Regression Analysis Of Longitudinal Data Research Articles

Regression analysis of longitudinal data with random change point.

A great deal of literature has been established for regression analysis of longitudinal data and in particular, many methods have been proposed for the situation where there exist some change points. However, most of these methods only apply to continuous response and focus on the situations where the change point only occurs on the response or the trend of the individual trajectory. In this article, we propose a new joint modeling approach that allows not only the change point to vary for different subjects or be subject-specific but also the effect heterogeneity of the covariates before and after the change point. The method combines a generalized linear mixed effect model with a random change point for the longitudinal response and a log-linear regression model for the random change point. For inference, a maximum likelihood estimation procedure is developed and the asymptotic properties of the resulting estimators, which differ from the standard asymptotic results, are established. A simulation study is conducted and suggests that the proposed method works well for practical situations. An application to a set of real data on COVID-19 is provided.

Respiratory motion correction in F-18-FDG PET/CT impacts lymph node assessment in lung cancer patients

BackgroundsElastic motion correction in PET has been shown to increase image quality and quantitative measurements of PET datasets affected by respiratory motion. However, little is known on the impact of respiratory motion correction on clinical image evaluation in oncologic PET. This study evaluated the impact of motion correction on expert readers’ lymph node assessment of lung cancer patients.MethodsForty-three patients undergoing F-18-FDG PET/CT for the staging of suspected lung cancer were included. Three different PET reconstructions were investigated: non-motion-corrected (“static”), belt gating-based motion-corrected (“BG-MC”) and data-driven gating-based motion-corrected (“DDG-MC”). Assessment was conducted independently by two nuclear medicine specialists blinded to the reconstruction method on a six-point scale s ranging from “certainly negative” (1) to “certainly positive” (6). Differences in s between reconstruction methods, accounting for variation caused by readers, were assessed by nonparametric regression analysis of longitudinal data. From s, a dichotomous score for N1, N2, and N3 (“negative,” “positive”) and a subjective certainty score were derived. SUV and metabolic tumor volumes (MTV) were compared between reconstruction methods.ResultsBG-MC resulted in higher scores for N1 compared to static (p = 0.001), whereas DDG-MC resulted in higher scores for N2 compared to static (p = 0.016). Motion correction resulted in the migration of N1 from tumor free to metastatic on the dichotomized score, consensually for both readers, in 3/43 cases and in 2 cases for N2. SUV was significantly higher for motion-corrected PET, while MTV was significantly lower (all p < 0.003). No significant differences in the certainty scores were noted.ConclusionsPET motion correction resulted in significantly higher lymph node assessment scores of expert readers. Significant effects on quantitative PET parameters were seen; however, subjective reader certainty was not improved.

Heterogeneity in the association between youth unemployment and mental health later in life: a quantile regression analysis of longitudinal data from English schoolchildren

ObjectivesAn association between youth unemployment and poorer mental health later in life has been found in several countries. Little is known about whether this association is consistent across individuals or...

Regression analysis of asynchronous longitudinal data with informative observation processes

A great deal of literature has been established for regression analysis of longitudinal data but most of the existing methods assume that covariates can be observed completely or at the same observation times for the response variable, and the observation process is independent of the response variable completely or given covariates. As pointed out by many authors, in practice, one may face the situation where the response variable and covariates are observed intermittently at different time points, leading to sparse asynchronous longitudinal data, or the observation process may be related to the response variable even given covariates. It is apparent that sometimes both issues can occur in the same time and although some literature has been developed to address each of the two issues, it does not seem to exist an established approach that can deal with both together. To address this, in this paper, a flexible semiparametric transformation conditional model is presented and for estimation, a kernel-weighted estimating equation-based approach is proposed. The proposed estimators of regression parameters are shown to be consistent and asymptotically follow the normal distribution. For the assessment of the finite sample performance of the method, an extensive simulation study is carried out and suggests that it performs well for practical situations. The approach is applied to a prospective HIV study that motivated this investigation.

