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PubMed1998

The design and analysis of longitudinal studies of development and psychopathology in context: statistical models and methodological recommendations.

The utility and flexibility of recent advances in statistical methods for the quantitative analysis of developmental data--in particular, the methods of individual growth modeling and survival analysis--are unquestioned by methodologists, but have yet to have a major impact on empirical research within the field of developmental psychopathology and elsewhere. In this paper, we show how these new methods provide developmental psychopathologists with powerful ways of answering their research questions about systematic changes over time in individual behavior and about the occurrence and timing of life events. In the first section, we present a descriptive overview of each method by illustrating the types of research questions that each method can address, introducing the statistical models, and commenting on methods of model fitting, estimation, and interpretation. In the following three sections, we offer six concrete recommendations for developmental psychopathologists hoping to use these methods. First, we recommend that when designing studies, investigators should increase the number of waves of data they collect and consider the use of accelerated longitudinal designs. Second, we recommend that when selecting measurement strategies, investigators should strive to collect equatable data prospectively on all time-varying measures and should never standardize their measures before analysis. Third, we recommend that when specifying statistical models, researchers should consider a variety of alternative specifications for the time predictor and should test for interactions among predictors, particularly interactions between substantive predictors and time. Our goal throughout is to show that these methods are essential tools for answering questions about life-span developmental processes in both normal and atypical populations and that their proper use will help developmental psychopathologists and others illuminate how important contextual variables contribute to various pathways of development.

Adolescent↗
PubMed1997

Selection related to musculoskeletal complaints among employees.

OBJECTIVES: To (a) describe differences in the outcome of cross sectional and longitudinal analysis on musculoskeletal complaints relative to age and work demands, and (b) to assess the entrance and drop out selection on musculoskeletal complaints among groups of employees relative to age and work demands. METHODS: A study population was selected on the basis of questionnaire data from periodical occupational health surveys of almost 45,000 employees collected between 1982 and 1993. From all companies within this data base that participated twice in company wide surveys four years apart, male employees were selected, and stratified for age and work demands. There were several populations: follow up (participation in both surveys); drop out (participation only in the first survey); entrance (participation only at the second survey); and two cross sectional populations (all participants at each survey). Prevalences of back complaints and turnover rates were analysed. RESULTS: Reported back complaints in the cross sectional analysis declined over the oldest age groups in heavy physical work versus a small increase in the longitudinal analysis. The age group 50-9 and back complaints were identified as predictors at the first survey for not participating at the second survey. Neither age nor work demands at the first survey indicated drop out among those employees with back complaints at the first survey. The effects of entrance selection on estimated prevalences were small. CONCLUSIONS: The results indicate that musculoskeletal disorders lead to selection out of work, affecting the validity of both cross sectional and longitudinal epidemiological studies. In future studies analyses of turnover figures on musculoskeletal complaints relative to work demands and age are recommended.

Adult↗
PubMed1994

Analysis of longitudinal data with unequally spaced observations and time-dependent correlated errors.

A linear model for repeated measurements is proposed in which the correlation structure includes a transformation of the time scale. This transformation can produce nonstationary covariance structures within subjects with stationarity as a special case. Restricted maximum likelihood methods for parameter estimation are discussed. The method is applied to simulated data as well as speech recognition data from the Iowa Cochlear Implant Project. The growth curve for this audiologic performance measure is shown together with estimates of the standard errors of predictions at given months.

Audiology↗
PubMed1993

The analysis of longitudinal polytomous data: generalized estimating equations and connections with weighted least squares.

In recent years, methods have been developed for modelling repeated observations of a categorical response obtained over time on the same individual. Although situations in which the repeated response is binary or Poisson have been studied extensively, relatively little attention has been given to polytomous categorical response variable. In this paper, we extend the estimating equations initially developed for clustered discrete data by Liang and Zeger (1986, Biometrika 73, 13-22), and subsequently extended by Prentice (1988, Biometrics 44, 1033-1048), to polytomous response variables. Under certain assumptions, we illustrate that these estimating equations simplify to the weighted least squares (WLS) equations formalized by Koch et al. (1977, Biometrics 33, 133-158). This connection provides a formal framework for obtaining iterated weighted least squares model parameter estimates. Cumulative logit models are developed and applied to a representative longitudinal data set. Simulation results comparing WLS, an iterative form of WLS, and independence estimating equations using a robust estimate of the variance are presented.

Analysis of Variance↗
PubMed1997

Now you see it, now you don't: a comparison of traditional versus random-effects regression models in the analysis of longitudinal follow-up data from a clinical trial.

