Genomic analysis of feed efficiency traits in beef cattle using random regression models.

Feed efficiency plays a major role in the overall profitability and sustainability of the beef cattle industry, as it is directly related to the reduction of the animal demand for input and methane emissions. Traditionally, the average daily feed intake and weight gain are used to calculate feed efficiency traits. However, feed efficiency traits can be analysed longitudinally using random regression models (RRMs), which allow fitting random genetic and environmental effects over time by considering the covariance pattern between the daily records. Therefore, the objectives of this study were to: (1) propose genomic evaluations for dry matter intake (DMI), body weight gain (BWG), residual feed intake (RFI) and residual weight gain (RWG) data collected during an 84-day feedlot test period via RRMs; (2) compare the goodness-of-fit of RRM using Legendre polynomials (LP) and B-spline functions; (3) evaluate the genetic parameters behaviour for feed efficiency traits and their implication for new selection strategies. The datasets were provided by the EMBRAPA-GENEPLUS beef cattle breeding program and included 2920 records for DMI, 2696 records for BWG and 4675 genotyped animals. Genetic parameters and genomic breeding values (GEBVs) were estimated by RRMs under ssGBLUP for Nellore cattle using orthogonal LPs and B-spline. Models were compared based on the deviance information criterion (DIC). The ranking of the average GEBV of each test week and the overall GEBV average were compared by the percentage of individuals in common and the Spearman correlation coefficient (top 1%, 5%, 10% and 100%). The highest goodness-of-fit was obtained with linear B-Spline function considering heterogeneous residual variance. The heritability estimates across the test period for DMI, BWG, RFI and RWG ranged from 0.06 to 0.21, 0.11 to 0.30, 0.03 to 0.26 and 0.07 to 0.27, respectively. DMI and RFI presented within-trait genetic correlations ranging from low to high magnitude across different performance test-day. In contrast, BWG and RWG presented negative genetic correlations between the first 3 weeks and the other days of performance tests. DMI and RFI presented a high-ranking similarity between the GEBV average of week eight and the overall GEBV average, with Spearman correlations and percentages of individuals selected in common ranging from 0.95 to 1.00 and 93 to 100, respectively. Week 11 presented the highest Spearman correlations (ranging from 0.94 to 0.98) and percentages of individuals selected in common (ranging from 85 to 94) of BWG and RWG with the average GEBV of the entire period of the test. In conclusion, the RRM using linear B-splines is a feasible alternative for the genomic evaluation of feed efficiency. Heritability estimates of DMI, RFI, BWG and RWG indicate enough additive genetic variance to achieve a moderate response to selection. A new selection strategy can be adopted by reducing the performance test to 56 days for DMI and RFI selection and 77 days for BWG and RWG selection.

Proposal for a new non-linear model to describe growth curves

This study was developed with longitudinal data measurements of Norfolk rabbits from birth to 119 days of age to estimate the average growth curve, with the primary objective of proposing a non-linear model. It also selected the most appropriate sigmoidal model to describe the growth of Norfolk rabbits. The adjustments provided by the logistic, von Bertalanffy, Gompertz, Brody, Richards, and proposed models were compared. The parameters were estimated using the "nls" function of the "stats" package in R software, the least-squares method, and the Gauss-Newton convergence algorithm. The goodness-of-fit comparison was based on the following criteria: adjusted coefficient of determination (), mean square error (MSE), mean absolute deviation (MAD), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Cluster analysis helped select and classify the non-linear growth models, considering the other goodness-of-fit criteria results. The proposed non-linear, von Bertalanffy, Gompertz, and Richards models described the growth curve of Norfolk rabbits satisfactorily, providing parameters with practical interpretations. The goodness-of-fit criteria showed that the proposed and von Bertalanffy models best represented the growth of rabbits.

A Bayesian approach for mixed effects state-space models under skewness and heavy tails.

