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Results for “longitudinal data”

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PubMed2005

Group sequential testing in dental clinical trials with longitudinal data on multiple outcome variables.

In this article, methods are proposed for design and analysis of clinical trials that gather longitudinal data on multiple outcome variables. A valid test of the null hypothesis of no treatment group differences can be obtained for any choice of a working alternative hypothesis and a working covariance matrix for the outcome variables. Increased power can be achieved by accurate modeling of the true treatment effect and covariance structure. Implementation of the procedure is simple using existing software for generalized estimating equations. The procedure is an extension of the 'derived variable' technique (univariate analysis applied to a linear combination of the outcome variables) and also of O'Brien's generalized least squares test. The procedure is extended to allow sequential testing using an arbitrary division of the total type I error rate among repeated hypothesis tests. The methods are illustrated by the design of a study on the safety of dental amalgam fillings, which served as the motivation for the research.

Clinical Trials as Topic↗

PubMed1995

Longitudinal data analysis for linear Gaussian models with random disturbed-highest-derivative-polynomial subject effects.

For linear regression analysis of longitudinal data with Gaussian response, I propose a new model to generalize the traditional class of random effects models in which the random effects are deterministic polynomials with coefficients randomly distributed over subjects with mean zero. The generalization is accomplished by adding zero mean Gaussian 'disturbances' to the highest derivative of each random coefficient subject polynomial, independently at each observation time. The resulting random effects, which have mean zero at each observation time, are called disturbed highest derivative polynomials (DHDPs). The disturbances induce serial correlation and also allow the subject-specific DHDP time trends to be non-linear. I do not estimate the subject-specific DHDP time trends. Analysis is based on the marginal model, that is, the fixed effects or population model obtained by integrating the random polynomial coefficients and all disturbances out of the joint distribution of themselves and the response vector. This allows a 'population averaged' interpretation. One can select the DHDP order by an information criterion. When the population time trend is not correctly modelled, the optimal DHDP order will be larger than when it is correctly modelled. One can make the covariance matrix of the regression coefficients robust to errors in modelling the within-subject dependence. I describe the relationship of a DHDP to a smoothing polynomial spline, and show how to replace the DHDP model with a smoothing polynomial spline model for the within-subject dependence in the marginal model.

Bias↗

PubMed1994

A PC program for classification into one of several groups on the basis of longitudinal data.

A stand-alone, menu-driven PC program, ZCLASS, written in GAUSS386i, for classifying subjects into one of several distinct, existing groups on the basis of longitudinal data is described, illustrated, and made available to interested readers. The program accepts data from studies where common times of measurement are planned, but missing data are accommodated in that one or more measurement sequences may be incomplete.

Anthropometry↗

PubMedDate not supplied

The Manton-Woodbury model for longitudinal data with dropouts.

Often in longitudinal studies one is not able to obtain a complete set of measurements of the variable recorded over time for each person in the study. This could be caused by some of the persons dying (or leaving the study for some other reasons) while the study is going on. If there is any concern that such missing data (which have been termed dropouts) and the variables measured over time affect each other, a model for the joint distribution is needed. For a review of several such models see Hogan and Laird (in this volume). A model of the same kind was proposed by Woodbury and Manton and developed further later on. In this model it is possible to describe the evolution of the distribution of the variable measured over time when exposed to mortality selection. In contrast to other models, this allows for an explicit description of the interaction between the variable measured over time and the time to dropout. We describe the model and propose some generalizations. The theory is illustrated by some Monte Carlo simulations.

Adult↗

PubMedDate not supplied

Dispersion models and longitudinal data analysis.

Dispersion models provide a flexible class of non-normal distributions with many potential applications in biostatistics, accommodating a wide range of continuous, discrete and mixed data. Starting with Liang and Zeger's generalized estimating equation method, we review some recent applications of dispersion models in longitudinal data analysis, including state space models based on the Tweedie class of exponential dispersion models. In medical applications the latent process of a state space model may often be interpreted as an unobserved potential morbidity process, which is modelled as a function of time varying covariates. By allowing a multivariate response vector of 'symptoms', the model integrates several response variables of mixed types into a single model. For growth curve models, the latent process reflects the 'true' growth.

Air Pollutants↗

PubMed1999

1996 Remington lecture: modeling multivariate longitudinal data that are incomplete.

PURPOSE: We describe the impact that missing data may have on model selection for longitudinal multivariate data. METHODS: Maximum likelihood was used to fit several models to ultrasonographic measurements from the Asymptomatic Carotid Artery Progression Study (ACAPS). Graphical techniques were used to examine evidence concerning the underlying missing data mechanisms associated with each model. RESULTS: Using statistical methodology that addressed missing data substantially increased the statistical efficiency of our analysis of ultrasonographic data. Only complex models that included segment-specific parameterizations for longitudinal correlations appeared to allow missing data to be assumed to occur at random. CONCLUSION: Ignoring the nature of missing data in conducting statistical analyses can have serious consequences when missingness is not rare. It may be necessary to fit models of high dimension with maximum likelihood techniques to address missing data appropriately, however these approaches may improve statistical efficiency.

