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Results for “longitudinal data”

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PubMed1990

Protecting against nonrandomly missing data in longitudinal studies.

Nonrandomly missing data can pose serious problems in longitudinal studies. We generally have little knowledge about how missingness is related to the data values, and longitudinal studies are often far from complete. Two approaches that have been used to handle missing data--use of maximum likelihood with an ignorable mechanism and direct modeling of the missing data mechanism--have the disadvantage of not giving consistent estimates under important classes of nonrandom mechanisms. We introduce two protective estimators, that is, estimators that retain their consistency over a wide range of nonrandom mechanisms. We compare these protective estimators using longitudinal data from a mental health panel study. We also investigate their robustness to certain departures from normality.

Data Interpretation, Statistical↗

PubMed1996

A functional decline model for prevalent cohort data.

Longitudinal designs are often used for studying the natural history of diseases. Data sets typically consist of short series of repeated measures on prevalent cases. We propose a growth model approach to the analysis of follow-up data to describe functional decline and associated risk factors in disease progression. We illustrate the model with an application to longitudinal data that describe the time-evolution of cognitive decline in a cohort of patients with Alzheimer's disease.

Alzheimer Disease↗

PubMed2002

Analysis of clustered and longitudinal binary data subject to response misclassification.

Misclassified clustered and longitudinal data arise in studies where the response indicates a condition identified through an imperfect diagnostic procedure. Examples include longitudinal studies that use an imperfect diagnostic test to assess whether or not an individual has been infected with a specific virus. This article presents methods to implement both population-averaged and cluster-specific analyses of such data when the misclassification rates are known. The methods exploit the fact that the class of generalized linear models enjoys a closure property in the case of misclassified responses. Data from longitudinal studies of infectious disease will illustrate the findings.

Biometry↗

PubMed2003

An illness-death stochastic model in the analysis of longitudinal dementia data.

A significant source of missing data in longitudinal epidemiological studies on elderly individuals is death. Subjects in large scale community-based longitudinal dementia studies are usually evaluated for disease status in study waves, not under continuous surveillance as in traditional cohort studies. Therefore, for the deceased subjects, disease status prior to death cannot be ascertained. Statistical methods assuming deceased subjects to be missing at random may not be realistic in dementia studies and may lead to biased results. We propose a stochastic model approach to simultaneously estimate disease incidence and mortality rates. We set up a Markov chain model consisting of three states, non-diseased, diseased and dead, and estimate the transition hazard parameters using the maximum likelihood approach. Simulation results are presented indicating adequate performance of the proposed approach.

Aged↗

PubMed2005

Regression models for the analysis of longitudinal Gaussian data from multiple sources.

We present a regression model for the joint analysis of longitudinal multiple source Gaussian data. Longitudinal multiple source data arise when repeated measurements are taken from two or more sources, and each source provides a measure of the same underlying variable and on the same scale. This type of data generally produces a relatively large number of observations per subject; thus estimation of an unstructured covariance matrix often may not be possible. We consider two methods by which parsimonious models for the covariance can be obtained for longitudinal multiple source data. The methods are illustrated with an example of multiple informant data arising from a longitudinal interventional trial in psychiatry.

Adolescent↗

PubMed2000

Semiparametric regression for periodic longitudinal hormone data from multiple menstrual cycles.

We consider semiparametric regression for periodic longitudinal data. Parametric fixed effects are used to model the covariate effects and a periodic nonparametric smooth function is used to model the time effect. The within-subject correlation is modeled using subject-specific random effects and a random stochastic process with a periodic variance function. We use maximum penalized likelihood to estimate the regression coefficients and the periodic nonparametric time function, whose estimator is shown to be a periodic cubic smoothing spline. We use restricted maximum likelihood to simultaneously estimate the smoothing parameter and the variance components. We show that all model parameters can be easily obtained by fitting a linear mixed model. A common problem in the analysis of longitudinal data is to compare the time profiles of two groups, e.g., between treatment and placebo. We develop a scaled chi-squared test for the equality of two nonparametric time functions. The proposed model and the test are illustrated by analyzing hormone data collected during two consecutive menstrual cycles and their performance is evaluated through simulations.

Biometry↗

PubMedDate not supplied

London Archive of Longitudinal Growth Data.

An Archive of longitudinal growth data, accessible to research workers under the usual safeguards, has been set up in the Department of Growth and Development. The present S.I.R. database contains seven British and one Indian study. The Archive is open to receive other contributions if researchers wish.

Adolescent↗

PubMed2000

Multiple imputation and posterior simulation for multivariate missing data in longitudinal studies.

This paper outlines a multiple imputation method for handling missing data in designed longitudinal studies. A random coefficients model is developed to accommodate incomplete multivariate continuous longitudinal data. Multivariate repeated measures are jointly modeled; specifically, an i.i.d. normal model is assumed for time-independent variables and a hierarchical random coefficients model is assumed for time-dependent variables in a regression model conditional on the time-independent variables and time, with heterogeneous error variances across variables and time points. Gibbs sampling is used to draw model parameters and for imputations of missing observations. An application to data from a study of startle reactions illustrates the model. A simulation study compares the multiple imputation procedure to the weighting approach of Robins, Rotnitzky, and Zhao (1995, Journal of the American Statistical Association 90, 106-121) that can be used to address similar data structures.