Human immunodeficiency virus (HIV) dynamics have been the focus of epidemiological and biostatistical research during the past decades to understand the progression of acquired immunodeficiency syndrome (AIDS) in the population. Although there are several approaches for modeling HIV dynamics, one of the most popular is based on Gaussian mixed-effects models because of its simplicity from the implementation and interpretation viewpoints. However, in some situations, Gaussian mixed-effects models cannot (a) capture serial correlation existing in longitudinal data, (b) deal with missing observations properly, and (c) accommodate skewness and heavy tails frequently presented in patients' profiles. For those cases, mixed-effects state-space models (MESSM) become a powerful tool for modeling correlated observations, including HIV dynamics, because of their flexibility in modeling the unobserved states and the observations in a simple way. Consequently, our proposal considers an MESSM where the observations' error distribution is a skew-t. This new approach is more flexible and can accommodate data sets exhibiting skewness and heavy tails. Under the Bayesian paradigm, an efficient Markov chain Monte Carlo algorithm is implemented. To evaluate the properties of the proposed models, we carried out some exciting simulation studies, including missing data in the generated data sets. Finally, we illustrate our approach with an application in the AIDS Clinical Trial Group Study 315 (ACTG-315) clinical trial data set.

Phenotype similarities in automatically grouped T2D patients by variation-based clustering of IL-1ß gene expression.

Background: Analyzing longitudinal gene expression data is extremely challenging due to limited prior information, high dimensionality, and heterogeneity. Similar difficulties arise in research of multifactorial diseases such as Type 2 Diabetes. Clustering methods can be applied to automatically group similar observations. Common clinical values within the resulting groups suggest potential associations. However, applying traditional clustering methods to gene expression over time fails to capture variations in the response. Therefore, shape-based clustering could be applied to identify patient groups by gene expression variation in a large time metabolic compensatory intervention. Objectives: To search for clinical grouping patterns between subjects that showed similar structure in the variation of IL-1ß gene expression over time. Methods: A new approach for shape-based clustering by IL-1ß expression behavior was applied to a real longitudinal database of Type 2 Diabetes patients. In order to capture correctly variations in the response, we applied traditional clustering methods to slopes between measurements. Results: In this setting, the application of K-Medoids using the Manhattan distance yielded the best results for the corresponding database. Among the resulting groups, one of the clusters presented significant differences in many key clinical values regarding the metabolic syndrome in comparison to the rest of the data. Conclusions: The proposed method can be used to group patients according to variation patterns in gene expression (or other applications) and thus, provide clinical insights even when there is no previous knowledge on the subject clinical profile and few timepoints for each individual.

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.

Rural-urban differentials in child body mass index over time.

BACKGROUND: The body mass index is a simple index based on weight and height that can be used to screen children and adults for potential weight problems. The objective of this study was to investigate urban-rural variations in child BMI and its distribution from 2006 to 2016 in four low and middle-income countries. METHODS: This study used data from the Young Lives prospective cohort study conducted in Ethiopia, India, Peru, and Vietnam to assess the BMI change for children aged 5 to 15 between 2006 and 2016. We adopted a mixed-effect model to analyze the data. RESULTS: The study revealed substantial changes and rises in BMI in Vietnam, Peru, India, and Ethiopia between 2006 and 2016. Peru had the highest BMI changes in both urban-rural areas. A low BMI was observed in Ethiopia and India. Urban-rural differences had a significant role in determining BMI variation. In urban Ethiopia, the mean BMI increased from 14.56 kg/m2 to 17.52 kg/m2, and in rural areas, it increased from 14.57 kg/m2 to 16.67 kg/m2. Similarly, in urban Vietnam, the BMI increased from 16 kg/m2 to 20.3 kg/m2, and in rural areas, it increased from 14.69 kg/m2 to 18.93 kg/m2. CONCLUSIONS: The findings showed an increase in BMI changes in Ethiopia, India, Peru, and Vietnam from 2006 to 2016. Urban-rural differences have a significant contribution to determining BMI variation.

Detection of atypical response trajectories in biomedical longitudinal databases.

Many health care professionals and institutions manage longitudinal databases, involving follow-ups for different patients over time. Longitudinal data frequently manifest additional complexities such as high variability, correlated measurements and missing data. Mixed effects models have been widely used to overcome these difficulties. This work proposes the use of linear mixed effects models as a tool that allows to search conceptually different types of anomalies in the data simultaneously.

An anonymised longitudinal GPS location dataset to understand changes in activity-travel behaviour between pre- and post-COVID periods.

Collecting GPS data using mobile devices is essential to understanding human mobility. However, getting this type of data is tricky because of some specific features of mobile operating systems, the high-power consumption of mobile devices, and users' privacy concerns. Therefore, data of this kind are rarely publicly available for scientific purposes, while private companies that own the data are often reluctant to share it. Here we present a large anonymous longitudinal dataset of Activity Point Location (APL) generated from mobile devices' GPS tracking. The GPS data were collected by using the Google Location History (GLH), accessible in the Google Maps application. Our dataset, named AnLoCOV hereafter, includes anonymised data from 338 persons with corresponding socio-demographics over approximately ten years (2012-2022), thus covering pre- and post-COVID periods, and calculates over 2 million weekly-classified APL extracted from approximately 16 million GPS tracking points in Ecuador. Furthermore, we made our models publicly available to enable advanced analysis of human mobility and activity spaces based on the collected datasets.

