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Results for “longitudinal data”

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PubMed1997

A test of missing completely at random for longitudinal data with missing observations.

Liang and Zeger proposed a generalized estimating equations approach to the analysis of longitudinal data. Their models assume that missing observations are missing completely at random in the sense of Rubin. However, when this assumption does not hold, their analysis may yield biased results. In this paper, we develop a simple and practical procedure for testing this assumption. The proposed procedure is related to that of Park and Davis.

Aged↗

PubMed2002

Joint modeling of event time and nonignorable missing longitudinal data.

Survival studies usually collect on each participant, both duration until some terminal event and repeated measures of a time-dependent covariate. Such a covariate is referred to as an internal time-dependent covariate. Usually, some subjects drop out of the study before occurrence of the terminal event of interest. One may then wish to evaluate the relationship between time to dropout and the internal covariate. The Cox model is a standard framework for that purpose. Here, we address this problem in situations where the value of the covariate at dropout is unobserved. We suggest a joint model which combines a first-order Markov model for the longitudinally measured covariate with a time-dependent Cox model for the dropout process. We consider maximum likelihood estimation in this model and show how estimation can be carried out via the EM-algorithm. We state that the suggested joint model may have applications in the context of longitudinal data with nonignorable dropout. Indeed, it can be viewed as generalizing Diggle and Kenward's model (1994) to situations where dropout may occur at any point in time and may be censored. Hence we apply both models and compare their results on a data set concerning longitudinal measurements among patients in a cancer clinical trial.

Algorithms↗

PubMed1997

Different statistical models to analyze epidemiological observational longitudinal data: an example from the Amsterdam Growth and Health Study.

With the development of new statistical techniques [such as generalized estimating equations (GEE)] it became possible to analyze longitudinal epidemiological relations, using all available longitudinal data. However, there are different possibilities in modeling longitudinal relations. In this paper four possible models were compared. (1) A simple model in which the actual values of the outcome and predictor variables were related (Y(it) = beta0 + beta1X(it)...); (2) A model with a time lag between outcome and predictor variables (Y(it) = beta0 + beta1X(it-1)...); (3) A model in which not the actual values, but changes in values between different time points were related ([Y(it)-Y(it-1)] = beta0 + beta1 [X(it)-X(it-1)]...); and (4) A first-order autoregressive model in which the actual value of the outcome variable at time point t is not only related to the actual value of the predictor variable at time point t, but also to the value of the outcome variable at t-1 (Y(it) = beta0 + beta1X(it) + beta2Y(it-1) +...). In this paper the use of the possible models was discussed by means of an example with data from the Amsterdam Growth and Health Study. In this longitudinal observational study six repeated measurements were carried out over a period of 15 years on subjects with an initial age of 13 years. It can be concluded that each model reflects different parts of the longitudinal relationships and the choice for a particular model must be based on logical considerations. However, in most cases epidemiologists should use the results of different models to obtain a more accurate answer to the particular epidemiological question.

Epidemiologic Methods↗

PubMed1993

Regression imputation of missing values in longitudinal data sets.

A stand-alone, menu-driven PC program, written in GAUSS, which can be used to estimate missing observations in longitudinal data sets is described and male available to interested readers. The program is limited to the situation in which we have complete data on N cases at each of the planned times of measurement t1, t2,..., tT; and we wish to use this information, together with the non-missing values for n additional cases, to estimate the missing values for those cases. The augmented data matrix may be saved in an ASCII file and subsequently imported into programs requiring complete data. The use of the program is illustrated. Ten percent of the observations in a data set consisting of mandibular ramus height measurements for N = 12 young male rhesus monkeys measured at T = 5 time points are randomly discarded. The augmented data matrix is used to determine the lowest degree polynomial adequate to fit the average growth curve (AGC); the regression coefficients are estimated and confidence intervals for them are determined; and confidence bands for the AGC are constructed. The results are compared with those obtained when the original complete data set is used.

Animals↗

PubMed2004

Generalized linear mixed models with varying coefficients for longitudinal data.

