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PubMedDate not supplied

Career-span analyses of track performance: longitudinal data present a more optimistic view of age-related performance decline.

Sport scientists (Starkes, Weir, Singh, Hodges, & Kerr, 1999; Starkes, Weir, & Young, 2003) have suggested that prolonged training is critical for the maintenance of athletic performance even in the face of predicted age-related decline. This study used polynomial regression analyses to examine the relationship between age and running performance in the 1500 and 10,000 metre events. We compared the age and career-longitudinal performances for 15 male Canadian Masters athletes with a cross-sectional sample of performances at different ages. We hypothesized that the 30 years of uninterrupted training characteristic of this longitudinal sample would moderate the patterns of age-related decline (retention hypothesis); alternatively, the cross-sectional data were expected to demonstrate pronounced age-related decline (quadratic hypothesis). Investigators performed multimodel regression analyses on the age and performance data. Based on the absence (for longitudinal data) or presence (for the cross-sectional data) of significant quadratic components in second-order polynomial models, the authors found support for their respective hypotheses. The longitudinal data showed that running performance declined with age in a more linear fashion than did cross-sectional data. Graphical trends showed that the moderation of age-related decline appeared greater for the longitudinal 10 km performances than for the 1500m event.

Adult↗
PubMed2004

Mixtures of varying coefficient models for longitudinal data with discrete or continuous nonignorable dropout.

The analysis of longitudinal repeated measures data is frequently complicated by missing data due to informative dropout. We describe a mixture model for joint distribution for longitudinal repeated measures, where the dropout distribution may be continuous and the dependence between response and dropout is semiparametric. Specifically, we assume that responses follow a varying coefficient random effects model conditional on dropout time, where the regression coefficients depend on dropout time through unspecified nonparametric functions that are estimated using step functions when dropout time is discrete (e.g., for panel data) and using smoothing splines when dropout time is continuous. Inference under the proposed semiparametric model is hence more robust than the parametric conditional linear model. The unconditional distribution of the repeated measures is a mixture over the dropout distribution. We show that estimation in the semiparametric varying coefficient mixture model can proceed by fitting a parametric mixed effects model and can be carried out on standard software platforms such as SAS. The model is used to analyze data from a recent AIDS clinical trial and its performance is evaluated using simulations.

Anti-HIV Agents↗
PubMed2003

Imputation of missing longitudinal data: a comparison of methods.

BACKGROUND AND OBJECTIVES: Missing information is inevitable in longitudinal studies, and can result in biased estimates and a loss of power. One approach to this problem is to impute the missing data to yield a more complete data set. Our goal was to compare the performance of 14 methods of imputing missing data on depression, weight, cognitive functioning, and self-rated health in a longitudinal cohort of older adults. METHODS: We identified situations where a person had a known value following one or more missing values, and treated the known value as a "missing value." This "missing value" was imputed using each method and compared to the observed value. Methods were compared on the root mean square error, mean absolute deviation, bias, and relative variance of the estimates. RESULTS: Most imputation methods were biased toward estimating the "missing value" as too healthy, and most estimates had a variance that was too low. Imputed values based on a person's values before and after the "missing value" were superior to other methods, followed by imputations based on a person's values before the "missing value." Imputations that used no information specific to the person, such as using the sample mean, had the worst performance. CONCLUSIONS: We conclude that, in longitudinal studies where the overall trend is for worse health over time and where missing data can be assumed to be primarily related to worse health, missing data in a longitudinal sequence should be imputed from the available longitudinal data for that person.

Aged↗
PubMed2005

Group sequential clinical trials for longitudinal data with analyses using summary statistics.

Longitudinal endpoints are used in clinical trials, and the analysis of the results is often conducted using within-individual summary statistics. When these trials are monitored, interim analyses that include subjects with incomplete follow-up can give incorrect decisions due to bias by non-linearity in the true time trajectory of the treatment effect. Linear mixed-effects models can be used to remove this bias, but there is a lack of software to support both the design and implementation of monitoring plans in this setting. This paper considers a clinical trial in which the measurement time schedule is fixed (at least for pre-trial design), and the scientific question is parameterized by a contrast across these measurement times. This setting assures generalizable inference in the presence of non-linear time trajectories. The distribution of the treatment effect estimate at the interim analyses using the longitudinal outcome measurements is given, and software to calculate the amount of information at each interim analysis is provided. The interim information specifies the analysis timing thereby allowing standard group sequential design software packages to be used for trials with longitudinal outcomes. The practical issues with implementation of these designs are described; in particular, methods are presented for consistent estimation of treatment effects at the interim analyses when outcomes are not measured according to the pre-trial schedule. Splus/R functions implementing this inference using appropriate linear mixed-effects models are provided. These designs are illustrated using a clinical trial of statin treatment for the symptoms of peripheral arterial disease.

