Regression Models For Longitudinal Data Research Articles

Estimation of Functional Sparsity in Nonparametric Varying Coefficient Models for Longitudinal Data Analysis

We study the simultaneous domain selection problem for varying coefficient models as a functional regression model for longitudinal data with many covariates. The domain selection problem in functional regression mostly appears under the functional linear regression with scalar response, but there is no direct correspondence to functional response models with many covariates. We reformulate the problem as nonparametric function estimation under the notion of functional sparsity. Sparsity is the recurrent theme that encapsulates interpretability in the face of regression with multiple inputs, and the problem of sparse estimation is well understood in the parametric setting as variable selection. For nonparametric models, interpretability not only concerns the number of covariates involved but also the functional form of the estimates, and so the sparsity consideration is much more complex. To distinguish the types of sparsity in nonparametric models, we call the former global sparsity and the latter local sparsity, which constitute functional sparsity. Most existing methods focus on directly extending the framework of parametric sparsity for linear models to nonparametric function estimation to address one or the other, but not both. We develop a penalized estimation procedure that simultaneously addresses both types of sparsity in a unified framework. We establish asymptotic properties of estimation consistency and sparsistency of the proposed method. Our method is illustrated in simulation study and real data analysis, and is shown to outperform the existing methods in identifying both local sparsity and global sparsity.

Heterogeneity in Food Expenditure amongst US families: Evidence from Longitudinal Quantile Regression

Empirical studies on food expenditure are largely based on cross-section data and for a few studies based on longitudinal (or panel) data the focus has been on the conditional mean. While the former, by construction, cannot model the dependencies between observations across time, the latter cannot look at the relationship between food expenditure and covariates (such as income, education, etc.) at lower (or upper) quantiles, which are of interest to policymakers. This paper analyzes expenditures on total food (TF), food at home (FAH) and food away from home (FAFH) using mean regression and quantile regression models for longitudinal data to examine the impact of economic recession and various demographic, socioeconomic, and geographic factors. The data is taken from the Panel Study of Income Dynamics (PSID) and comprises of 2174 families in the United States (US) observed between 2001-2015. Results indicate that age and education of the head, family income, female headed family, marital status, and economic recession are important determinants for all three types of food expenditure. Spouse education, family size and some regional indicators are important for expenditures on TF and FAH, but not for FAFH. Quantile analysis reveals considerable heterogeneity in the covariate effects for all types of food expenditure, which cannot be captured by models focused on conditional mean. The study ends by showing that modeling conditional dependence between observations across time for the same family unit is crucial to reducing/avoiding heterogeneity bias and better model fitting.

Adjusting for baseline information in comparing the efficacy of treatments using bivariate varying-coefficient models

ABSTRACT In biomedical studies, patients' reaction to the treatment can be different depending on their health condition at baseline. In this paper, we develop a bivariate varying-coefficient regression model for longitudinal data with the baseline outcome. The proposed model enables the exploration of the dynamic trend of response variables over time and to provide an effective treatment based on an individual's baseline level of disease by allowing the coefficients to vary with time and baseline. The varying coefficients are modelled through basis function approximation and a set of basis functions is selected by the proposed criterion based on the empirical loglikelihood. After the proposed model is fitted to data, the hypothesis test is designed to evaluate the efficacy of treatments across baseline levels. Theoretical and empirical studies confirm that the proposed methods choose the most parsimonious model consistently and compare the treatment effects successfully across baseline levels. The entire procedure is illustrated with depression data analysis.

The Estimation Function Approach Smoothing Spline Regression Analysis for Longitudinal Data

It is given the paired data following a nonparametric regression model for longitudinal data. The regression curve is approached by the smoothing spline function. The smoothing spline is a function that is able to map the data well and has a small error variance. This current study aims to obtained from completing PWLS (Penalized Weighted Least Square) optimaziton. Besides, the GCV method is used to select the smoothing parameter.