Shifting self-perceptions of ageing: differential effects of value priorities on self-perceptions of ageing beyond age stereotypes

Self-perceptions of ageing (SPA) are important predictors of health in later life. However, research on antecedents of SPA other than age stereotypes is scarce. To address this gap, this study investigates the impact of personal value priorities beyond age stereotypes on SPA. Can values as the motivational basis of attitudes and evaluations predict gain- and loss-related SPA? To answer this question, we conducted multiple regression analyses of longitudinal data from two waves (2008, 2011) of the German Ageing Survey (DEAS; N = 6089, age range in 2008: 40–93 years). Gain- and loss-related SPA as well as age stereotypes were assessed with two AgeCog scales and personal values with the 21-item Portrait Values Questionnaire. Results indicate that value priorities relate to SPA longitudinally in domain-specific ways: People with a value priority of openness to change and self-transcendence reported more gain-related SPA at follow-up, whereas those who prioritized conservation reported less gain-related SPA. In the domain of loss-related SPA, those people with a value priority of self-enhancement reported more and those prioritizing self-transcendence reported less loss-related SPA at follow-up. These results complement and extend recent findings on the role of personality for SPA. They suggest that whether people focus on the gains or losses that occur with age, whether they perceive ageing as a threat or chance, is not only shaped by their age stereotypes, but also by what they find important—their values.

ESL-Based Robust Estimation for Mean-Covariance Regression with Longitudinal Data

When longitudinal data contains outliers, the classical least-squares approach is known to be not robust. To solve this issue, the exponential squared loss (ESL) function with a tuning parameter has been investigated for longitudinal data. However, to our knowledge, there is no paper to investigate the robust estimation procedure against outliers within the framework of mean-covariance regression analysis for longitudinal data using the ESL function. In this paper, we propose a robust estimation approach for the model parameters of the mean and generalized autoregressive parameters with longitudinal data based on the ESL function. The proposed estimators can be shown to be asymptotically normal under certain conditions. Moreover, we develop an iteratively reweighted least squares (IRLS) algorithm to calculate the parameter estimates, and the balance between the robustness and efficiency can be achieved by choosing appropriate data adaptive tuning parameters. Simulation studies and real data analysis are carried out to illustrate the finite sample performance of the proposed approach.

Regression analysis of longitudinal data with outcome-dependent sampling and informative censoring.

We consider regression analysis of longitudinal data in the presence of outcome-dependent observation times and informative censoring. Existing approaches commonly require correct specification of the joint distribution of the longitudinal measurements, observation time process and informative censoring time under the joint modeling framework, and can be computationally cumbersome due to the complex form of the likelihood function. In view of these issues, we propose a semi-parametric joint regression model and construct a composite likelihood function based on a conditional order statistics argument. As a major feature of our proposed methods, the aforementioned joint distribution is not required to be specified and the random effect in the proposed joint model is treated as a nuisance parameter. Consequently, the derived composite likelihood bypasses the need to integrate over the random effect and offers the advantage of easy computation. We show that the resulting estimators are consistent and asymptotically normal. We use simulation studies to evaluate the finite-sample performance of the proposed method, and apply it to a study of weight loss data that motivated our investigation.

A PRESS statistic for working correlation structure selection in generalized estimating equations

ABSTRACTGeneralized estimating equations (GEE) is one of the most commonly used methods for regression analysis of longitudinal data, especially with discrete outcomes. The GEE method accounts for the association among the responses of a subject through a working correlation matrix and its correct specification ensures efficient estimation of the regression parameters in the marginal mean regression model. This study proposes a predicted residual sum of squares (PRESS) statistic as a working correlation selection criterion in GEE. A simulation study is designed to assess the performance of the proposed GEE PRESS criterion and to compare its performance with its counterpart criteria in the literature. The results show that the GEE PRESS criterion has better performance than the weighted error sum of squares SC criterion in all cases but is surpassed in performance by the Gaussian pseudo-likelihood criterion. Lastly, the working correlation selection criteria are illustrated with data from the Coronary Artery Risk Development in Young Adults study.

Procedural Information and Behavioral Control: Longitudinal Analysis of the Intention-Behavior Gap in the Context of Recycling

The theory of planned behavior states that individuals act on their intentions, especially when they have behavioral control. The current study examines how seeking recycling-related procedural information—i.e., information about how and where to recycle—is related to behavioral control. Hypothesis testing used hierarchical ordinary least squares regression analysis of longitudinal data from 553 survey respondents. Results supported seven hypotheses. Most notably, procedural information seeking both mediated and moderated the relationship between intention and behavior. Further, the moderation effect was itself mediated by behavioral control. The argument for this mediated moderation is that information seeking enhances behavioral control, and it is primarily behavioral control that moderates the relationship between intention and behavior. These results have implications for the theory of planned behavior and, more generally, for how individuals use information to support their behaviors.

