Clustered Longitudinal Data Research Articles

A dynamic social relations model for clustered longitudinal dyadic data with continuous or ordinal responses.

Social relations models allow the identification of cluster, actor, partner, and relationship effects when analysing clustered dyadic data on interactions between individuals or other units of analysis. We propose an extension of this model which handles longitudinal data and incorporates dynamic structure, where the response may be continuous, binary, or ordinal. This allows the disentangling of the relationship effects from temporal fluctuation and measurement error and the investigation of whether individuals respond to their partner's behaviour at the previous observation. We motivate and illustrate the model with an application to Canadian data on pairs of individuals within families observed working together on a conflict discussion task.

The effect of inadequate access to peri-implant hygiene on marginal bone level. A 4-year cohort prospective study.

The objective of this four-year cohort prospective study was to evaluate the effect of inadequate access to peri-implant hygiene on marginal bone level (MBL). Forty-one partially edentulous patients (16 males and 25 females, aged 49.8±11.9years) who had implants with at least one year in function were selected. Patients were clinically and radiographically evaluated at three different times: baseline (T0), 2-year (T1), and 4-year (T2) follow-up intervals. At baseline, implants were classified and allocated into two groups: those presenting adequate access (ACC) and inadequate access (no-ACC) to peri-implant hygiene. A linear mixed-effects model for clustered longitudinal data was used to analyze MBL, probing depth (PD), plaque index (PI), and bleeding on probing (BoP). Of 131 implants, 74 were considered as having ACC, and 57 as having no-ACC at T0. Implants in the no-ACC group presented a statistically greater mean MBL measurement at T2 than implants in the ACC group (p=.011). In the no-ACC group, a significant reduction in PD from T0 to T1 (p=.019) and from T0 to T2 (p=.010) was observed. Regardless of the group, PI significantly increased at both T1 (p=.00001) and T2 (p=.00004). Regardless of time, the prevalence of BoP was significantly higher in the no-ACC group than in the ACC group (p=.012). Inadequate access to peri-implant hygiene frequently resulted in more peri-implant inflammation and MBL over time. Proper accessibility to peri-implant hygiene should be carefully considered during planning of implant restoration, and patients properly motivated into maintenance care.

Change and Stability in Sibling Physical Fitness: The Portuguese Sibling Study.

This study aims to 1) describe mean changes in muscular and motor fitness components in sibships over 2 yr, 2) analyze individual tracking of fitness within sibships, 3) investigate sibling resemblance in fitness over time, and 4) examine the joint influence of biological, behavioral, and familial characteristics on fitness. The sample comprises 166 Portuguese biological sibling pairs (brother-brother, sister-sister, brother-sister) age 9-17 yr assessed at baseline and 2 yr later. Physical fitness components were measured with standardized tests. Percentage body fat and biological maturation were assessed, and physical activity, diet, screen time, and familial characteristics were obtained by questionnaires. Multilevel models were used to analyze the clustered longitudinal data. Crude results showed that, on average, all sib-types increased their muscular and motor fitness components from baseline to follow-up (except sister-sister pairs in standing long jump and shuttle run). When adjusted for covariates, the mean changes were no longer significant. Individual tracking was moderate to high for the muscular component but low to moderate for the motor component. Consistency in sibling resemblance was higher in sister-sister pairs than in brother-brother and brother-sister pairs. More mature sibs were fitter in both components, whereas siblings with higher body fat percentage were less fit. Screen time, physical activity, and parental occupation were not associated with fitness components. Biological characteristics were more strongly associated with fitness components than individual behaviors and familial characteristics. Furthermore, the muscular component tracked better than the motor component. Sister-sister pairs had greater resemblance in fitness over time compared with brother-brother or sister-brother pairs.

Change and Stability in Sibling Resemblance in Obesity Markers: The Portuguese Sibling Study on Growth, Fitness, Lifestyle, and Health.

