LASSO-type estimators for semiparametric nonlinear mixed-effects models estimation

Arribas-Gil, Ana; Bertin, Karine; Meza, Cristian; Rivoirard, Vincent

doi:10.1007/s11222-013-9380-x

Cited by 17 publications

(26 citation statements)

References 50 publications

(93 reference statements)

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“…We consider a special case of the semiparametric nonlinear mixed‐effects model proposed by Ke and Wang () (also studied in Arribas‐Gil et al, ): let denote N the number of individuals with

n_{i}

observations each. For each individual i , let us note

{boldY}_{i} = false(Y_{i 1}, \dots, Y_{{in}_{i}})^{'}

f false({boldt}_{i} false) = false(f false(t_{i 1} false), \dots, f false(t_{{in}_{i}} false))^{'}

{boldϵ}_{i} = false(ϵ_{i 1}, \dots, ϵ_{{in}_{i}})^{'}

and let

{boldZ}_{i}

be a

n_{i} \times d

design matrix (we use bold fonts for vectors and matrices).…”

Section: Semiparametric Linear Mixed‐effects Modelmentioning

confidence: 99%

“…The challenge here is to combine classical estimation procedures for parametric mixed‐models estimation with the estimation of the unknown function f that we propose to model in a nonparametric fashion. In the context of SNMM's, Arribas‐Gil et al () proposed an iterative method combining the SAEM algorithm for parametric estimation with a lasso‐type procedure to estimate f . We now follow the same strategy for the estimation of f .…”

Section: Estimation In Slmmmentioning

confidence: 99%

“…The popular lasso estimator (least absolute shrinkage and selection operator, Tibshirani ()), based on

ℓ_{1}

penalized least squares, has been extended in the last years to nonparametric regression, as in Bunea, Tsybakov, and Wegkamp (, ,), Bunea (), Bickel, Ritov, and Tsybakov (), van de Geer (), and Bühlmann and van de Geer (), among others. Arribas‐Gil et al () proposed to reconstruct a sparse approximation of f with linear combinations of elements of a given set of functions

{ψ_{1}, \dots, ψ_{M}}

, called dictionary:

f_{λ} = \sum_{k = 1}^{M} λ_{k} ψ_{k},

where

λ \in ℝ^{M}

. In practice, for the nonparametric regression problem, the dictionary can be a collection of basis functions from different bases (splines with fixed knots, wavelets, Fourier, etc.).…”

Section: Estimation In Slmmmentioning

confidence: 99%

“…Several semiparametric mixed‐effects models have been proposed as extension of mixed‐effects models, where an unknown function is included as an infinite dimensional parameter, which provides flexibility to the model. Different semiparametric mixed‐effects models have been recently used to model, among many other applications, HIV dynamics (Wu and Zhang, ; Liu and Wu, , ), time course microarray gene expression data (Luan and Li, ), weather data (Ke and Wang, ), pharmacokinetic and pharmacodynamic models (Wang, Eskridge, and Zhang, ) or price evolution in on‐line auctions (Arribas‐Gil et al, ). The more general form of these models, the semiparametric nonlinear mixed‐effects model, SNMM, appears when the unknown function interacts in a nonlinear way with the random effects.…”

Section: Introductionmentioning

confidence: 99%

“…In this setting, maximum likelihood estimation has to be performed through iterative procedures based on EM‐type algorithms (Dempster, Laird, and Rubin, ), for parametric estimation, and non‐parametric techniques to estimate the unknown function, as originally formulated by Ke and Wang (). As an alternative to this estimation procedure, Arribas‐Gil et al () considered a novel estimation strategy for a specific semiparametric nonlinear mixed‐effects model based on a stochastic approximation of the EM algorithm (Delyon, Lavielle, and Moulines, ) and a lasso‐type method to estimate the unknown function. The authors showed via a simulation study that the use of the lasso method to estimate f is justified by the fact that it may outperform the spline‐based estimator when little knowledge about the nonparametric function is available.…”

Section: Introductionmentioning

confidence: 99%

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Classification of Longitudinal Data Through a Semiparametric Mixed-Effects Model Based on Lasso-Type Estimators

et al. 2015

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We propose a classification method for longitudinal data. The Bayes classifier is classically used to determine a classification rule where the underlying density in each class needs to be well modeled and estimated. This work is motivated by a real dataset of hormone levels measured at the early stages of pregnancy that can be used to predict normal versus abnormal pregnancy outcomes. The proposed model, which is a semiparametric linear mixed-effects model (SLMM), is a particular case of the semiparametric nonlinear mixed-effects class of models (SNMM) in which finite dimensional (fixed effects and variance components) and infinite dimensional (an unknown function) parameters have to be estimated. In SNMM's maximum likelihood estimation is performed iteratively alternating parametric and nonparametric procedures. However, if one can make the assumption that the random effects and the unknown function interact in a linear way, more efficient estimation methods can be used. Our contribution is the proposal of a unified estimation procedure based on a penalized EM-type algorithm. The Expectation and Maximization steps are explicit. In this latter step, the unknown function is estimated in a nonparametric fashion using a lasso-type procedure. A simulation study and an application on real data are performed.

