpolation method is often chosen linear. This method is simple and fast. Another method relies on compartmental modelling. In this case, nonlinear methods are used to estimate parameters of a chosen compartmental model. This method provides generally good results. However, if the data are sparse and noisy, two difficulties can arise with this method. The first one is related to the choice of the suitable compartmental model given the small number of data available in preclinical experiment for instance. Second, nonlinear methods can fail to converge. Much work has been done recently to circumvent these problems (J. Pharmacokinet. Pharmacodyn. 2007; 34:229-249, Stat. Comput., to appear, Biometrical J., to appear, ESAIM P&S 2004; 8:115-131).In this paper, we propose a Bayesian nonparametric model based on P-splines. This method provides good PK parameters estimation, whatever be the number of available observations and the level of noise in the data. Simulations show that the proposed method provides better PK parameters estimations than the interpolation method, both in terms of bias and precision. The Bayesian nonparametric method provides also better AUC and t(1/2) estimations than a correctly specified compartmental model, whereas this last method performs better in t(max) and C(max) estimations.We extend the basic model to a hierarchical one that treats the case where we have concentrations from different subjects. We are then able to get individual PK parameter estimations. Finally, with Bayesian methods, we can get easily some uncertainty measures by obtaining credibility sets for each PK parameter.

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“…Even for Euclidean response variables, efficient estimation methods for nonlinear mixed effects models are still being actively studied in literature, e.g., Alternating algorithms [44], Laplacian and adaptive Gaussian quadrature algorithms [46], as well as generalized EM algorithms with MCMC [47]. Unfortunately, this issue only gets worse in the manifold setting.…”

Section: Parameter Estimation Proceduresmentioning

confidence: 99%

Riemannian Nonlinear Mixed Effects Models: Analyzing Longitudinal Deformations in Neuroimaging

Kim

Adluru

Suri

et al. 2017

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

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Statistical machine learning models that operate on manifold-valued data are being extensively studied in vision, motivated by applications in activity recognition, feature tracking and medical imaging. While non-parametric methods have been relatively well studied in the literature, efficient formulations for parametric models (which may offer benefits in small sample size regimes) have only emerged recently. So far, manifold-valued regression models (such as geodesic regression) are restricted to the analysis of cross-sectional data, i.e., the so-called “fixed effects” in statistics. But in most “longitudinal analysis” (e.g., when a participant provides multiple measurements, over time) the application of fixed effects models is problematic. In an effort to answer this need, this paper generalizes non-linear mixed effects model to the regime where the response variable is manifold-valued, i.e., f : Rd → ℳ. We derive the underlying model and estimation schemes and demonstrate the immediate benefits such a model can provide — both for group level and individual level analysis — on longitudinal brain imaging data. The direct consequence of our results is that longitudinal analysis of manifold-valued measurements (especially, the symmetric positive definite manifold) can be conducted in a computationally tractable manner.

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REML Estimation of Variance Parameters in Nonlinear Mixed Effects Models Using the SAEM Algorithm

Cited by 19 publications

References 28 publications

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

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

Pharmacokinetic parameters estimation using adaptive Bayesian P‐splines models

Riemannian Nonlinear Mixed Effects Models: Analyzing Longitudinal Deformations in Neuroimaging

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