To illustrate the limitations of commonly used methods of handling missing data when using traditional analysis of variance (ANOVA) models and highlight the relative advantages of random-effects regression models, multiple analytic strategies were applied to follow-up data from a clinical trial. Traditional ANOVA and random-effects models produced similar results when underlying assumptions were met and data were complete. However, analyses based on subsamples, to which investigators would have been limited with traditional models, would have led to different conclusions about treatment effects over time than analyses based on intention-to-treat samples using random-effects regression models. These findings underscore the advantages of models that use all data collected and the importance of complete data collection to minimize sample bias.

Adult↗
PubMedDate not supplied

The use of an autoregressive model for the analysis of longitudinal data in epidemiologic studies.

Korn and Whittemore have presented methods for analyzing longitudinal data where the number of observations per individual is large relative to the number of variables considered for each subject. However, this is often not the case in epidemiologic studies, since one usually collects data at relatively few time points, and the quantity of data collected for each individual at each time point is typically extensive. We present here an autoregressive model for analyzing longitudinal data of this type for the case of a continuous outcome variable. Some of the important features of this model are that one can in the same analysis, consider both independent variables that are time-dependent and those that are fixed over time, partially use data for an individual where some examinations are missing, assess relationships between changes in outcome and exposure over short periods of time, use ordinary multiple regression methods. Anderson has considered this type of model, but, to our knowledge, the model has never been applied to biostatistical problems. We illustrate these methods with data from a longitudinal study that seeks to identify the role of personal cigarette smoking on changes in pulmonary function in children.

Adolescent↗
PubMed1999

Changes in parents' mental distress after the violent death of an adolescent or young adult child: a longitudinal prospective analysis.

This study examined changes in bereaved parents' mental distress following the violent deaths of their 12- to 28-year-old children. A community-based sample of 171 bereaved mothers and 90 fathers was recruited by a review of medical examiner records. Data were collected 4, 12, and 24 months post-death. Repeated measures analysis of variance showed significant reductions in 8 of 10 measures of mental distress among mothers and 4 of 10 for fathers, with the most change for both genders occurring between 4 and 12 months post-death. During the 2nd year of bereavement, mothers' symptoms continued to decline, whereas fathers, who started out with less distress than mothers, reported slight increases in 5 of 10 symptom domains. Nonetheless, 2 years after the deaths, mothers' mental distress scores were up to 5 times higher than those of "typical" U.S. women and fathers' scores were up to 4 times higher than "typical" U.S. men. Of the 7 intervening variables examined, higher scores on self-esteem and self-efficacy predicted lower distress for both mothers and fathers 4, 12, and 24 months post-death. Repressive coping was predictive of distress among fathers. It was concluded that violent death bereavement has sustained, distressing consequences on parents of children who die as a result of accidents, homicides, and suicide.

Adaptation, Psychological↗
PubMed2006

Longitudinal genetic analysis of executive function in elderly men.

The objective of this study was to characterize the relative contribution of genetic and environmental influences to individual differences in longitudinal performance and decline of executive function (EF) using a population-based prospective study of male, WWII veteran twins (NHLBI twin study). Three tests of EF were administered when the twins were 59-70 years old, with 9- and 13-year follow-up. APOE epsilon4 allele status was incorporated in the genetic models to determine its contribution to longitudinal genetic variability. Mean EF performance significantly worsened over time. EF performance was highly genetically correlated across repeat assessment. There were significant genetic influences on 9- and 13-year decline in digit symbol performance. For all tasks decline over the last 4-year follow-up was influenced by individual-specific environmental effects. Controlling for APOE epsilon4 allele presence did not appreciably change the magnitude of genetic effects. These results suggest that common genetic factors underlie longitudinal EF task performance. Genetic influences on EF decline, however, appear to be evident at longer time intervals between assessments.

Aged↗
PubMed2003

Bayesian meta-analysis for longitudinal data models using multivariate mixture priors.

We propose a class of longitudinal data models with random effects that generalizes currently used models in two important ways. First, the random-effects model is a flexible mixture of multivariate normals, accommodating population heterogeneity, outliers, and nonlinearity in the regression on subject-specific covariates. Second, the model includes a hierarchical extension to allow for meta-analysis over related studies. The random-effects distributions are decomposed into one part that is common across all related studies (common measure), and one part that is specific to each study and that captures the variability intrinsic between patients within the same study. Both the common measure and the study-specific measures are parameterized as mixture-of-normals models. We carry out inference using reversible jump posterior simulation to allow a random number of terms in the mixtures. The sampler takes advantage of the small number of entertained models. The motivating application is the analysis of two studies carried out by the Cancer and Leukemia Group B (CALGB). In both studies, we record for each patient white blood cell counts (WBC) over time to characterize the toxic effects of treatment. The WBCs are modeled through a nonlinear hierarchical model that gathers the information from both studies.