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“…We consider a special case of the semiparametric nonlinear mixed‐effects model proposed by Ke and Wang () (also studied in Arribas‐Gil et al, ): let denote N the number of individuals with

n_{i}

observations each. For each individual i , let us note

{boldY}_{i} = false(Y_{i 1}, \dots, Y_{{in}_{i}})^{'}

f false({boldt}_{i} false) = false(f false(t_{i 1} false), \dots, f false(t_{{in}_{i}} false))^{'}

{boldϵ}_{i} = false(ϵ_{i 1}, \dots, ϵ_{{in}_{i}})^{'}

and let

{boldZ}_{i}

be a

n_{i} \times d

design matrix (we use bold fonts for vectors and matrices).…”

Section: Semiparametric Linear Mixed‐effects Modelmentioning

confidence: 99%

Section: Estimation In Slmmmentioning

confidence: 99%

“…The popular lasso estimator (least absolute shrinkage and selection operator, Tibshirani ()), based on

ℓ_{1}

{ψ_{1}, \dots, ψ_{M}}

, called dictionary:

f_{λ} = \sum_{k = 1}^{M} λ_{k} ψ_{k},

where

λ \in ℝ^{M}

. In practice, for the nonparametric regression problem, the dictionary can be a collection of basis functions from different bases (splines with fixed knots, wavelets, Fourier, etc.).…”

Section: Estimation In Slmmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Classification of Longitudinal Data Through a Semiparametric Mixed-Effects Model Based on Lasso-Type Estimators

et al. 2015

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show abstract

Predicting pregnancy outcomes using longitudinal information: a penalized splines mixed-effects model approach

et al. 2017

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We propose a semiparametric nonlinear mixed-effects model (SNMM) using penalized splines to classify longitudinal data and improve the prediction of a binary outcome. The work is motivated by a study in which different hormone levels were measured during the early stages of pregnancy, and the challenge is using this information to predict normal versus abnormal pregnancy outcomes. The aim of this paper is to compare models and estimation strategies on the basis of alternative formulations of SNMMs depending on the characteristics of the data set under consideration. For our motivating example, we address the classification problem using a particular case of the SNMM in which the parameter space has a finite dimensional component (fixed effects and variance components) and an infinite dimensional component (unknown function) that need to be estimated. The nonparametric component of the model is estimated using penalized splines. For the parametric component, we compare the advantages of using random effects versus direct modeling of the correlation structure of the errors. Numerical studies show that our approach improves over other existing methods for the analysis of this type of data. Furthermore, the results obtained using our method support the idea that explicit modeling of the serial correlation of the error term improves the prediction accuracy with respect to a model with random effects, but independent errors. Copyright © 2017 John Wiley & Sons, Ltd.

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Classification of longitudinal profiles using semi‐parametric nonlinear mixed models with P‐Splines and the SAEM algorithm

Márquez,

Meza,

Lee

et al. 2023

Statistics in Medicine

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In this work, we propose an extension of a semiparametric nonlinear mixed‐effects model for longitudinal data that incorporates more flexibility with penalized splines (P‐splines) as smooth terms. The novelty of the proposed approach consists of the formulation of the model within the stochastic approximation version of the EM algorithm for maximum likelihood, the so‐called SAEM algorithm. The proposed approach takes advantage of the formulation of a P‐spline as a mixed‐effects model and the use of the computational advantages of the existing software for the SAEM algorithm for the estimation of the random effects and the variance components. Additionally, we developed a supervised classification method for these non‐linear mixed models using an adaptive importance sampling scheme. To illustrate our proposal, we consider two studies on pregnant women where two biomarkers are used as indicators of changes during pregnancy. In both studies, information about the women's pregnancy outcomes is known. Our proposal provides a unified framework for the classification of longitudinal profiles that may have important implications for the early detection and monitoring of pregnancy‐related changes and contribute to improved maternal and fetal health outcomes. We show that the proposed models improve the analysis of this type of data compared to previous studies. These improvements are reflected both in the fit of the models and in the classification of the groups.

show abstract

LASSO-type estimators for semiparametric nonlinear mixed-effects models estimation

Cited by 17 publications

References 50 publications

Classification of Longitudinal Data Through a Semiparametric Mixed-Effects Model Based on Lasso-Type Estimators

Classification of Longitudinal Data Through a Semiparametric Mixed-Effects Model Based on Lasso-Type Estimators

Predicting pregnancy outcomes using longitudinal information: a penalized splines mixed-effects model approach

Classification of longitudinal profiles using semi‐parametric nonlinear mixed models with P‐Splines and the SAEM algorithm

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