The Impact of Adolescent Work in Family Business on Child–Parent Relationships and Psychological Well-Being

Previous ecological theory of human development research shows mixed results concerning the impact of adolescent work on psychological and family outcomes. We show the consequences of working in the family firm on adolescents’ parental relationships, self-esteem, and depression, highlighting the importance of high-quality work experiences in the early life course. Weighted regression analysis of longitudinal data from Statistics Canada’s National Longitudinal Survey of Children and Youth shows that those adolescents who work in their family firms on a year-round basis report a better relationship with their parents, and better psychological well-being than their nonfamily firm working counterparts.

Robust Regression Analysis of Longitudinal Data under Censoring

We consider regression analysis of longitudinal data when the temporal correlation is modeled by an autoregressive process. Robust R estimators of regression and autoregressive parameters are obtained. Our estimators are valid under censoring caused by detection limits. Efficient computation of the estimators is discussed. Theoretical and simulation studies of the estimators are presented. We analyze a real data set on air pollution using our methodology.

Multiple quantile regression analysis of longitudinal data: Heteroscedasticity and efficient estimation

The objective of this paper is two-fold: to propose efficient estimation of multiple quantile regression analysis of longitudinal data and to develop a new test for the homogeneity of independent variable effects across multiple quantiles. Estimating multiple regression quantile coefficients simultaneously entails accommodating both association among the multiple quantiles and association among the repeated measurements of the response within subjects. We formulate simultaneous estimating equations using basis matrix expansion which accounts for the above-mentioned associations. The empirical likelihood method is adopted to estimate multiple regression quantile coefficients. Theoretical results show that the proposed simultaneous estimation is asymptotically more efficient than separate estimation of individual regression quantiles or ignoring the within-subject dependency. The proposed method also offers an empirical likelihood ratio test examining the homogeneity of the independent variable effects across the multiple quantiles. The Wilk’s theorem holds for the test statistic, and thus the test is easy to implement. Simulation studies and real data example of a multi-center AIDS cohort study are included to illustrate the proposed estimation and testing methods, and empirically examine their properties.

Variable selection for multiply-imputed data with penalized generalized estimating equations

Generalized estimating equations (GEE) are useful tools for marginal regression analysis for longitudinal data. Having a high number of variables along with the presence of missing data presents complex issues when working in a longitudinal context. In variable selection for instance, penalized generalized estimating equations have not been systematically developed to integrate missing data. The MI-PGEE: multiple imputation-penalized generalized estimating equations, an extension of the multiple imputation-least absolute shrinkage and selection operator (MI-LASSO) is presented. MI-PGEE allows integration of missing data and within-subject correlation in variable selection procedures. Missing data are dealt with using multiple imputation, and variable selection is performed using a group LASSO penalty. Estimated coefficients for the same variable across multiply-imputed datasets are considered as a group while applying penalized generalized estimating equations, leading to a unique model across multiply-imputed datasets. In order to select the tuning parameter, a new BIC-like criterion is proposed. In a simulation study, the advantage of using MI-PGEE compared to simple imputation PGEE is shown. The usefulness of the new method is illustrated by an application to a subgroup of the placebo arm of the strontium ranelate efficacy in knee osteoarthritis trial study.

Health literacy and fear of cancer progression in elderly women newly diagnosed with breast cancer—A longitudinal analysis

ObjectiveThis study aims to investigate the distribution of health literacy levels and the association of health literacy with fear of cancer progression (FoP) over the course of cancer treatment in a sample of elderly women newly diagnosed with breast cancer. MethodsThe analyses are part of a prospective, multicenter cohort-study (PIAT) that took place in Germany between 2013 and 2014. Elderly women (aged 65 years and older) newly diagnosed with breast cancer completed validated measures of health literacy and FoP directly after the breast cancer surgery and 40 weeks later. Multivariate random-effects regression analysis for longitudinal data was applied to estimate the association of health literacy with FoP considering socio-demographic, clinical and psychosocial characteristics of the patients. ResultsAbout half of the elderly breast cancer patients in our sample were classified as having limited health literacy (inadequate and problematic levels). Inadequate and problematic health literacy were significantly associated with higher levels of FoP in the elderly breast cancer patients. ConclusionLimited health literacy is an independent risk factor for increased FoP. Practice implicationsEnhancing health literacy could contribute to reducing patients’ cancer-related fears.

Robust estimation for longitudinal data with informative observation times

AbstractIn this paper we focus on regression analysis of irregularly observed longitudinal data that often occur in medical follow‐up studies and observational investigations. The analysis of these data involves two processes. One is the underlying longitudinal response process of interest and the other is the observation process that controls observation times. Most of the existing methods, however, rely on some restrictive models or assumptions such as the Poisson assumption. For this we propose a class of more flexible joint models and a robust estimation approach for regression analysis of longitudinal data with related observation times. The asymptotic properties of the proposed estimators are established and a model checking procedure is also presented. The numerical studies indicate that the proposed methods work well for practical situations. The Canadian Journal of Statistics 43: 519–533; 2015 © 2015 Statistical Society of Canada

Regression analysis of longitudinal data with correlated censoring and observation times.