Humans↗
PubMed1993

Random-effects models, for longitudinal data using Gibbs sampling.

Analysis of longitudinal studies is often complicated through differences amongst individuals in the number and spacing of observations. Laird and Ware (1982, Biometrics 38, 963-974) proposed a linear random-effects model to deal with this problem. We propose a generalisation of this model to accommodate multiple random effects, and show how Gibbs sampling can be used to estimate it. We illustrate the methodology with an analysis of long-term response to hepatitis B vaccination, and demonstrate that the methodology can be easily and effectively extended to deal with censoring in the dependent variable.

Follow-Up Studies↗
PubMed1995

Inference for smooth curves in longitudinal data with application to an AIDS clinical trial.

We discuss a longitudinal study where data for many subjects are collected at irregular intervals. The study is a randomized trial of HIV infected subjects and the response variable of interest is serum neopterin. The mean of the outcome variable, taken over patients in each treatment group, is assumed to follow a smooth curve. Piecewise cubic polynomials with a moderate number of knots are used to model the curves. A general parametric form is assumed for the covariance structure. Maximum penalized likelihood estimation is used to smooth the over-parameterized curves. Statistical inference for the mean curves, including confidence bands and hypothesis tests, is discussed. Two approaches, one using a Bayesian interpretation of the penalized likelihood and the other based on the asymptotic distribution of the maximum penalized likelihood estimates, are discussed and contrasted. The properties of the confidence bands obtained from these two approaches are evaluated by examining their coverage rates in a simulation study.

Acquired Immunodeficiency Syndrome↗
PubMed1989

An analysis of genotype effects and their interactions by using the apolipoprotein E polymorphism and longitudinal data.

We investigate the interaction between the apolipoprotein E polymorphism and changes in weight and height as they affect the longitudinal profile of total cholesterol, triglyceride, beta lipoprotein, and glucose levels. Data were available on a sample of 466 individuals in 158 nuclear families from Nancy, France. Longitudinal data analyses were carried out on 128 unrelated adults and 56 unrelated children. We estimate the relative frequencies of the epsilon 2, epsilon 3, and epsilon 4 apolipoprotein E alleles in this population to be .120, .764, and .116, respectively. There is no significant evidence from these data that supports an effect of the apolipoprotein E polymorphism on the longitudinal profile of any of the variables considered. There is a significant interaction between the effects of this gene and weight change on the longitudinal change of serum triglyceride and beta lipoprotein levels in adults. In conjunction with weight gain, individuals with an epsilon 4 allele are expected to show a larger increase in triglyceride levels (0.15 +/- 0.03 mmol/L/kg) compared with individuals with no epsilon 4 allele. An increased production of very-low-density lipoprotein (VLDL) as one gains weight, along with retarded VLDL clearance attributable to the effects of the epsilon 4 allele, may account for this results. The significant interaction between the apolipoprotein E polymorphism and changes in weight on the longitudinal change in triglyceride levels corroborates epidemiological studies reporting that the epsilon 4 allele increases the risk of hypertriglyceridemia among obese individuals.

Apolipoproteins E↗
PubMed2000

Linear discriminant models for unbalanced longitudinal data.

This paper discusses statistical methods for the classification of observations into one of two or more groups based on longitudinal observations. Measurements on subjects in longitudinal medical studies are often collected at different times and on a different number of occasions. Classical multivariate methods for linear discriminant analysis are difficult to apply to repeated measurements due to the highly unbalanced structure observed in these data. Linear models for the analysis of longitudinal data proposed by Laird and Ware and non-linear models proposed by Lindstrom and Bates can be used to estimate population parameters for a discriminant model that classifies individuals into distinct predefined groups or populations. An example is presented using data from a study in 150 pregnant women in Santiago, Chile, in order to predict normal versus abnormal pregnancy outcomes.

Abortion, Spontaneous↗
PubMed2006

Quantile regression for longitudinal data using the asymmetric Laplace distribution.

In longitudinal studies, measurements of the same individuals are taken repeatedly through time. Often, the primary goal is to characterize the change in response over time and the factors that influence change. Factors can affect not only the location but also more generally the shape of the distribution of the response over time. To make inference about the shape of a population distribution, the widely popular mixed-effects regression, for example, would be inadequate, if the distribution is not approximately Gaussian. We propose a novel linear model for quantile regression (QR) that includes random effects in order to account for the dependence between serial observations on the same subject. The notion of QR is synonymous with robust analysis of the conditional distribution of the response variable. We present a likelihood-based approach to the estimation of the regression quantiles that uses the asymmetric Laplace density. In a simulation study, the proposed method had an advantage in terms of mean squared error of the QR estimator, when compared with the approach that considers penalized fixed effects. Following our strategy, a nearly optimal degree of shrinkage of the individual effects is automatically selected by the data and their likelihood. Also, our model appears to be a robust alternative to the mean regression with random effects when the location parameter of the conditional distribution of the response is of interest. We apply our model to a real data set which consists of self-reported amount of labor pain measurements taken on women repeatedly over time, whose distribution is characterized by skewness, and the significance of the parameters is evaluated by the likelihood ratio statistic.