Admission Test Modelling of State Islamic College in Indonesia Using Local Linear for Bivariate Longitudinal Data

The main challenge in the development of education is improving the quality of education and equitable education. Improving the quality of education is needed in order to create high-quality human resources. Equitable education carried out also still has problems with the uneven quality of education in each region. The aim of this research is to determine the effect of public senior high school status on the admission test scores, i.e., scholastic aptitude test score and Islamic test score of state Islamic colleges in Indonesia. In this research we use a local linear estimator to estimate nonparametric regression model for longitudinal data, and then apply it to the data of admission test scores of state islamic colleges in Indonesia based on the percentage of public senior high school. The result shows that the pattern of the scholastic aptitude test and Islamic test based on the percentage of public senior high school of state Islamic colleges in western Indonesia is different from that in eastern Indonesia. The result of this research can be used by the government to make policies so that the quality of state Islamic colleges will be better by increassing the admission test scores.

Partitioned GMM logistic regression models for longitudinal data.

Correlation is inherent in longitudinal studies due to the repeated measurements on subjects, as well as due to time-dependent covariates in the study. In the National Longitudinal Study of Adolescent to Adult Health (Add Health), data were repeatedly collected on children in grades 7-12 across four waves. Thus, observations obtained on the same adolescent were correlated, while predictors were correlated with current and future outcomes such as obesity status, among other health issues. Previous methods, such as the generalized method of moments (GMM) approach have been proposed to estimate regression coefficients for time-dependent covariates. However, these approaches combined all valid moment conditions to produce an averaged parameter estimate for each covariate and thus assumed that the effect of each covariate on the response was constant across time. This assumption is not necessarily optimal in applications such as Add Health or health-related data. Thus, we depart from this assumption and instead use the Partitioned GMM approach to estimate multiple coefficients for the data based on different time periods. These extra regression coefficients are obtained using a partitioning of the moment conditions pertaining to each respective relationship. This approach offers a deeper understanding and appreciation into the effect of each covariate on the response. We conduct simulation studies, as well as analyses of obesity in Add Health, rehospitalization in Medicare data, and depression scores in a clinical study. The Partitioned GMM methods exhibit benefits over previously proposed models with improved insight into the nonconstant relationships realized when analyzing longitudinal data.

Role of reproductive and menopausal factors in functional and structural progression of rheumatoid arthritis: results from the SCQM cohort.

To study the relationship between female reproductive and menopausal factors on functional and structural joint damage progression in women with RA. This is an observational cohort study of RA patients enrolled in the Swiss Clinical Quality Management Program for Rheumatoid Arthritis. Information about female hormonal factors, such as pregnancies, menopause and hormonal therapy, were retrospectively retrieved using a specific questionnaire. The primary outcome was functional disability progression (HAQ) and the secondary outcome radiographic joint damage progression. We compared the functional progression between pre- and post-menopausal women using a multilevel regression model for longitudinal data, adjusting for potential confounders, such as baseline age, years of education, disease duration, seropositivity, DAS28 and treatment. A total of 1667 women were analysed, of whom 1025 (61%) were post-menopausal. Participants had a median of 6 HAQ assessments (interquartile range 3-10) during 5.1 (interquartile range 2.2-9.8) years of follow-up. At baseline, post-menopausal women had higher HAQ and erosion scores than pre-menopausal women. The evolution of HAQ scores over time differed between pre- and post-menopausal women (P < 0.001), with a less favourable evolution in post-menopausal women, particularly with earlier age at menopause. Erosion progression did not differ between pre- and post-menopausal women. In women with RA, functional disability progression differed between pre- and post-menopausal women. The more favourable evolution of function in pre-menopausal women was not explained by disease duration, age or radiographic damage.

Robust estimation in linear regression models for longitudinal data with covariate measurement errors and outliers

Measurement errors and outliers commonly arise during the process of longitudinal data collection and ignoring them in data analysis can lead to large deviations in estimates. Therefore, it is important to take into account the effect of measurement errors and outliers in longitudinal data analysis. In this paper, a robust estimating equation method for analyzing longitudinal data with covariate measurement errors and outliers is proposed. Specifically, the biases caused by measurement errors are reduced via using the independence between replicate measurements and the biases caused by outliers are corrected via centralizing the observed covariate matrix. The proposed method does not require specifying the distributions of the true covariates, response and measurement errors. In practice, it can be easily implemented via the standard generalized estimating equations algorithms. The asymptotic normality of the proposed estimator is established under regularity conditions. Extensive simulation studies show that the proposed method performs better in handling measurement errors and outliers than several existing methods. For illustration, the proposed method is applied to a data set from the Lifestyle Education for Activity and Nutrition (LEAN) study.