Acoustic Stimulation↗

PubMed1991

Multilevel modelling of longitudinal cephalometric data explained for orthodontists.

Multilevel modelling of longitudinal data is an important new statistical technique. In this article some of the basic concepts and ideas of multilevel modelling are explained. The model is introduced by showing how individual and average growth can be modelled. The intercept, linear and quadratic coefficient, between and within variance, fixed and random part, and other concepts of multilevel modelling are explained. Attention is also given to the reading of statistical tables of the results of multilevel analysis. In the conclusion some of the advantages of multilevel modelling of cephalometric data are mentioned.

Aging↗

PubMed1998

[Effect of smoking cessation on body mass index, blood pressure and serum lipids in middle-aged male workers].

The purpose of this study was to examine the effects of smoking cessation on body mass index (BMI), blood pressure and serum lipids in middle-aged male workers considering the effect of BMI which would increase by smoking cessation. The subjects were 1431 middle-aged men who worked in an enterprise in Hiroshima prefecture. Cross-sectional data measured in 1989 and longitudinal data measured from 1985 to 1989 were used in this analysis. The effect of smoking cessation on BMI, blood pressure and serum lipids were evaluated by two models of analysis of covariance (PC-SAS: GLM procedure) for the cross-sectional data and longitudinal data. In analysis of the cross-sectional data, model 1 was controlled for BMI and model 2 was not controlled for BMI. In analysis of the longitudinal data, model 3 was controlled for BMI change and model 4 was not controlled for BMI change. The main results are summarized as follows: 1. BMI was increased over the short period by smoking cessation, but over the long period BMI of ex-smokers remained at almost the same level as non-smokers'. 2. Blood pressure was increased over the short period by both the effect of smoking cessation and BMI increase from abstention from smoking. But over the long period blood pressure of ex-smokers remained at almost the same level as non-smokers. 3. Triglycerides (TG) and atherogenic index (AI) tended to decrease and HDL-cholesterol (HDLC) tended to increase over the short period by smoking cessation, but the concomitant BMI increase may have blunted any independent beneficial effect of smoking cessation on TG, AI and HDLC. But over the long period TG, AI and HDLC of ex-smokers recovered to almost the same level as non-smokers', and remained at that level. 4. These results suggest that smoking cessation have beneficial effects for health promotion in middle-aged men.

Age Factors↗

PubMed2004

The utility of the zero-inflated Poisson and zero-inflated negative binomial models: a case study of cross-sectional and longitudinal DMF data examining the effect of socio-economic status.

OBJECTIVES: To examine the utility of the zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) modelling approaches for modelling four sets of dental caries data from the same cohort study [with particular attention to the influence of childhood socioeconomic status (SES)]: cross-sectional data on the deciduous dentition at age 5 years; cross-sectional data on the permanent dentition at age 18 and 26 years; and longitudinal data on caries increment between ages 18 and 26 years. METHODS: Data on dental caries occurrence at ages 5, 18 and 26 years were obtained from the Dunedin Multidisciplinary Health and Development Study (DMHDS). ZIP and ZINB models were fitted to the cross-sectional (n = 745) and longitudinal (n = 809) data sets using Stata (Intercooled Stata 7.0). The dependent variables for the three cross-sectional analyses were the DMFS indices at age 5, 18, and 26 years, and net DFS increment (NETDFS) was the dependent variable for the longitudinal analysis. RESULTS: The empty ZIP model was a poor fit for all four data sets, whereas the empty ZINB model showed good fit; consequently both the cross-sectional and longitudinal analyses were conducted using ZINB modelling. Being in the high-SES group during childhood was associated with a greater probability of being caries-free by age 18 years, over and above that which would be expected from the negative binomial process. Low childhood SES also had the largest coefficient in the modelling of the negative binomial process, but at age 5 years, where the adjusted mean dmfs score in the low-SES group was 6.8 (compared with 4.7 and 2.9 in the medium- and high-SES groups, respectively). The substantial SES differences which existed at age 5 years (in the deciduous dentition) had reduced somewhat by age 18 years, and had widened again by age 26 years. In the longitudinal analysis, "baseline" caries experience (age 18-year DMFS) was a predictor both of being an extra zero and of caries severity. CONCLUSION: This investigation of the utility of the zero-inflated approach for modelling both cross-sectional and longitudinal caries data has shown that ZIP/ZINB models can provide new insight into disease patterns. It is anticipated that they will become increasingly useful in epidemiological studies that use the DMF index as the outcome measure.

Adolescent↗

PubMed2000

Local estimation of age-dependent variance components from longitudinal twin data.