Bayes Theorem↗
PubMed1993

The worksite component of variance: design effects and the Healthy Worker Project.

Variance estimates in worksite health promotion studies depend partly on the intraclass correlation coefficient (ICC). ICC quantifies homogeneity of a variable within worksites. ICC would be zero for randomly formed worksites, but is generally positive because employees tend to share personal characteristics. The ratio comparing the variance estimated from worksite means with that estimated from individuals under simple random sampling is the design effect (DEFF). A DEFF of 1.0 indicates no excess variance due to worksite. The Healthy Worker Project (HWP) was a 32 worksite cross-sectional and longitudinal study of a weight and smoking intervention program. ICCs in cross-sectional surveys for health-related outcome variables ranged from 0.006 to 0.009, DEFFs from 2.0 to 2.6 ICCs/DEFF's in longitudinal analysis were smaller; ICCs ranged from -0.002 to 0.003, DEFFs from 0.7 to 1.5. Positive ICCs substantially increased variance estimates at a single measurement, yet variance of longitudinal analysis was less subject to worksite dependence. It is concluded the worksite component of variance is real and should not be ignored, although the worksite component of variance is small in these longitudinal analyses. This observation should be replicated before it is used in other worksite health promotion research.

Analysis of Variance↗
PubMedDate not supplied

Behavioral traits and marijuana use and abuse: a meta-analysis of longitudinal studies.

The present study uses data from a meta-analytic archive of prospective longitudinal studies (N= 3206) to examine the association between negative affect, emotionality, and unconventionality on the use, misuse, and abuse of marijuana. For each of the three constructs, variables were divided into two categories--a "trait," which refers to a personality characteristic or attitudes and beliefs, and a "behavior," which refers to something that a subject does. A total of 63 reports from 40 studies provided effect sizes on the bivariate relationship of one or more of these six categories with current or later marijuana use, misuse, or abuse. Pooling partially redundant estimates for independence reduced the dataset from 358 estimates to 93 aggregated effect sizes for the cross-sectional data included in the archive, and from 478 estimates to 73 aggregated effect sizes for the longitudinal data. The effect sizes obtained from the longitudinal data were modest, none above 0.20. Indeed, only those for unconventionality-trait and emotionality-trait and marijuana use were of sufficient magnitude and reliably to warrant attention. Of the behavioral constructs assessed using the cross-sectional data, only unconventionality was associated with marijuana use and misuse. The emotionality-behavior construct and both unconventionality constructs were most strongly associated with marijuana abuse. The conceptual and methodological limitations of the study along with the implications of its findings for prevention are briefly discussed.

Behavior, Addictive↗
PubMed2004

Semiparametric regression analysis on longitudinal pattern of recurrent gap times.

In longitudinal studies, individual subject may experience recurrent events of the same type over a relatively long period of time. The longitudinal pattern of gaps between successive recurrent events is often of great research interest. In this article, the probability structure of the recurrent gap times is first explored in the presence of censoring. According to the discovered structure, we introduce the stratified proportional reverse-time hazards models with unspecified baseline functions to accommodate individual heterogeneity, when the longitudinal pattern parameter is of main interest. Inference procedures are proposed and studied by way of proper riskset construction. The proposed methodology is demonstrated by the Monte Carlo simulations and an application to a well-known Denmark schizophrenia cohort study data set.

Age of Onset↗
PubMed1992

A parametric family of correlation structures for the analysis of longitudinal data.

In epidemiological settings, we are often faced with numerous short time series, and a parsimonious parametrization of the correlation structure is desired in order to optimize the efficiency of the estimation procedure. We propose a damped exponential correlation structure for modeling multivariate Gaussian outcomes. The correlation between two observations separated by s units of time is modeled as gamma s theta, where gamma is the correlation between elements separated by one s-unit, and theta is a damping parameter. For (theta = 0), (theta = 1), and theta----infinity), the correlation structures of compound symmetry, first-order autoregressive, and first-order moving average processes are obtained. Although the AR(2) dependency structure, and the combination of random effects and AR(1) errors are not special cases of the proposed parametric family, these structures can be well approximated within the family for short time series. Maximum likelihood methods for parameter estimation and interpretations of intermediate models (0 less than theta less than 1) are discussed in the context of modeling pulmonary function in an adult population in The Netherlands and T-cell subsets in homosexual men infected with human immunodeficiency virus Type I.

Adult↗
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↗