Sedentary patterns and cardiometabolic risk factors in Mexican children and adolescents: analysis of longitudinal data.

BACKGROUND: Sedentary behavior is a modifiable risk factor for cardiometabolic health; however, the assessment of total sedentary time may not capture youth's highly active and interrupted activity patterns. This study examined the associations between sedentary activity patterns and cardiometabolic risk factors among Mexican youth, who have a disproportionate burden of metabolic diseases, using a repeated measure design out of a longitudinal data. METHODS: 570 subjects in the Early Life Exposure in Mexico to ENvironmental Toxicants (ELEMENT) birth cohort, who were followed up to three-time points during adolescence, were included. Bout duration, and frequency and percentages of waking time spent in specific intensities of activity, were quantified using ActiGraph wGT3X-BT wrist accelerometers. Self-reported questionnaires were used to query the usual duration of different sedentary behaviors. Outcomes were fasting lipid profile, markers for glucose homeostasis, anthropometry, and blood pressure. Associations were modeled using linear mixed-effects models, and isotemporal substitution approach was additionally used to assess the effect of replacing objectively assessed sedentary activity with other activity intensities, adjusting for potential confounders. RESULTS: Each hour of self-reported screen-based time was positively associated with diastolic blood pressure (mm Hg) [ß = 0.30, 95% confidence interval (95% CI) = 0.10, 0.51], and an hour of other sedentary time was associated with log serum glucose (mg/dL) [ß = 0.01, 95% CI = 0.004, 0.017]. Substitution models showed that replacing 5% of sedentary time with moderate to vigorous physical activity (MVPA) was associated with lower waist circumference (cm) [ß = - 1.35, 95% CI = - 1.91, - 0.79] and log serum triglycerides (mg/dL) [ß = - 0.11, 95% CI = - 0.18, - 0.03]. Substituting one uninterrupted sedentary bout with light activity was associated with lower insulin (µIU/mL) [ß = - 0.06, 95% CI = - 0.10, - 0.02]. CONCLUSIONS: Sedentary time was associated with cardiometabolic risk factors in Mexican youth in a context-specific manner. Replacing sedentary time with higher intensities was associated with improvements in some cardiometabolic markers.

Health Shocks and Economic Well-being of the Aging Population: Evidence from Mexico.

We exploit the longitudinal Mexican Health and Aging Study to estimate the effects of health shocks in the short-run on the subsequent economic well-being of the aging population in Mexico. While there is substantial evidence indicating negative economic effects of such changes in industrialized countries, little is known about health impacts on the future economic position of older adults in low- and middle-income countries. This paper takes an important step towards filling this gap in knowledge. Our results are widely relevant, with a large percentage of the world's population residing in developing countries such as Mexico that are experiencing rapid aging. We find evidence of negative impacts of health shocks on subsequent economic well-being of older adults in Mexico, but the effect varies according to several dimensions. First, the impact is clearly on income, not wealth. Second, responses are heterogenous across sources of income, with evidence of an impact mainly on labor income. Third, we find clear differences by gender in the impact of a health shock, with a larger negative impact on men. Fourth, we conclude that the population groups most negatively affected are those with the greatest degree of vulnerability prior to the shock, as measured by education and access to health insurance. Even though Mexico has made important gains with anti-poverty programs such as the Programa 70+ pension and a move towards universal health insurance, additional interventions targeted at the most vulnerable subsets of the aging population might be warranted.

A new approach to modeling positive random variables with repeated measures.

In many situations, it is common to have more than one observation per experimental unit, thus generating the experiments with repeated measures. In the modeling of such experiments, it is necessary to consider and model the intra-unit dependency structure. In the literature, there are several proposals to model positive continuous data with repeated measures. In this paper, we propose one more with the generalization of the beta prime regression model. We consider the possibility of dependence between observations of the same unit. Residuals and diagnostic tools also are discussed. To evaluate the finite-sample performance of the estimators, using different correlation matrices and distributions, we conducted a Monte Carlo simulation study. The methodology proposed is illustrated with an analysis of a real data set. Finally, we create an R package for easy access to publicly available the methodology described in this paper.