Background/Objectives Obesity markers evolve over time and these changes are shared within the family orbit and governed by individual and environmental characteristics. Available reports often lack an integrated approach, in contrast to a multilevel framework that considers their concurrent influence. Hence, this study aims to (1) describe mean changes in obesity markers (body fat (%BF), body mass index (BMI), and waist circumference (WC)) across sib-ships; (2) analyze tracking of individuals within their sib-ship in these markers during 2 years of follow-up; (3) probe consistency in sibling resemblance in these markers; and (4) analyze the joint influence of individual and familial characteristics in these markers. Subjects/Methods The sample comprises 168 biological Portuguese siblings (brother-brother (BB), sister-sister (SS), and brother-sister (BS)) aged 9–17 years. %BF, BMI, and WC were measured using standardized protocols, and biological maturation was assessed. Physical activity, diet, screen time, and familial characteristics were obtained by questionnaires. Multilevel models were used to analyze the clustered longitudinal data. Sibling resemblance was estimated with the intraclass correlation. Results On average, all sib types increased in BMI and WC over 2 years of follow-up, and SS pairs increased in %BF. Individuals within sib-ships track high in all obesity markers across time. Consistency in siblings' resemblance was also noted, except for BB pairs in %BF which decreased at follow-up. More maturing siblings tend to have higher values in all markers. Greater screen time was associated with higher %BF, whereas those consuming more sugary drinks had lower %BF and BMI values. Siblings whose mothers had less qualified occupations tended to have lower BMI values. Conclusions Longitudinal individual tracking and sibling resemblance for obesity markers were found. Yet, different trajectories were also identified depending on the marker and sib type. Individual and familial characteristics exert different influences on each obesity marker.

Analyzing individual growth with clustered longitudinal data: A comparison between model-based and design-based multilevel approaches.

To prevent biased estimates of intraindividual growth and interindividual variability when working with clustered longitudinal data (e.g., repeated measures nested within students; students nested within schools), individual dependency should be considered. A Monte Carlo study was conducted to examine to what extent two model-based approaches (multilevel latent growth curve model - MLGCM, and maximum model - MM) and one design-based approach (design-based latent growth curve model - D-LGCM) could produce unbiased and efficient parameter estimates of intraindividual growth and interindividual variability given clustered longitudinal data. The solutions of a single-level latent growth curve model (SLGCM) were also provided to demonstrate the consequences of ignoring individual dependency. Design factors considered in the present simulation study were as follows: number of clusters (NC = 10, 30, 50, 100, 150, 200, and 500) and cluster size (CS = 5, 10, and 20). According to our results, when intraindividual growth is of interest, researchers are free to implement MLGCM, MM, or D-LGCM. With regard to interindividual variability, MLGCM and MM were capable of producing accurate parameter estimates and SEs. However, when D-LGCM and SLGCM were applied, parameter estimates of interindividual variability were not comprised exclusively of the variability in individual (e.g., students) growth but instead were the combined variability of individual and cluster (e.g., school) growth, which cannot be interpreted. The take-home message is that D-LGCM does not qualify as an alternative approach to analyzing clustered longitudinal data if interindividual variability is of interest.

A class of flexible models for analysis of complex structured correlated data with application to clustered longitudinal data

Generalized linear mixed models have been widely used in correlated data analysis. The applicability of these models is, however, hampered when data possess multilevel complex association structures. For instance, for longitudinal data arising in clusters, modelling complexity is a serious issue, and it is desirable to develop flexible models that are both computationally manageable and interpretatively meaningful. For these purposes, we propose a new class of flexible models, pairwise generalized linear mixed models, to facilitate correlated data that may possess multilevel complex association structures. Inferential procedures are developed to accommodate the proposed modelling framework, and asymptotic properties of the proposed method are established. The proposed models are evaluated through numerical studies. Copyright © 2017 John Wiley & Sons, Ltd.

Application of Mixed Linear Models in the Analysis of Road Surface Features

The data were collected by researchers at the Road Research Institute, in a study investigating the impact of differentfactors on road surface strength. In this statistical analysis, we apply linear mixed models (LMMs) to clustered longitudinal data, inwhich the units of analysis (points in the road) are nested within clusters (sample of four different road segments), and repeatedmeasures of road strength in these different points are collected over time with unequally spaced time intervals. The data arebalanced – each cluster has the same number of units, which are measured at the same number of time points. Because of correlateddata and different clusters in which data could be correlated, linear regression models are not appropriate here, and therefore linearmixed models are applied.

Cluster adjusted regression for displaced subject data (CARDS): Marginal inference under potentially informative temporal cluster size profiles.

Ignorance of the mechanisms responsible for the availability of information presents an unusual problem for analysts. It is often the case that the availability of information is dependent on the outcome. In the analysis of cluster data we say that a condition for informative cluster size (ICS) exists when the inference drawn from analysis of hypothetical balanced data varies from that of inference drawn on observed data. Much work has been done in order to address the analysis of clustered data with informative cluster size; examples include Inverse Probability Weighting (IPW), Cluster Weighted Generalized Estimating Equations (CWGEE), and Doubly Weighted Generalized Estimating Equations (DWGEE). When cluster size changes with time, i.e., the data set possess temporally varying cluster sizes (TVCS), these methods may produce biased inference for the underlying marginal distribution of interest. We propose a new marginalization that may be appropriate for addressing clustered longitudinal data with TVCS. The principal motivation for our present work is to analyze the periodontal data collected by Beck et al. (1997, Journal of Periodontal Research 6, 497-505). Longitudinal periodontal data often exhibits both ICS and TVCS as the number of teeth possessed by participants at the onset of study is not constant and teeth as well as individuals may be displaced throughout the study.