Unsupervised learning of mixture regression models for longitudinal data

This paper is concerned with learning of mixture regression models for individuals that are measured repeatedly. The adjective “unsupervised” implies that the number of mixing components is unknown and has to be determined, ideally by data driven tools. For this purpose, a novel penalized method is proposed to simultaneously select the number of mixing components and to estimate the mixture proportions and unknown parameters in the models. The proposed method is capable of handling both continuous and discrete responses by only requiring the first two moment conditions of the model distribution. It is shown to be consistent in both selecting the number of components and estimating the mixture proportions and unknown regression parameters. Further, a modified EM algorithm is developed to seamlessly integrate model selection and estimation. Simulation studies are conducted to evaluate the finite sample performance of the proposed procedure. And it is further illustrated via an analysis of a primary biliary cirrhosis data set.

Socioeconomic and Environmental Determinants to Preterm Birth in Tibetan Women: An Analysis Based on the Hierarchically Conceptual Frame.

Background:Preterm birth is a common cause of death in newborns and may result from many determinants, but evidence for the socioeconomic and environmental determinants of preterm birth in Tibetan women of childbearing age is limited. The aim of this study was to understand the current status of preterm birth in native Tibetan women and investigate the socioeconomic and environmental determinants.Methods:Data were drawn from a cohort study which was conducted from August 2006 to August 2012 in rural Lhasa, Tibet, China. A total of 1419 Tibetan pregnant women were followed from 20 weeks’ gestation until delivery; the loss to follow-up rate was 4.69%. The incidence of preterm birth was estimated to show the status of preterm births in Tibet. Logistic regression models for longitudinal data were established, and odds ratios (ORs) together with 95% confidence intervals (CIs) were used to evaluate the association between the occurrence of preterm birth and 16 selected potential determinants based on the hierarchical conceptual frame.Results:The incidence of preterm birth was 4.58% (95% CI = 3.55–5.80%). After adjusting for health-related variables of the mothers and newborns, socioeconomic and environmental determinants associated with preterm birth included season (spring: OR = 0.28, 95% CI = 0.09–0.84; autumn: OR = 0.21, 95% CI = 0.06–0.69; and winter: OR = 0.31, 95% CI = 0.12–0.82) and calendar year of delivery (2010: OR = 5.03, 95% CI = 1.24–20.35; 2009: OR = 6.62, 95% CI = 1.75–25.10; and 2007–2008: OR = 5.93, 95% CI = 1.47–23.90).Conclusions:The incidence of preterm birth among native Tibetan women was low and there was a decreasing trend in recent years; however, it is still essential to strengthen seasonal maternal care, extend the spacing between pregnancies, and reinforce adequate maternal nutrition.

Semiparametric statistical inferences for longitudinal data with nonparametric covariance modelling

ABSTRACTIn this paper, semiparametric modelling for longitudinal data with an unstructured error process is considered. We propose a partially linear additive regression model for longitudinal data in which within-subject variances and covariances of the error process are described by unknown univariate and bivariate functions, respectively. We provide an estimating approach in which polynomial splines are used to approximate the additive nonparametric components and the within-subject variance and covariance functions are estimated nonparametrically. Both the asymptotic normality of the resulting parametric component estimators and optimal convergence rate of the resulting nonparametric component estimators are established. In addition, we develop a variable selection procedure to identify significant parametric and nonparametric components simultaneously. We show that the proposed SCAD penalty-based estimators of non-zero components have an oracle property. Some simulation studies are conducted to examine the finite-sample performance of the proposed estimation and variable selection procedures. A real data set is also analysed to demonstrate the usefulness of the proposed method.