The routinely assumed parametric functional form in the linear predictor of a generalized linear mixed model for longitudinal data may be too restrictive to represent true underlying covariate effects. We relax this assumption by representing these covariate effects by smooth but otherwise arbitrary functions of time, with random effects used to model the correlation induced by among-subject and within-subject variation. Due to the usually intractable integration involved in evaluating the quasi-likelihood function, the double penalized quasi-likelihood (DPQL) approach of Lin and Zhang (1999, Journal of the Royal Statistical Society, Series B61, 381-400) is used to estimate the varying coefficients and the variance components simultaneously by representing a nonparametric function by a linear combination of fixed effects and random effects. A scaled chi-squared test based on the mixed model representation of the proposed model is developed to test whether an underlying varying coefficient is a polynomial of certain degree. We evaluate the performance of the procedures through simulation studies and illustrate their application with Indonesian children infectious disease data.

Biometry↗

PubMed1994

Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters.

The paper describes a semiparametric model for longitudinal data which is illustrated by its application to data on the time evolution of CD4 cell numbers in HIV seroconverters. The essential ingredients of the model are a parametric linear model for covariate adjustment, a nonparametric estimation of a smooth time trend, serial correlation between measurements on an individual subject, and random measurement error. A back-fitting algorithm is used in conjunction with a cross-validation prescription to fit the model. A notable feature in the application is that the onset of HIV infection is associated with a sudden drop in CD4 cells followed by a longer-term slower decay. The model is also used to estimate an individual's curve by combining his data with the population curve. Shrinkage toward the population mean trajectory is controlled in a natural way by the estimated covariance structure of the data.

Acquired Immunodeficiency Syndrome↗

PubMed1991

Using longitudinal data to estimate nonresponse bias.

In a recent survey of depressive symptoms among former prisoners of war, longitudinal data were used to estimate nonresponse bias. A predictive model was fitted to the data of current respondents and then was used to predict the scores of nonrespondents who had earlier provided similar convariate data. This analysis showed that, despite differences between respondents and nonrespondents in age, education, and severity of treatment during captivity, differences between the observed scores of respondents and the predicted scores of nonrespondents were small. For an estimation of the overall impact of nonresponse bias, revised estimates for the entire sample were calculated by combining observed data from respondents and predicted data for nonrespondents; the revised estimates differed little from those for respondents alone.

Adult↗

PubMed1988

Models for longitudinal data: a generalized estimating equation approach.

This article discusses extensions of generalized linear models for the analysis of longitudinal data. Two approaches are considered: subject-specific (SS) models in which heterogeneity in regression parameters is explicitly modelled; and population-averaged (PA) models in which the aggregate response for the population is the focus. We use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes. When the subject-specific parameters are assumed to follow a Gaussian distribution, simple relationships between the PA and SS parameters are available. The methods are illustrated with an analysis of data on mother's smoking and children's respiratory disease.

Child↗

PubMedDate not supplied

Multivariate methods for binary longitudinal data with heterogeneous correlation over time.

Clustered binary data occur frequently in biostatistical work. One particular application is in binary longitudinal data, where several visits are available for the same individual. Several approaches have been proposed for the analysis of clustered binary data. In Rosner, a polychotomous logistic regression model was proposed which is a generalization of the beta-binomial distribution and allows for person- and visit-specific covariates, while controlling for clustering effects. One assumption of this model is that all pairs of visits within an individual are equally correlated, which may be inappropriate if several visits are available over a long follow-up period. In this paper, this approach is extended to allow for heterogeneous correlation over time. The total time period is divided into subintervals and a beta-binomial mixture model is introduced to estimate odds ratios relating outcomes for pairs of visits both within a subinterval as well as in different subintervals. To include covariates, an extension of the polychotomous logistic regression model is proposed, which allows one to estimate effects of person-, subinterval-, and visit-specific covariates, while controlling for clustering using the beta-binomial mixture model. This model is applied to the analysis of respiratory symptom data in children collected over a 14-year period in East Boston, MA, in relation to maternal and child smoking, where the unit is the child and symptom history is divided into early-adolescent and late-adolescent symptom experience.

Humans↗

PubMed2000

A robust mixed linear model analysis for longitudinal data.