Time-varying coefficient model estimation through radial basis functions.

In this paper, we estimate the dynamic parameters of a time-varying coefficient model through radial kernel functions in the context of a longitudinal study. Our proposal is based on a linear combination of weighted kernel functions involving a bandwidth, centered around a given set of time points. In addition, we study different alternatives of estimation and inference including a Frequentist approach using weighted least squares along with bootstrap methods, and a Bayesian approach through both Markov chain Monte Carlo and variational methods. We compare the estimation strategies mention above with each other, and our radial kernel functions proposal with an expansion based on regression spline, by means of an extensive simulation study considering multiples scenarios in terms of sample size, number of repeated measurements, and subject-specific correlation. Our experiments show that the capabilities of our proposal based on radial kernel functions are indeed comparable with or even better than those obtained from regression splines. We illustrate our methodology by analyzing data from two AIDS clinical studies.

Studying latent change process in height growth of children in Ethiopia, India, Peru and Vietnam.

BACKGROUND: Anthropometric measurements of healthy children differ in different parts of the world due to the diverse ethnicity and cultural backgrounds of families. In longitudinal studies, appropriate modeling of repeated anthropometric measures can improve the understanding of patterns of change, determinants of patterns, and variations in patterns of change over time. The objective of this study was to examine the latent change in physical height of children in Ethiopia, India, Peru, and Vietnam. METHOD: Longitudinal data of 6601 children aged 1 to 15 years were obtained from the Young Lives cohort study. The data were analyzed using a latent basis growth curve model. RESULTS: The findings of the study revealed that the rates of growth did not remain constant across the time intervals, which indicates the nonlinearity of the growth trajectory over time. For instance, children had the highest rate of growth between age 1 and 5 years, then between age 8 and 12 years, and a low rate of growth was observed between age 12 and 15 years. At the first measurement occasion (age 1 year) females were 0.826 cm (p < 0.0001) times shorter than males. The mean height at one year of age ranged from 72.13 cm in Ethiopia to 72.62 cm in India. Children in India and Vietnam had higher mean height at age one year. However, no significant difference in mean height at age one year was found between Ethiopian and Peruvian children, ([Formula: see text]). Peruvian and Vietnamese children grew at a faster rate, while Indian children grew at a slower rate than Ethiopian children. CONCLUSION: We found substantial latent growth variations among children in four low- and middle-income countries. The latent trajectories differed by gender and country. The outcomes of the study could aid in detecting inequalities in children's height growth.

Mixed Models in Nonlinear Regression for Description of the Growth of Nelore Cattle.

Body weight records were used to characterize the growth curve of Nelore cattle. Body weight was regressed as a function of age, for both sexes, by using nonlinear models through the functions of Brody, Gompertz, Logistic, Richards, Meloun 1, Von Bertalanffy, and Von Bertalanffy. The quality of the model arrangements was evaluated by employing Akaike and Bayesian Schwarz information criteria. The Brody function provided the best adaptations by the evaluators and, considering the asymptotic weight and the maturation rate as random, a reduction in residual variance of 79% for males and 83% for females was obtained in relation to the models under fixed contexts. In males, the absolute and relative growth rates ranged from 0.921 to 0.261 kg/day and 2.39 to 0.08%, respectively. For the same rates, under another approach, females ranged from 0.922 to 0.198 kg/day and 2.55 to 0.06%, respectively. Males showed greater growth acceleration at the beginning of the growth trajectory, being equal to females at 397 days of age and from that age onward they presented lower estimates. The nonlinear regression model approach under the mixed-models context allows reduction of residual variance, increasing model accuracy.

Nonlinear mixed models for characterization of growth trajectory of New Zealand rabbits raised in tropical climate.