A Comparison of Inflammatory Responses Between Robotically Enhanced Coronary Artery Bypass Grafting and Conventional Coronary Artery Bypass Grafting: Implications for Hybrid Revascularization

The inflammatory response elicited by robotically enhanced coronary artery bypass grafting (r-CABG) has not been well described. When r-CABG is performed as part of hybrid coronary revascularization, the inflammatory milieu and the timing of percutaneous coronary intervention may affect the stent patency negatively in the short and long term. The goal of this study was to describe the extent and time course of cytokine release after r-CABG compared with conventional CABG (c-CABG) and to elucidate the optimal timing for r-CABG in the setting of hybrid coronary revascularization for a future study. Prospective, observational study. Tertiary-care center in a university hospital. The study comprised patients scheduled to undergo r-CABG or c-CABG from October 2012 to November 2014. Cytokine levels of interleukin (IL)-6, IL-8, IL-10; tumor necrosis factor-α; and C-reactive protein (CRP) were measured at the following time points: preprocedure; at the end of the procedure; and at 4, 8, 12, 24, and 48 hours after the procedure. Twenty-eight patients undergoing r-CABG and 10 patients undergoing c-CABG were enrolled. The levels of cytokines after r-CABG and c-CABG were compared using the mixed-effect linear regression model for longitudinal data. Cytokine release in the r-CABG group was comparatively less for IL-6, IL-10, tumor necrosis factor, and CRP levels. They all trended toward the baseline by the 48th hour in both groups, except CRP levels, which reached their peak at 48 hours in both groups. The inflammatory response to r-CABG was blunted compared with that of c-CABG. The high CRP levels on the second postoperative day after r-CABG were a cause for concern in regard to percutaneous coronary intervention performed at that time period, but additional studies are necessary.

GEE analysis for longitudinal single-index quantile regression

We consider a single-index quantile regression model for longitudinal data. Based on generalized estimating equations, an estimation procedure is proposed by taking into account the correlation within subject. Under mild assumptions, we derive the convergence rate of the estimator of the unknown link function and the asymptotic normality of estimator of the index parameter using the “projection” technique. Since the estimating equations are non-continuous, we further adopt the smoothing approach and show that estimators obtained from the smoothed estimating equations are asymptotically equivalent to that from the unsmoothed estimating equations. It is also shown that the estimator is more efficient when the correlation is correctly specified. Finally, we present numerical examples including simulations and analysis of a lung function data.

Systems Biology-Derived Biomarkers to Predict Progression of Renal Function Decline in Type 2 Diabetes.

Chronic kidney disease (CKD) in diabetes has a complex molecular and likely multifaceted pathophysiology. We aimed to validate a panel of biomarkers identified using a systems biology approach to predict the individual decline of estimated glomerular filtration rate (eGFR) in a large group of patients with type 2 diabetes and CKD at various stages. We used publicly available "omics" data to develop a molecular process model of CKD in diabetes and identified a representative parsimonious set of nine molecular biomarkers: chitinase 3-like protein 1, growth hormone 1, hepatocyte growth factor, matrix metalloproteinase (MMP) 2, MMP7, MMP8, MMP13, tyrosine kinase, and tumor necrosis factor receptor-1. These biomarkers were measured in baseline serum samples from 1,765 patients recruited into two large clinical trials. eGFR decline was predicted based on molecular markers, clinical risk factors (including baseline eGFR and albuminuria), and both combined, and these predictions were evaluated using mixed linear regression models for longitudinal data. The variability of annual eGFR loss explained by the biomarkers, indicated by the adjusted R2 value, was 15% and 34% for patients with eGFR ≥60 and <60 mL/min/1.73 m2, respectively; variability explained by clinical predictors was 20% and 31%, respectively. A combination of molecular and clinical predictors increased the adjusted R2 to 35% and 64%, respectively. Calibration analysis of marker models showed significant (all P < 0.0001) but largely irrelevant deviations from optimal calibration (calibration-in-the-large: -1.125 and 0.95; calibration slopes: 1.07 and 1.13 in the two groups, respectively). A small set of serum protein biomarkers identified using a systems biology approach, combined with clinical variables, enhances the prediction of renal function loss over a wide range of baseline eGFR values in patients with type 2 diabetes and CKD.

Variable selection in rank regression for analyzing longitudinal data.