Carotid Stenosis↗

PubMed1993

Using orthogonal polynomial scores in summarizing and evaluating longitudinal data collected in phase I and II clinical pharmacology studies.

Orthogonal polynomial scores (OPS) is a simple, biologically meaningful approach to characterize longitudinal data in phase I and II clinical pharmacology trials. It describes average, linear, quadratic and higher order polynomial characteristics of each subject's response over time with use of composite scores computed from linear combinations of the observed data. The statistical evaluation of the composite scores is univariate. For studies with a small number of experimental units and with many repeated measures, OPS may offer advantages over the use of summary measures such as the maximum response (MAX), the time at which MAX occurred (TMAX), or the area under the response curve (AUC), and other popular approaches such as time-point-by-time-point, split-plot, and multivariate analyses.

Adult↗

PubMed1992

Multivariate methods for clustered binary data with multiple subclasses, with application to binary longitudinal data.

Clustered binary data occur frequently in biostatistical work. Several approaches have been proposed for the analysis of clustered binary data. In Rosner (1984, Biometrics 40, 1025-1035), a polychotomous logistic regression model was proposed that is a generalization of the beta-binomial distribution and allows for unit- and subunit-specific covariates, while controlling for clustering effects. One assumption of this model is that all pairs of subunits within a cluster are equally correlated. This is appropriate for ophthalmologic work where clusters are generally of size 2, but may be inappropriate for larger cluster sizes. A beta-binomial mixture model is introduced to allow for multiple subclasses within a cluster and to estimate odds ratios relating outcomes for pairs of subunits within a subclass as well as in different subclasses. To include covariates, an extension of the polychotomous logistic regression model is proposed, which allows one to estimate effects of unit-, class-, and subunit-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, Massachusetts, 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.

Adolescent↗

PubMed2000

Summarizing the goodness of fit of generalized linear models for longitudinal data.

This paper extends four goodness-of-fit measures of a generalized linear model (GLM) to random effects and marginal models for longitudinal data. The four measures are the proportional reduction in entropy measure, the proportional reduction in deviance measure, the concordance correlation coefficient and the concordance index. The extended measures satisfy the basic requirements for measures of association. Two examples illustrate their use in model selection.

Adolescent↗

PubMedDate not supplied

A comparative study of the fit of four different functions to longitudinal data of growth in height of Belgian girls.

We have fitted Preece-Baines model 1, double logistic, logistic and Gompertz functions to longitudinal data on the growth in height of 35 Belgian girls, followed from birth to 18.0 years. The Preece-Baines model 1 showed significantly lower residual mean squares than the double logistic function, when fitted to data beyond the age of 1.0 year. The former model was also most robust towards variations in the lower age bound by the subject's data series and always described the adolescent spurt better than the latter. Both models fitted the data badly when measurements before the age of 1.0 year were included, and they usually estimated the point at take-off too early. Over the adolescent cycle, only, the logistic function fitted our data slightly better than the Gompertz function, with significantly lower pooled residual mean squares, though a slightly worse performance in the runs-test.

Adolescent↗

PubMedDate not supplied

Guttman scale analysis of longitudinal data: a methodology and drug use applications.

Traditional Guttman scalogram analysis is limited to evaluating item order cross-sectionally. This paper describes a new methodology, Longitudinal Scalogram Analysis (LSA), that is a direct extension of cross-sectional scalogram analysis to longitudinal data. Example applications of the LSA method to drug use data are provided. The benefits of LSA relative to cross-sectional methods for drug use analysis are discussed.

Adolescent↗

PubMed2007

LongCriSP: a test for bump hunting in longitudinal data.

We propose an extension of the Harezlak and Heckman (J. Comput. Graph. Statist. 2001; 10(4): 713-729) test for detecting local extrema to the longitudinal data setting. We use penalized spline regression techniques (Statist. Sci. 1996; 11:89-102) to provide a computationally efficient method of testing for relatively large data sets. We estimate the p-values of our test, LongCriSP, with a smoothed bootstrap. Our simulation studies indicate that the test is generally conservative and has power exceeding 70 per cent at the alpha = 0.1 nominal level in most considered settings. Finally, we apply our testing procedure to the longitudinal measurements of body mass index of former prisoners of war in Vietnam and conclude that the mean population curve exhibits non-monotone behaviour.

Body Mass Index↗

PubMedDate not supplied

EM-REML estimation of covariance parameters in Gaussian mixed models for longitudinal data analysis.

This paper presents procedures for implementing the EM algorithm to compute REML estimates of variance covariance components in Gaussian mixed models for longitudinal data analysis. The class of models considered includes random coefficient factors, stationary time processes and measurement errors. The EM algorithm allows separation of the computations pertaining to parameters involved in the random coefficient factors from those pertaining to the time processes and errors. The procedures are illustrated with Pothoff and Roy's data example on growth measurements taken on 11 girls and 16 boys at four ages. Several variants and extensions are discussed.