This paper describes robust procedures for estimating parameters of a mixed effects linear model as applied to longitudinal data. In addition to fixed regression parameters, the model incorporates random subject effects to accommodate between-subjects variability and autocorrelation for within-subject variability. Robust empirical Bayesian estimation of subject effects is briefly discussed. As an illustration, the procedures are applied to data from a multiple sclerosis clinical trial.

Adjuvants, Immunologic↗

PubMed2003

Consistency of genetic analyses in longitudinal data: observations from the GAW13 Framingham Heart Study data.

This paper examines the consistency of genetic analyses across time, both in the context of replicating results from one data collection point to the next, and from the perspective of modeling longitudinal processes. This summary originates from the examination of findings from nine papers from Genetic Analysis Workshop (GAW) 13 that reported on analyses of longitudinal data of a variety of traits from the Framingham Heart Study. These analyses include both assessments of consistency of aggregate genetic effects, in the form of estimation of heritability and relative risk of disease, as well as localization of quantitative trait loci (QTLs) by genome-wide linkage screens. Consistency varied widely by trait, possibly reflecting differences in measurement error, secular trends, or underlying biological features such as genotype x age interaction. Quantitatively, comparing magnitudes of estimates across age or time, heritability estimates showed greater consistency than LOD scores. However, qualitatively, the same regions of interest were often identified in genome scans from different time points or different ages. Estimates of sibling recurrence risk, on the other hand, showed little consistency. Heritabilities were greater when participants were matched by age than when they were matched by date of examination. Multivariate approaches, either in use of multiple traits or in use of multiple measures of the same trait, appeared to provide stronger genetic signals both for relative risk and for linkage. Finally, modeling of longitudinal processes provided evidence for genotype x age interactions that may partially explain variation in results of genetic analyses across time or age.

Age Factors↗

PubMed1998

Compliance in an anti-hypertension trial: a latent process model for binary longitudinal data.

We propose an alternative to the method of generalized estimating equations (GEE) for inference about binary longitudinal data. Unlike GEE, the method is practicable when the data consist of long time series on each subject and the set of observation times is not necessarily common to all subjects. Instead of modelling the intra-series correlations explicitly, we assume that a subject's propensity to respond is governed by an underlying, but unobserved, stationary continuous process. Given a realization of this process, we assume that the binary responses are conditionally independent, with the probability that a subject responds positively at any given time t depending on the value of the underlying process at that time and also on any covariates specific to the subject at that time. We develop an algorithm for estimating the parameters in this model, and investigate its effectiveness using simulation methods. We also apply the methodology to data collected in a trial investigating the effect of self-measurement of blood pressure on compliance in taking medication during a course of anti-hypertension treatment.

Angiotensin-Converting Enzyme Inhibitors↗

PubMed2005

[Markov Chain Monte Carlo Method of multiple imputation for longitudinal data with missing values in the survey of maternal and children health].

OBJECTIVE: To deal with arbitrary missing pattern in longitudinal data of the Survey of Maternal and Child Health and make the most appropriate inferences with multiple imputation (MI) for further analysis. METHODS: SAS 9.0 was used for Markov Chain Monte Carlo (MCMC) method of MI procedure to impute missing values and combine inferences. RESULTS: The result is acceptable as the data set was imputed 5 times. CONCLUSION: MI is able to solve a variety of problems in missing data sets and to improve the statistical power, especially with the use of MCMC method, for complicated missing data sets.

Bias↗

PubMed1993

Cause and course of psychopathology: some lessons from longitudinal data.

Case-control studies of clinic samples constitute the usual research method for the investigation of the causes and course of psychiatric disorder. However, they carry substantial disadvantages and if causal hypotheses are to be tested in rigorous fashion, it is necessary to use longitudinal research strategies applied to epidemiologically based samples. Their advantages are reviewed with respect to the use of 'experiments of nature' for testing causal mechanisms through the study of within-individual change over time in relation to some prospectively measured alteration in the risk variable. Attention is drawn to the value of longitudinal data in studying the processes involved in 'escape' from risk; in examining differential vulnerability to risk experiences; in validating diagnostic categories; in investigating the timing of disorders; and in evaluating the role of variables that cannot be recalled. The data from a range of longitudinal studies are used to note some of the key implications for developmental and psychopathological concepts.