EFFECT OF BREASTFEEDING ON GASTROINTESTINAL INFECTION IN INFANTS: A TARGETED MAXIMUM LIKELIHOOD APPROACH FOR CLUSTERED LONGITUDINAL DATA.

The PROmotion of Breastfeeding Intervention Trial (PROBIT) cluster-randomized a program encouraging breastfeeding to new mothers in hospital centers. The original studies indicated that this intervention successfully increased duration of breastfeeding and lowered rates of gastrointestinal tract infections in newborns. Additional scientific and popular interest lies in determining the causal effect of longer breastfeeding on gastrointestinal infection. In this study, we estimate the expected infection count under various lengths of breastfeeding in order to estimate the effect of breastfeeding duration on infection. Due to the presence of baseline and time-dependent confounding, specialized "causal" estimation methods are required. We demonstrate the double-robust method of Targeted Maximum Likelihood Estimation (TMLE) in the context of this application and review some related methods and the adjustments required to account for clustering. We compare TMLE (implemented both parametrically and using a data-adaptive algorithm) to other causal methods for this example. In addition, we conduct a simulation study to determine (1) the effectiveness of controlling for clustering indicators when cluster-specific confounders are unmeasured and (2) the importance of using data-adaptive TMLE.

Marginal methods for clustered longitudinal binary data with incomplete covariates

Many analyses for incomplete longitudinal data are directed to examining the impact of covariates on the marginal mean responses. We consider the setting in which longitudinal responses are collected from individuals nested within clusters. We discuss methods for assessing covariate effects on the mean and association parameters when covariates are incompletely observed. Weighted first and second order estimating equations are constructed to obtain consistent estimates of mean and association parameters when covariates are missing at random. Empirical studies demonstrate that estimators from the proposed method have negligible finite sample biases in moderate samples. An application to the National Alzheimer's Coordinating Center (NACC) Uniform Data Set (UDS) demonstrates the utility of the proposed method.

Inference for marginal linear models for clustered longitudinal data with potentially informative cluster sizes

Clustered longitudinal data are often collected as repeated measures on subjects arising in clusters. Examples include periodontal disease study, where the measurements related to the disease status of each tooth are collected over time for each patient, which can be considered as a cluster. For such applications, the number of teeth for each patient may be related to the overall oral health of the individual and hence may influence the distribution of the outcome measure of interest leading to an informative cluster size. Under such situations, generalised estimating equations (GEE) may lead to invalid inferences. In this article, we investigate the performance of three competing proposals of fitting marginal linear models to clustered longitudinal data, namely, GEE, within-cluster resampling (WCR) and cluster-weighted generalised estimating equations (CWGEE). We show by simulations and theoretical calculations that, when the cluster size is informative, GEE provides biased estimators, while both WCR and CWGEE achieve unbiasedness under a variety of 'working' correlation structures for temporal measurements within each subject. Statistical properties of confidence intervals have been investigated using the probability-probability plots. Overall, CWGEE appears to be the recommended choice for marginal parametric inference with clustered longitudinal data that achieves similar parameter estimates and test statistics as WCR while avoiding Monte Carlo computation. The corresponding Wald tests have desirable power properties as well. We illustrate our analysis using a temporal data set on periodontal disease, which clearly demonstrates the need for CWGEE over GEE.

Model‐based clustering of longitudinal data

AbstractA new family of mixture models for the model‐based clustering of longitudinal data is introduced. The covariance structures of eight members of this new family of models are given and the associated maximum likelihood estimates for the parameters are derived via expectation–maximization (EM) algorithms. The Bayesian information criterion is used for model selection and a convergence criterion based on the Aitken acceleration is used to determine the convergence of these EM algorithms. This new family of models is applied to yeast sporulation time course data, where the models give good clustering performance. Further constraints are then imposed on the decomposition to allow a deeper investigation of the correlation structure of the yeast data. These constraints greatly extend this new family of models, with the addition of many parsimonious models. The Canadian Journal of Statistics 38:153–168; 2010 © 2010 Statistical Society of Canada

A Bayesian Model for Longitudinal Count Data with Non-Ignorable Dropout

Asthma is an important chronic disease of childhood. An intervention programme for managing asthma was designed on principles of self-regulation and was evaluated by a randomized longitudinal study.The study focused on several outcomes, and, typically, missing data remained a pervasive problem. We develop a pattern-mixture model to evaluate the outcome of intervention on the number of hospitalizations with non-ignorable dropouts. Pattern-mixture models are not generally identifiable as no data may be available to estimate a number of model parameters. Sensitivity analyses are performed by imposing structures on the unidentified parameters.We propose a parameterization which permits sensitivity analyses on clustered longitudinal count data that have missing values due to non-ignorable missing data mechanisms. This parameterization is expressed as ratios between event rates across missing data patterns and the observed data pattern and thus measures departures from an ignorable missing data mechanism. Sensitivity analyses are performed within a Bayesian framework by averaging over different prior distributions on the event ratios. This model has the advantage of providing an intuitive and flexible framework for incorporating the uncertainty of the missing data mechanism in the final analysis.