OBJECTIVE: The identification of nonlinear mixed models that describe the growth trajectory of New Zealand rabbits was performed based on weight records and carcass measures obtained using ultrasonography. METHODS: Phenotypic records of body weight (BW) and loin eye area (LEA) were collected from 66 animals raised in a didactic-productive module of cuniculture located in the southern Piauí state, Brazil. The following nonlinear models were tested considering fixed parameters: Brody, Gompertz, Logistic, Richards, Meloun 1, modified Michaelis-Menten, Santana, and von Bertalanffy. The coefficient of determination (R2), mean squared error, percentage of convergence of each model (%C), mean absolute deviation of residuals, Akaike information criterion (AIC), and Bayesian information criterion (BIC) were used to determine the best model. The model that best described the growth trajectory for each trait was also used under the context of mixed models, considering two parameters that admit biological interpretation (A and k) with random effects. RESULTS: The von Bertalanffy model was the best fitting model for BW according to the highest value of R2 (0.98) and lowest values of AIC (6,675.30) and BIC (6,691.90). For LEA, the Logistic model was the most appropriate due to the results of R2 (0.52), AIC (783.90), and BIC (798.40) obtained using this model. The absolute growth rates estimated using the von Bertalanffy and Logistic models for BW and LEA were 21.51g/d and 3.16 cm2, respectively. The relative growth rates at the inflection point were 0.028 for BW (von Bertalanffy) and 0.014 for LEA (Logistic). CONCLUSION: The von Bertalanffy and Logistic models with random effect at the asymptotic weight are recommended for analysis of ponderal and carcass growth trajectories in New Zealand rabbits. The inclusion of random effects in the asymptotic weight and maturity rate improves the quality of fit in comparison to fixed models.

Interrelations between productive, vegetative, and fruit quality traits in Tahiti acid lime through Bayesian inference / Inter-relações entre características produtivas, vegetativas e de qualidade de fruto em lima ácida Tahiti através de inferência Bayesiana

Although the fruit yield has a core importance in Tahiti acid lime breeding programs, other traits stand out among the quality fruit and vegetative traits as ones that still need to be improved in selection of superior genotypes. Appling efficient tools aiming selection, such as the Bayesian inference, becomes an alternative in perennial crops. This study applied Bayesian inference in the genetic evaluation of Tahiti acid lime genotypes and estimated the interrelation between vegetative, productive and fruit quality traits. Twenty-four acid lime genotypes were evaluated for number of fruits, fruit yield, canopy volume, stem diameter, soluble solids content, shell thickness, and juice yield traits. The genotypic values were estimated through Bayesian inference and models with different residual structure were tested via deviance information criterion. Pearson's correlation and the path analysis were estimated, removing the multicollinearity effect. The Bayesian inference estimates genotypic values with high selective accuracy. The correlations obtained between traits from different groups can be useful in selection strategies for improvement of Tahiti acid lime. The Bayesian inference demonstrated to be an important tool and should be considered in perennial breeding programs.

Embora a produtividade seja uma característica fundamental em programas de melhoramento da lima ácida Tahiti, outras características se destacam por proporcionar uma seleção mais eficiente ou mesmo influenciar na expressão de atributos produtivos. A aplicação de inferência Bayesiana, pode tornar o processo de identificação de indivíduos superiores e o estudo das correlações entre as características ainda mais acurado. Objetivou-se, por meio deste estudo, estimar valores genéticos em genótipos de lima ácida Tahiti através de inferência Bayesiana e estimar coeficientes de correlação e de trilha entre características vegetativas, produtivas e de qualidade de frutos. Vinte e quatro genótipos de lima ácida foram avaliados durante dois anos para peso e número de frutos, volume de copa, diâmetro de caule, teor de sólidos solúveis dos frutos, espessura de casca e rendimento de suco. Os valores genéticos foram estimados por meio de inferência Bayesiana e modelos com diferentes estruturas residuais foram testados via critério de informação de deviance. Coeficiente de correlação de Pearson e de análise de trilha foram determinados, removendo o efeito de multicolinearidade. A estimação de valores genéticos via inferência Bayesiana apresentou alta acurácia seletiva. As correlações obtidas entre caracteres de diferentes grupos podem ser úteis em estratégias de seleção para melhoramento da lima ácida Tahiti. A inferência Bayesiana demonstrou ser uma ferramenta importante e deve ser considerada em programas de melhoramento de culturas perenes.

How changes in menu quality associate with subsequent expenditure on (un)healthy foods and beverages in school cafeterias: A three-year longitudinal study.