Adolescent↗

PubMed1976

Estimation of incidence and recovery rates of Plasmodium falciparum parasitaemia from longitudinal data.

A method is described of estimating the malaria incidence rate ĥ and the recovery rate r from longitudinal data. The method is based on the assumption that the phenomenon of patent parasitaemia can be represented by a reversible two-state catalytic model; it is applicable to all problems that can be represented by such a model.The method was applied to data on falciparum malaria from the West African savanna and the findings suggested that immunity increases the rate of recovery from patent parasitaemia by a factor of up to 10, and also reduces the number of episodes of patent parasitaemia resulting from one inoculation. Under the effect of propoxur, ĥ varies with the estimated man-biting rate of the vector while r increases, possibly owing to reduced super-infection.

Adolescent↗

PubMed2000

Population norms for the MMSE in the very old: estimates based on longitudinal data. Mini-Mental State Examination.

OBJECTIVE: To report the percentile distribution of Mini-Mental State Examination (MMSE) scores in older people by age, sex, and education level, estimated from longitudinal data, after correcting for loss due to dropout. METHODS: The Cambridge City over 75 Cohort is a population-based study of a cohort of 2106 subjects age 75 years and older at study entry followed up over 9 years. At each of the four waves, cognitive function was assessed using MMSE. Based on these data, the relationship between age and MMSE score was modeled. Percentile distributions by age, sex, and education level were provided using inverse probability weighting to correct for dropouts. RESULTS: Performance on MMSE was related to age in men and women. In women, at age 75, MMSE score ranged from 21 (10th percentile) to 29 (90th percentile). At age 95, the range was 10 (10th percentile) to 27 (90th percentile). The upper end of MMSE distribution was slightly modified with age, whereas the lower end of the distribution was very sensitive to age effect. A similar pattern was observed in both sexes. CONCLUSION: These findings provide norms for MMSE scores in subjects age 75 years and older from longitudinal population-based data. Such norms can be used as reference values to determine where an individual's score lies in relation to his or her age, sex, and education level.

Aged↗

PubMed2005

A nonparametric approach to the analysis of longitudinal data via a set of level crossing problems with application to the analysis of microarray time course experiments.

Here we develop a completely nonparametric method for comparing two groups on a set of longitudinal measurements. No assumptions are made about the form of the mean response function, the covariance structure or the distributional form of disturbances around the mean response function. The solution proposed here is based on the realization that every longitudinal data set can also be thought of as a collection of survival data sets where the events of interest are level crossings. The method for testing for differences in the longitudinal measurements then is as follows: for an arbitrarily large set of levels, for each subject determine the first time the subject has an upcrossing and a downcrossing for each level. For each level one then computes the log rank statistic and uses the maximum in absolute value of all these statistics as the test statistic. By permuting group labels we obtain a permutation test of the hypothesis that the joint distribution of the measurements over time does not depend on group membership. Simulations are performed to investigate the power and it is applied to the area that motivated the method-the analysis of microarrays. In this area small sample sizes, few time points and far too many genes to consider genuine gene level longitudinal modeling have created a need for a simple, model free test to screen for interesting features in the data.

Computer Simulation↗

PubMed1989

A cautionary note on the use of autoregressive models in analysis of longitudinal data.

Rosner et al. presented a simple, easily implemented modelling method for retaining time order relationships in analyses of longitudinal data when successive measures are correlated. Evaluation of time order is particularly useful in epidemiologic studies concerned with exposure to potentially toxic substances and subsequent outcome, but may also have use in more traditional growth studies that relate intake to subsequent development. The analysis allows for unequally spaced measures and missing data. The estimation method permits varying numbers of observations per subject and, with measures equally spaced, one can fit the model with use of ordinary least squares regression software. We report on a potential false association that can result when both exposure and outcome are related to time. We illustrate this problem with a small scale simulation and example. We also note a more serious problem with Rosner's approach in interpreting parameters. Although the model may be useful for prediction, parameters depend on the autocorrelation and are not readily interpretable. We recommend alternative modelling strategies be used when autocorrelation of errors is suspected.

Age Factors↗