Sample size determination for hierarchical longitudinal designs with differential attrition rates.

We consider the problem of sample size determination for three-level mixed-effects linear regression models for the analysis of clustered longitudinal data. Three-level designs are used in many areas, but in particular, multicenter randomized longitudinal clinical trials in medical or health-related research. In this case, level 1 represents measurement occasion, level 2 represents subject, and level 3 represents center. The model we consider involves random effects of the time trends at both the subject level and the center level. In the most common case, we have two random effects (constant and a single trend), at both subject and center levels. The approach presented here is general with respect to sampling proportions, number of groups, and attrition rates over time. In addition, we also develop a cost model, as an aid in selecting the most parsimonious of several possible competing models (i.e., different combinations of centers, subjects within centers, and measurement occasions). We derive sample size requirements (i.e., power characteristics) for a test of treatment-by-time interaction(s) for designs based on either subject-level or cluster-level randomization. The general methodology is illustrated using two characteristic examples.

A Bayesian Approach for Clustered Longitudinal Ordinal Outcome With Nonignorable Missing Data

Asthma, a chronic inflammatory disease of the airways, affects an estimated 6.3 million children under age 18 in the United States. A key to successful asthma management, and hence improved quality of life (QOL), calls for an active partnership between asthma patients and their health care providers. To foster this partnership, an intervention program was designed and evaluated using a randomized longitudinal study. The study focused on several outcomes where typically missing data remained a pervasive problem. We suspected that the underlying missing-data mechanism may not be ignorable. Thus here we present a method for analyzing clustered longitudinal data with missing values resulting from a nonignorable missing-data mechanism. The transition Markov model with random effects was used to investigate changes in ordinal outcomes over time. A Bayesian pattern-mixture model with the flexibility to incorporate models for missing data in both outcome and time-varying covariates was used to model the nonignorable missing-data mechanism. The pattern-mixture model uses easy-to-understand parameters—namely, ratios of the cumulative odds across patterns with the complete-data pattern—as the reference pattern. Sensitivity analysis was performed using different prior distributions for the parameters. A fully Bayesian approach was derived by integrating over a class of prior distributions. The data from the Asthma Intervention Study were analyzed to explore the effect of the intervention program on improving QOL.

Hierarchical Generalized Linear Models in the Analysis of Variations in Health Care Utilization

In recent years many studies have reported large differences in the use of medical treatments and procedures across geographic regions, hospitals, and individual health care providers. Beyond reporting on the extent of observed variations, these studies examine the role of contributing factors including patient, regional, and provider characteristics. In addition, they may assess the relation between health care processes and outcomes, such as patient mortality, morbidity, and functioning. Studies of variations in health care utilization and outcomes involve the analysis of multilevel clustered data; for example, data on patients clustered by hospital and/or geographic region. The goals of the analysis include the estimation of cluster-specific adjusted responses, covariate effects, and components of variance. The analytic strategy needs to account for correlations induced by clustering and to handle the presence of large variations in cluster size. In this article we formulate a broad class of hierarchical generalized linear models (HGLMs) and discuss their applications to the analysis of health care utilization data. The models can incorporate covariates at each level of the hierarchical data structure, can account for greater variation than what is allowed by the variance in a one-parameter exponential family, and permit the use of heavy-tailed distributions for the random effects. We develop a Bayesian approach to fitting HGLMs using Markov chain Monte Carlo methods and discuss several methods for model checking. The HGLM analysis is presented in the context of two examples of applications to the study of variations in the utilization of medical procedures for elderly Medicare beneficiaries who sustained a heart attack. The first example involves the analysis of clustered longitudinal data with binomial responses and examines geographic and temporal trends in the utilization of coronary angiography across the United States during the 4-year period 1987–1990. The second example involves the analysis of multilevel, clustered data with Poisson responses and examines hospital variations in the utilization of coronary artery bypass graft surgery in 1990. The HGLM analysis incorporates state-level and hospital-level covariates and makes it possible to estimate covariate effects and cluster-specific rates of utilization for both hospitals and states.