Analgesics↗
PubMed1993

Detecting treatment effects in patients with rheumatoid arthritis: the advantage of longitudinal data.

Assessment of therapy in patients with rheumatoid arthritis is important but difficult. We examined 4 different methods of analyzing pretreatment data and assessed the difference that each made in detecting a positive effect of intramuscular gold on the patient's overall disability. The methods were (1) calculating the arithmetic mean of prior data points, (2) taking the last data point pretreatment, (3) fitting a straight line to pretreatment points and (4) fitting the pretreatment points with a quadratic equation. After comparison with matched controls (not taking remittive agents) the most significant difference was found by fitting a straight line to pretreatment data. This technique demonstrated about one-third more of intramuscular gold's effectiveness than the usual technique of using the last data point pretreatment. We conclude that statistical power is improved by obtaining and analyzing longitudinal pretreatment data appropriately.

Arthritis, Rheumatoid↗
PubMed2003

Testing mediational models with longitudinal data: questions and tips in the use of structural equation modeling.

R. M. Baron and D. A. Kenny (1986; see record 1987-13085-001) provided clarion conceptual and methodological guidelines for testing mediational models with cross-sectional data. Graduating from cross-sectional to longitudinal designs enables researchers to make more rigorous inferences about the causal relations implied by such models. In this transition, misconceptions and erroneous assumptions are the norm. First, we describe some of the questions that arise (and misconceptions that sometimes emerge) in longitudinal tests of mediational models. We also provide a collection of tips for structural equation modeling (SEM) of mediational processes. Finally, we suggest a series of 5 steps when using SEM to test mediational processes in longitudinal designs: testing the measurement model, testing for added components, testing for omitted paths, testing the stationarity assumption, and estimating the mediational effects.

Cross-Sectional Studies↗
PubMed1997

A joint model for survival and longitudinal data measured with error.

The relationship between a longitudinal covariate and a failure time process can be assessed using the Cox proportional hazards regression model. We consider the problem of estimating the parameters in the Cox model when the longitudinal covariate is measured infrequently and with measurement error. We assume a repeated measures random effects model for the covariate process. Estimates of the parameters are obtained by maximizing the joint likelihood for the covariate process and the failure time process. This approach uses the available information optimally because we use both the covariate and survival data simultaneously. Parameters are estimated using the expectation-maximization algorithm. We argue that such a method is superior to naive methods where one maximizes the partial likelihood of the Cox model using the observed covariate values. It also improves on two-stage methods where, in the first stage, empirical Bayes estimates of the covariate process are computed and then used as time-dependent covariates in a second stage to find the parameters in the Cox model that maximize the partial likelihood.

Algorithms↗
PubMed2001

The cognitive decline scale of the psychogeriatric assessment scales (PAS): longitudinal data on its validity.

OBJECTIVE: The Cognitive Decline scale of the Psychogeriatric Assessment Scales (PAS)1 uses informant data to assess retrospectively change from earlier in life. Data from a 7-8-year longitudinal study were used to assess the validity of this scale against changes in cognitive performance and mortality. DESIGN AND MEASURES: PAS data were collected on three occasions, with gaps of 3.6 and 4.1 years between the waves. The Cognitive Decline score at Wave 3 was validated retrospectively against actual change on a brief test of current cognitive status (the PAS Cognitive Impairment scale) over the three waves, while the Cognitive Decline score at Wave 1 was assessed for predictive validity against future mortality and cognitive change. SETTING: A community survey in the Australian cities of Canberra and Queanbeyan. PARTICIPANTS: Participants were aged 70+ at the beginning of the study. The sample size varied from 729 to 279, depending on the number of waves involved. RESULTS: Participants with scores of 4+ on the Cognitive Decline scale at Wave 3 showed substantial deterioration over the previous 7-8 years. Scores of 4+ at Wave 1 predicted mortality and further cognitive deterioration. CONCLUSIONS: The Cognitive Decline scale allows a valid retrospective assessment of change and has predictive validity for subsequent cognitive deterioration and increased mortality.

Aged↗
PubMedDate not supplied

Effect of low-level body burdens of lead on the mental development of children: limitations of meta-analysis in a review of longitudinal data.

