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

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.

New insights from GWAS on BMI-related growth traits in a longitudinal cohort of admixed children with Native American and European ancestry.

Body-mass index (BMI) is a hallmark of adiposity. In contrast with adulthood, the genetic architecture of BMI during childhood is poorly understood. The few genome-wide association studies (GWAS) on children have been performed almost exclusively in Europeans and at single ages. We performed cross-sectional and longitudinal GWAS for BMI-related traits on 904 admixed children with mostly Mapuche Native American and European ancestries. We found regulatory variants of the immune gene HLA-DQB3 strongly associated with BMI at 1.5 - 2.5 years old. A variant in the sex-determining gene DMRT1 was associated with the age at adiposity rebound (Age-AR) in girls (P = 9.8 × 10 - 9 ). BMI was significantly higher in Mapuche than in Europeans between 5.5 and 16.5 years old. Finally, Age-AR was significantly lower (P = 0.004 ) by 1.94 years and BMI at AR was significantly higher (P = 0.04 ) by 1.2 kg/ m 2 , in Mapuche children compared with Europeans.

Effects of 4 Weeks of Active Exergames Training on Muscular Fitness in Elderly Women.

ABSTRACT: Gallardo-Meza, C, Simon, K, Bustamante-Ara, N, Ramirez-Campillo, R, García-Pinillos, F, Keogh, JWL, and Izquierdo, M. Effects of 4 weeks of active exergames training on muscular fitness in elderly women. J Strength Cond Res 36(2): 427-432, 2022-To analyze the effects of 4 weeks of an active exergames training program on muscular fitness in older women, 2 groups of community dwelling physically active subjects were formed by block-design randomization. One was deemed the control group (CG, n = 37; age 68.1 ± 3.3 years), and a second group completed 4 weeks of an active exergames training program (ExG, n = 35; age, 69.2 ± 3.7 years). Training included active exergames (Wii Fit Plus) performed on the Wii Balanceboard, 2 sessions per week. The exergames required mainly balance-related movements, such as leaning forward, leftward, and rightward, also requiring isometric squat positions and explosive leg extension. A supervisor-to-subject ratio method of 2:1 was used. An intensity-based individual progressive overload was applied. There were no significant (all p > 0.05, d = 0.01-0.07) baseline differences between-groups for all dependent variables. For the ExG, significant improvements were observed in static balance right leg test (Δ75.5%, d = 0.89), static balance left leg (Δ33.7%, d = 0.57), timed up-and-go test (Δ14.8%, d = 0.85) and sit-to-stand velocity test (Δ83.8%, d = 1.62). For the control group, trivial to small decrements in performance were observed across all tests (Δ -2.1 to -8.4%, d = -0.08 to 0.32). Group × time interactions were observed for the static balance right and left leg, timed up-and-go test, and the mean velocity achieved in the 5-repetition sit-to-stand test (all p < 0.001; d = 0.33-0.60). In conclusion, exergames training improves muscular fitness in older women. These results should be considered when designing appropriate and better exercise training programs for older women.

Error-rate estimation in discriminant analysis of non-linear longitudinal data: A comparison of resampling methods.

Consider longitudinal observations across different subjects such that the underlying distribution is determined by a non-linear mixed-effects model. In this context, we look at the misclassification error rate for allocating future subjects using cross-validation, bootstrap algorithms (parametric bootstrap, leave-one-out, .632 and [Formula: see text]), and bootstrap cross-validation (which combines the first two approaches), and conduct a numerical study to compare the performance of the different methods. The simulation and comparisons in this study are motivated by real observations from a pregnancy study in which one of the main objectives is to predict normal versus abnormal pregnancy outcomes based on information gathered at early stages. Since in this type of studies it is not uncommon to have insufficient data to simultaneously solve the classification problem and estimate the misclassification error rate, we put special attention to situations when only a small sample size is available. We discuss how the misclassification error rate estimates may be affected by the sample size in terms of variability and bias, and examine conditions under which the misclassification error rate estimates perform reasonably well.

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

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.

Bayesian regression analysis of data with random effects covariates from nonlinear longitudinal measurements.

Joint models for a wide class of response variables and longitudinal measurements consist on a mixed-effects model to fit longitudinal trajectories whose random effects enter as covariates in a generalized linear model for the primary response. They provide a useful way to assess association between these two kinds of data, which in clinical studies are often collected jointly on a series of individuals and may help understanding, for instance, the mechanisms of recovery of a certain disease or the efficacy of a given therapy. When a nonlinear mixed-effects model is used to fit the longitudinal trajectories, the existing estimation strategies based on likelihood approximations have been shown to exhibit some computational efficiency problems (De la Cruz et al., 2011). In this article we consider a Bayesian estimation procedure for the joint model with a nonlinear mixed-effects model for the longitudinal data and a generalized linear model for the primary response. The proposed prior structure allows for the implementation of an MCMC sampler. Moreover, we consider that the errors in the longitudinal model may be correlated. We apply our method to the analysis of hormone levels measured at the early stages of pregnancy that can be used to predict normal versus abnormal pregnancy outcomes. We also conduct a simulation study to assess the importance of modelling correlated errors and quantify the consequences of model misspecification.

Classification of longitudinal data through a semiparametric mixed-effects model based on lasso-type estimators.

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.

REML estimation of variance parameters in nonlinear mixed effects models using the SAEM algorithm.

Nonlinear mixed effects models are now widely used in biometrical studies, especially in pharmacokinetic research or for the analysis of growth traits for agricultural and laboratory species. Most of these studies, however, are often based on ML estimation procedures, which are known to be biased downwards. A few REML extensions have been proposed, but only for approximated methods. The aim of this paper is to present a REML implementation for nonlinear mixed effects models within an exact estimation scheme, based on an integration of the fixed effects and a stochastic estimation procedure. This method was implemented via a stochastic EM, namely the SAEM algorithm. The simulation study showed that the proposed REML estimation procedure considerably reduced the bias observed with the ML estimation, as well as the residual mean squared error of the variance parameter estimations, especially in the unbalanced cases. ML and REML based estimators of fixed effects were also compared via simulation. Although the two kinds of estimates were very close in terms of bias and mean square error, predictions of individual profiles were clearly improved when using REML vs. ML. An application of this estimation procedure is presented for the modelling of growth in lines of chicken.

Genetic analysis of growth curves using the SAEM algorithm.

The analysis of nonlinear function-valued characters is very important in genetic studies, especially for growth traits of agricultural and laboratory species. Inference in nonlinear mixed effects models is, however, quite complex and is usually based on likelihood approximations or Bayesian methods. The aim of this paper was to present an efficient stochastic EM procedure, namely the SAEM algorithm, which is much faster to converge than the classical Monte Carlo EM algorithm and Bayesian estimation procedures, does not require specification of prior distributions and is quite robust to the choice of starting values. The key idea is to recycle the simulated values from one iteration to the next in the EM algorithm, which considerably accelerates the convergence. A simulation study is presented which confirms the advantages of this estimation procedure in the case of a genetic analysis. The SAEM algorithm was applied to real data sets on growth measurements in beef cattle and in chickens. The proposed estimation procedure, as the classical Monte Carlo EM algorithm, provides significance tests on the parameters and likelihood based model comparison criteria to compare the nonlinear models with other longitudinal methods.