Evidence of the association between the school food environment and children's and adolescents' diet is mostly cross-sectional, usually based on self-reported behavior, and often conducted in high-income countries. Also, relatively little is known about how variations in menu quality associate with the subsequent expenditure on food and beverages of the same- (vs. cross-) nutritional value. Based on a three-year longitudinal dataset comprised of 4,268,457 purchases made by 20,333 children and adolescents from 54 private schools in Brazil, we unobtrusively assess how changes in (un)healthy product availability associate with students' subsequent purchase behavior. Our results reveal that, on average, only 11.6% of the products offered in the school cafeterias were of high nutritional value (HNV). Critically, expenditure on HNV products increased following both the addition of one HNV product (ß = 0.18; 95% CI = 0.128, 0.240) and, to a lesser extent, the subtraction of one low nutritional value (LNV) product from the menu (ß = -0.03; 95% CI = -0.042, -0.016). Cross-nutritional value effects were stronger for beverages. The inclusion of one HNV beverage was associated not only with a subsequent increase in expenditure on HNV beverages (ß = 0.19; 95% CI = 0.115, 0.264), but also with a decrease in expenditure on LNV beverages (ß = -0.18; 95% CI = -0.352, -0.010).Although only a small percentage of foods and beverages consumed in private school cafeterias in Brazil are of high nutritional value, improvements to menu quality have the potential to increase the consumption of healthier products and decrease the consumption of unhealthy ones.

Selection for Test-Day Milk Yield and Thermotolerance in Brazilian Holstein Cattle.

Intense selection for milk yield has increased environmental sensitivity in animals, and currently, heat stress is an expensive problem in dairy farming. The objectives were to identify the best model for characterizing environmental sensitivity in Holstein cattle, using the test-day milk yield (TDMY) combined with the temperature-humidity index (THI), and identify sires genetically superior for heat-stress (HS) tolerance and milk yield, through random regression. The data comprised 94,549 TDMYs of 11,294 first-parity Holstein cows in Brazil, collected from 1997 to 2013. The yield data were fitted to Legendre orthogonal polynomials, linear splines and the Wilmink function. The THI (the average of two days before the dairy control) was used as an environmental gradient. An animal model that fitted production using a Legendre polynomials of quartic order for the days in milk and quadratic equations for the THI presented a better quality of fit (Akaike's information criterion (AIC) and Bayesian information criterion (BIC)). The Spearman correlation coefficient of greatest impact was 0.54, between the top 1% for TDMY and top 1% for HS. Only 9% of the sires showed plasticity and an aptitude for joint selection. Thus, despite the small population fraction allowed for joint selection, sufficient genetic variability for selecting more resilient sires was found, which promoted concomitant genetic gains in milk yield and thermotolerance.

Scale mixture of skew-normal linear mixed models with within-subject serial dependence.

In longitudinal studies, repeated measures are collected over time and hence they tend to be serially correlated. These studies are commonly analyzed using linear mixed models (LMMs), and in this article we consider an extension of the skew-normal/independent LMM, where the error term has a dependence structure, such as damped exponential correlation or autoregressive correlation of order p. The proposed model provides flexibility in capturing the effects of skewness and heavy tails simultaneously when continuous repeated measures are serially correlated. For this robust model, we present an efficient EM-type algorithm for parameters estimation via maximum likelihood and the observed information matrix is derived analytically to account for standard errors. The methodology is illustrated through an application to schizophrenia data and some simulation studies. The proposed algorithm and methods are implemented in the new R package skewlmm.

Nonlinear Physical Growth of Children from Infancy to Middle Adolescence in Low- and Middle-Income Countries.

BACKGROUND: The growth curve has a significant role in understanding the growth trajectories over time and examining the mathematical relationship between the outcome variable and time. STUDY DESIGN: A longitudinal prospective cohort study. METHODS: This study aimed to identify a nonlinear growth curve that best represents the growth trajectories in children's physical growth from ages 1 to 15 years. The data were obtained from the Young Lives study conducted in Ethiopia, India, Peru, and Vietnam. Nonlinear growth curves were studied through the families of three-parameter nonlinear mixed-effects models. RESULTS: The study examined the performances of different three-parameter nonlinear growth curves for the growth trajectory analysis, and the Logistic curve was chosen for the trajectory analysis. Gender and country differences had significant effects on the child's growth. Females reached asymptotic height earlier and shorter than males. The mean height values at the end of the growth stage for children in Ethiopia, India, Peru, and Vietnam were 171.78, 170.37, 171.30, 174.31cm, respectively. Children in Ethiopia approached adult height earlier than those in India but later than children in Peru. However, no significant growth change was observed between children in Ethiopia and Vietnam. This indicates that children in Ethiopia and Vietnam have no significant differences regarding approaching adult height. CONCLUSION: The study concludes that the Logistic curve was found to be the best growth curve to describe the growth trajectories. Children in all four countries exhibited different growth parameters.