The effect of low-level body burdens of lead on the intelligence of children, as measured by intelligence quotient (IQ), was assessed. We reviewed 35 reports from five longitudinal studies conducted in the United States and Australia. In each of these studies, infants were followed for 58 mo or less. The study populations consisted of low- and middle-socioeconomic-class infants who had low-level exposure to environmental lead. Blood-lead levels were measured in a standard fashion at various times, beginning in the prenatal period, and intelligence was first measured at 6 mo of age and was followed by subsequent assessments. Studies were assessed for quality by a review panel blinded to the identity of the investigators and their affiliations. Efforts were made to pool the data with meta-analytic techniques, but efforts were unsuccessful because the methods used to analyze and report data were inconsistent. Inconsistencies were as follows: (a) there were few instances in which IQ and blood-lead levels were measured at comparable times in different studies; (b) incompatibilities existed among the studies, including differences in independent variables, data transformations, and statistical parameters reported; (c) results conflicted when measurement intervals were comparable (i.e., heterogeneity); (d) patterns of regression and correlation coefficients were inconsistent; and (e) data were insufficient to interconvert the parameters reported. Consequently, definitive conclusions regarding the effect of low-level body burdens of lead on IQ could not be determined from the longitudinal data. Examination of the weight of the evidence from this and other studies, however, suggests an adverse relationship of lead on the intelligence of children.

Bias↗
PubMed1995

PC program extending the Potthoff-Roy longitudinal data analysis model to allow missing data: Kleinbaum's method.

Potthoff and Roy (Biometrika, 51 (1964) 313-326) generalized the multivariate analysis of variance model into a form that is especially useful for the study of longitudinal growth curve data. Applications of this method have, however, been limited by the requirement that each case in the sample be measured at the same set of time points, i.e. there can be no missing data. In this paper we describe, illustrate, and make available a user-friendly, interactive PC program implementing Kleinbaum's (J Mult Anal, 3 (1973) 117-124) extension of the Potthoff-Roy model to allow incomplete measurement sequences. These missing data are permitted to arise either randomly or by design as in mixed longitudinal studies.

Analysis of Variance↗
PubMedDate not supplied

[Multilevel model applications to the analysis of longitudinal data].

This work is an introduction to repeated measurement analysis for longitudinal studies. It uses a two stage modelling framework, using hierarchical linear models with two levels. The first level pertains to the repeated measures, the second level pertains to the individual. For the last 25 years, hierarchical linear models have been used in the Social Sciences to analyse data coming from organizations with multiple levels. Their applications have been extended to the study of change in populations, both to describe the average change in an outcome variable in a population and to analyse the factors associated with variability in the individual trajectories of change. In this article, the basic concepts are introduced: between subjects and within subjects variability, the person-specific model for the individual trajectory and the between person model to describe how individuals vary in their trajectories, fixed and random effects, linear and quadratic growth models. At the end of each section, an illustration is given for the study of cognitive function of the older people cohort "Aging in Leganés", followed in four occasions between 1993 and 1999. Results from fitting the models to answer the most frequently asked research questions in the descriptions and analysis of individual change are presented. Lastly, we present possible generalizations of these linear models to non linear situations which arise when outcomes are dichotomous, nominal or ordinal.

Aging↗
PubMed2003

A comparison of two methods for the estimation of precision with incomplete longitudinal data, jointly modelled with a time-to-event outcome.

Several methods for the estimation and comparison of rates of change in longitudinal studies with staggered entry and informative drop-outs have been recently proposed. For multivariate normal linear models, REML estimation is used. There are various approaches to maximizing the corresponding log-likelihood; in this paper we use a restricted iterative generalized least squares method (RIGLS) combined with a nested EM algorithm. An important statistical problem in such approaches is the estimation of the standard errors adjusted for the missing data (observed data information matrix). Louis has provided a general technique for computing the observed data information in terms of completed data quantities within the EM framework. The multiple imputation (MI) method for obtaining variances can be regarded as an alternative to this. The aim of this paper is to develop, apply and compare the Louis and a modified MI method in the setting of longitudinal studies where the source of missing data is either death or disease progression (informative) or end of the study (assumed non-informative). Longitudinal data are simultaneously modelled with the missingness process. The methods are illustrated by modelling CD4 count data from an HIV-1 clinical trial and evaluated through simulation studies. Both methods, Louis and MI, are used with Monte Carlo simulations of the missing data using the appropriate conditional distributions, the former with 100 simulations, the latter with 5 and 10. It is seen that naive SEs based on the completed data likelihood can be seriously biased. This bias was largely corrected by Louis and modified MI methods, which gave broadly similar estimates. Given the relative simplicity of the modified MI method, it may be preferable.

Algorithms↗