In this paper, we consider variable selection in rank regression models for longitudinal data. To obtain both robustness and effective selection of important covariates, we propose incorporating shrinkage by adaptive lasso or SCAD in the Wilcoxon dispersion function and establishing the oracle properties of the new method. The new method can be conveniently implemented with the statistical software R. The performance of the proposed method is demonstrated via simulation studies. Finally, two datasets are analyzed for illustration. Some interesting findings are reported and discussed.

Mixed hidden Markov quantile regression models for longitudinal data with possibly incomplete sequences.

Quantile regression provides a detailed and robust picture of the distribution of a response variable, conditional on a set of observed covariates. Recently, it has be been extended to the analysis of longitudinal continuous outcomes using either time-constant or time-varying random parameters. However, in real-life data, we frequently observe both temporal shocks in the overall trend and individual-specific heterogeneity in model parameters. A benchmark dataset on HIV progression gives a clear example. Here, the evolution of the CD4 log counts exhibits both sudden temporal changes in the overall trend and heterogeneity in the effect of the time since seroconversion on the response dynamics. To accommodate such situations, we propose a quantile regression model, where time-varying and time-constant random coefficients are jointly considered. Since observed data may be incomplete due to early drop-out, we also extend the proposed model in a pattern mixture perspective. We assess the performance of the proposals via a large-scale simulation study and the analysis of the CD4 count data.

Weighted quantile regression for longitudinal data using empirical likelihood

This paper proposes a new weighted quantile regression model for longitudinal data with weights chosen by empirical likelihood (EL). This approach efficiently incorporates the information from the conditional quantile restrictions to account for within-subject correlations. The resulted estimate is computationally simple and has good performance under modest or high within-subject correlation. The efficiency gain is quantified theoretically and illustrated via simulation and a real data application.

Bayesian Approach to Nonlinear Mixed-Effects Quantile Regression Models for Longitudinal Data with Non-normality and Left-censoring

Bayesian Approach to Nonlinear Mixed-Effects Quantile Regression Models for Longitudinal Data with Non-normality and Left-censoring

Daily life negative mood and exhaled nitric oxide in asthma

BackgroundPsychosocial stress and negative affect have been linked to asthma exacerbations, but longitudinal studies demonstrating a daily life association between negative affect and airway nitric oxide are missing. ObjectiveThe longitudinal association between negative mood fluctuations, exhaled nitric oxide, and lung function in asthma was examined. MethodsSelf-assessments of the fraction of exhaled nitric oxide (FeNO), spirometry (forced expiratory volume in the first second, FEV1), negative mood, and daily activities were obtained from 20 patients with asthma for 2 months, resulting in 1108 assessments for the analyses (approximately 55 per patient). Concurrent and prospective associations between FeNO, FEV1, and negative mood were analyzed using mixed effects regression models for longitudinal data. ResultsNegative mood was positively associated with changes in FeNO during the same day, and to a stronger extent when prior day negative mood was included in the prediction. FeNO and negative mood were positively associated with same-day FEV1, with the latter relation being partially mediated by changes in FeNO. Associations between FeNO and FEV1 were stronger in younger patients, with earlier onset of asthma, or with lower asthma control. Findings were not changed when controlling for physical activity, medication, cold symptoms, air pollution, and hours spent outside. ConclusionDaily life changes of negative mood in asthma are positively associated with FeNO changes and FeNO increases are associated with a mild bronchodilation. These findings indicate that psychological influences need to be considered when using FeNO as indicator of airway inflammation and guide for treatment decisions.

Weighted quantile regression for longitudinal data

Quantile regression is a powerful statistical methodology that complements the classical linear regression by examining how covariates influence the location, scale, and shape of the entire response distribution and offering a global view of the statistical landscape. In this paper we propose a new quantile regression model for longitudinal data. The proposed approach incorporates the correlation structure between repeated measures to enhance the efficiency of the inference. In order to use the Newton–Raphson iteration method to obtain convergent estimates, the estimating functions are redefined as smoothed functions which are differentiable with respect to regression parameters. Our proposed method for quantile regression provides consistent estimates with asymptotically normal distributions. Simulation studies are carried out to evaluate the performance of the proposed method. As an illustration, the proposed method was applied to a data on the time evolution of CD4 cell numbers in HIV (human immune-deficiency virus) seroconverters and a real-life data that contains self-reported labor pain for women in two groups.