Longitudinal data occur in many fields such as the medical follow-up studies that involve repeated measurements. For their analysis, most existing approaches assume that the observation or follow-up times are independent of the response process either completely or given some covariates. In practice, it is apparent that this may not be true. In this paper, we present a joint analysis approach that allows the possible mutual correlations that can be characterized by time-dependent random effects. Estimating equations are developed for the parameter estimation and the resulted estimators are shown to be consistent and asymptotically normal. The finite sample performance of the proposed estimators is assessed through a simulation study and an illustrative example from a skin cancer study is provided.

Model selection for marginal regression analysis of longitudinal data with missing observations and covariate measurement error.

Missing observations and covariate measurement error commonly arise in longitudinal data. However, existing methods for model selection in marginal regression analysis of longitudinal data fail to address the potential bias resulting from these issues. To tackle this problem, we propose a new model selection criterion, the Generalized Longitudinal Information Criterion, which is based on an approximately unbiased estimator for the expected quadratic error of a considered marginal model accounting for both data missingness and covariate measurement error. The simulation results reveal that the proposed method performs quite well in the presence of missing data and covariate measurement error. On the contrary, the naive procedures without taking care of such complexity in data may perform quite poorly. The proposed method is applied to data from the Taiwan Longitudinal Study on Aging to assess the relationship of depression with health and social status in the elderly, accommodating measurement error in the covariate as well as missing observations.

Regression analysis of longitudinal data with irregular and informative observation times.

In longitudinal data analyses, the observation times are often assumed to be independent of the outcomes. In applications in which this assumption is violated, the standard inferential approach of using the generalized estimating equations may lead to biased inference. Current methods require the correct specification of either the observation time process or the repeated measure process with a correct covariance structure. In this article, we construct a novel pairwise likelihood method for longitudinal data that allows for dependence between observation times and outcomes. This method investigates the marginal covariate effects on the repeated measure process, while leaving the probability structure of the observation time process unspecified. The novelty of this method is that it yields consistent estimator of the marginal covariate effects without specification of the observation time process or the covariance structure of the repeated measures process. Large sample properties of the regression coefficient estimates and a pairwise likelihood ratio test procedure are established. Simulation studies demonstrate that the proposed method performs well in finite samples. An analysis of weight loss data from a web-based program is presented to illustrate the proposed method.

Semiparametric partial Linear quantile regression of longitudinal data with time varying coefficients and informative observation times

Regression analysis of longitudinal data has been a popular topic in many fields for long time. However, only limited research exists for the case where observation times may be informative and for quantile regression of longitudinal data. In particular, to our knowledge, there does not exist any established method for quantile regression of longitudinal data with informative observation times, the focus of this paper. More specifically, we will discuss this problem and present a semiparametric partial linear model with time-varying coefficients. For estimation, B-splines are used to approximate the time-varying coefficients and in addition to the estimation approach, model checking and selection procedures are also provided. The latter can be used to determine the covariates that indeed have time-varying effects on the longitudinal process of interest. The proposed method could identify the underlying true model structure and estimate the parameters simultaneously. Also we establish the convergence rate of the proposed estimators and the asymptotic normality of the estimated time-independent regression parameters. For the assessment of the finite sample performance of the proposed methods, an extensive simulation study is conducted and suggests that they work well for practical situations. Finally they are applied to a set of longitudinal medical cost data on chronic heart failure patients that motivated this study.

Varying-coefficient mean–covariance regression analysis for longitudinal data

By considering within-subject correlation among repeated measures over time, we propose a new and efficient estimation of varying-coefficient models for longitudinal data. Based on a modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit triangular matrix involving generalized autoregressive coefficients and a diagonal matrix involving innovation variances. Local polynomial smoothing method is used to estimate the unknown varying coefficient functions of marginal mean and innovation variances. A method is also developed to estimate the autoregressive coefficients. All the resulting estimators are shown to be consistent and asymptotically normal. The proposed estimator of varying coefficient functions are asymptotically more efficient than the ones which ignore the within-subject correlation structure. Simulations are conducted to demonstrate finite sample behaviors of the proposed estimators, and a real example is given to illustrate the value of the proposed methodology.