Journal Article↗

PubMed1979

A quantitative index for evaluating patient care with longitudinal data.

This paper describes a patient-outcome based index of the quality of health care useful to health services researchers and planners. This index is applicable in any health care situation where longitudinal data are available from patients who can be classified into mutually exclusive stages of severity by functional status, psychological well-being or diagnosis and followed over a period of time. The rationale of the index is presented, along with an illustrative example based on a study on long-term care. The procedure for generating weights for the index is briefly described.

Data Collection↗

PubMed2002

Penalized likelihood approach to estimate a smooth mean curve on longitudinal data.

This paper aims to propose a penalized likelihood approach to estimate a smooth mean curve for the evolution with time of a Gaussian variable taking into account the correlation structure of longitudinal data. The model is an extension of the mixed effects linear model including an unspecified function of time f(t). The estimator (circumflex)f(t) is defined as the solution of the maximization of the penalized likelihood and is approximated on a basis of cubic M-spline with a reduced number of knots. We present modifications of four criteria (cross-validation, generalized cross-validation, T of Rice, Akaike's criterion) to estimate the smoothing parameter when data are correlated; these four criteria gave very similar results in the simulation study. The simulation study showed also the superiority of the Bayesian confidence bands of the mean curve over the frequentist ones. We develop empirical Bayes estimates of subject-specific deviations. This approach was applied to study the progression of CD4+ lymphocyte counts in a cohort of HIV patients treated with protease inhibitors.

Acquired Immunodeficiency Syndrome↗

PubMed2002

Insights from longitudinal data on the earnings growth of U.S. foreign-born men.

Does the growth in earnings of foreign-born men exceed that of U.S. natives? We use longitudinal data on earnings from a Social Security Administration (SSA) database matched to the 1994 March Current Population Survey to shed new light on this important issue. We also examine the trend over time in the foreign-born men's earnings growth and illuminate the various ways that SSA data can be used to explore the earnings patterns of immigrants.

Adult↗

PubMed2004

Shifts in percentiles of growth during early childhood: analysis of longitudinal data from the California Child Health and Development Study.

OBJECTIVE: To document growth-velocity changes across major percentiles during the preschool years. DESIGN: Analyses of longitudinal data using height-for-age, weight-for-age, weight-for-height, and body mass index (BMI)-for-age percentiles were performed to examine crossing of major percentiles of the Centers for Disease Control and Prevention 2000 growth charts. The 5th, 10th, 25th, 50th, 75th, 90th, and 95th percentiles were defined as the major percentiles. SETTING: Data from the California Child Health and Development Study were used. SUBJECTS: A total of 10,844 children up to 60 months of age, with 44,296 height and weight measurements, were included in our final analysis. RESULTS: For height-for-age, 32% of children between birth and 6 months of age, 13% to 15% of children between 6 and 24 months of age, and 2% to 10% of children between 24 and 60 months of age crossed 2 major percentiles. For weight-for-age, 39% of children between birth and 6 months of age, 6% to 15% of children between 6 and 24 months of age, and 1% to 5% of children between 24 and 60 months of age crossed 2 major percentiles. In contrast, for weight-for-height, 62% of children between birth and 6 months of age, 20% to 27% of children between 6 and 24 months of age, and 6% to 15% of children between 24 to 60 months of age crossed 2 major percentiles. Similar to the pattern observed for weight-for-height, 8% to 15% of children between 24 and 60 months of age crossed 2 major BMI-for-age percentiles. During the preschool years, weight-for-height had the highest percentages of children who crossed 2 major percentiles, and weight-for-age had the lowest percentages of children who crossed 2 major percentiles among these 3 indices. CONCLUSIONS: Shifts in growth rates were very common for children from birth to 6 months of age, somewhat less common for children 6 to 24 months of age, and least common for children 24 to 60 months of age. Shifts in weight-for-height occurred more frequently than did other growth changes. Pediatricians must consider the prevalence of growth rate shifts during infancy and early childhood before they counsel parents regarding growth or refer children for additional evaluations of growth.

Body Height↗

PubMed2007

Latent-variable models for longitudinal data with bivariate ordinal outcomes.

We use the concept of latent variables to derive the joint distribution of bivariate ordinal outcomes, and then extend the model to allow for longitudinal data. Specifically, we relate the observed ordinal outcomes using threshold values to a bivariate latent variable, which is then modelled as a linear mixed model. Random effects terms are used to tie all together repeated observations from the same subject. The cross-sectional association between the two outcomes is modelled through the correlation coefficient of the bivariate latent variable, conditional on random effects. Assuming conditional independence given random effects, the marginal likelihood, under the missing data at random assumption, is approximated using an adaptive Gaussian quadrature for numerical integration. The model provides fixed effects parameters that are subject-specific, but retain the population-averaged interpretation when properly scaled. This is particularly well suited for the situation in which population comparisons and individual level contrasts are of equal importance. Data from a psychiatric trial, the Fluvoxamine (an antidepressant drug) study, are used to illustrate the methodology.

Antidepressive Agents, Second-Generation↗