In the study of longitudinal twin and family data, interest is often in the covariance structure of the data and the decomposition of this covariance structure into genetic and environmental components rather than in estimating the mean function. Various parametric models for covariance structures have been proposed but, e.g., in studies of children where growth spurts occur at various ages, it is difficult to a priori determine an appropriate parametric model for the covariance structure. In particular, there is a general lack of the visualization procedures, such as lowess, that are invaluable in the initial stages of constructing a parametric model for a mean function. Here we use kernel smoothing to modify a cross-sectional approach based on the sample covariance matrices to obtain smoothed estimates of the genetic and environmental variances and correlations for longitudinal twin data. The methods are proposed to be exploratory as an aid to parametric modeling rather than inferential, although approximate asymptotic standard errors are derived in the Appendix.

Age Factors↗

PubMed2002

A latent autoregressive model for longitudinal binary data subject to informative missingness.

Longitudinal clinical trials often collect long sequences of binary data. Our application is a recent clinical trial in opiate addicts that examined the effect of a new treatment on repeated binary urine tests to assess opiate use over an extended follow-up. The dataset had two sources of missingness: dropout and intermittent missing observations. The primary endpoint of the study was comparing the marginal probability of a positive urine test over follow-up across treatment arms. We present a latent autoregressive model for longitudinal binary data subject to informative missingness. In this model, a Gaussian autoregressive process is shared between the binary response and missing-data processes, thereby inducing informative missingness. Our approach extends the work of others who have developed models that link the various processes through a shared random effect but do not allow for autocorrelation. We discuss parameter estimation using Monte Carlo EM and demonstrate through simulations that incorporating within-subject autocorrelation through a latent autoregressive process can be very important when longitudinal binary data is subject to informative missingness. We illustrate our new methodology using the opiate clinical trial data.

Algorithms↗

PubMed2004

Semiparametric estimation of time-dependent ROC curves for longitudinal marker data.

One approach to evaluating the strength of association between a longitudinal marker process and a key clinical event time is through predictive regression methods such as a time-dependent covariate hazard model. For example, a Cox model with time-varying covariates specifies the instantaneous risk of the event as a function of the time-varying marker and additional covariates. In this manuscript we explore a second complementary approach which characterizes the distribution of the marker as a function of both the measurement time and the ultimate event time. Our goal is to extend the standard diagnostic accuracy concepts of sensitivity and specificity so as to recognize explicitly both the timing of the marker measurement and the timing of disease. The accuracy of a longitudinal marker can be fully characterized using time-dependent receiver operating characteristic (ROC) curves. We detail a semiparametric estimation method for time-dependent ROC curves that adopts a regression quantile approach for longitudinal data introduced by Heagerty and Pepe (1999, Applied Statistics, 48, 533-551). We extend the work of Heagerty and Pepe (1999, Applied Statistics, 48, 533-551) by developing asymptotic distribution theory for the ROC estimators where the distributional shape for the marker is allowed to depend on covariates. To illustrate our method, we analyze pulmonary function measurements among cystic fibrosis subjects and estimate ROC curves that assess how well the pulmonary function measurement can distinguish subjects that progress to death from subjects that remain alive. Comparing the results from our semiparametric analysis to a fully parametric method discussed by Etzioni et al. (1999, Medical Decision Making, 19, 242-251) suggests that the ability to relax distributional assumptions may be important in practice.

Adolescent↗

PubMed2006

Mixture analysis of longitudinal binary data.

The dependence of longitudinal binary outcomes on covariates and the covariation observed between them is often modelled by (multivariate) logistic and probit models, respectively, assuming specified association structure or random effects. Alternatively, latent class models may be used that capture the covariation by assuming heterogeneity of the observational units regarding their reaction tendencies while postulating independence within classes. In the presence of a few categorical covariates, the multi-group method of latent class analysis allows one to relate the class sizes and the class-specific response probabilities to these covariates. Wheeze data from the Harvard Six-Cities study on respiratory health are a typical example for such a situation: at four occasions, the wheeze status of 537 children was examined, 187 among them exposed to maternal smoking and 350 not exposed. Thus, there is a single binary covariate (maternal smoking versus no maternal smoking) making easily applicable the multi-group method of latent class analysis. Based on a series of unrestricted and restricted models having up to three classes for the exposed and not-exposed subgroup each, no statistically significant effect of maternal smoking on children's wheeze status could be substantiated. Moreover, it was not possible to show statistically significant difference at all between the two distributions of wheeze patterns collected from exposed and not-exposed children.

Child↗

PubMed1999

Marginally specified logistic-normal models for longitudinal binary data.

Likelihood-based inference for longitudinal binary data can be obtained using a generalized linear mixed model (Breslow, N. and Clayton, D. G., 1993, Journal of the American Statistical Association 88, 9-25; Wolfinger, R. and O'Connell, M., 1993, Journal of Statistical Computation and Simulation 48, 233-243), given the recent improvements in computational approaches. Alternatively, Fitzmaurice and Laird (1993, Biometrika 80, 141-151), Molenberghs and Lesaffre (1994, Journal of the American Statistical Association 89, 633-644), and Heagerty and Zeger (1996, Journal of the American Statistical Association 91, 1024-1036) have developed a likelihood-based inference that adopts a marginal mean regression parameter and completes full specification of the joint multivariate distribution through either canonical and/or marginal higher moment assumptions. Each of these marginal approaches is computationally intense and currently limited to small cluster sizes. In this manuscript, an alternative parameterization of the logistic-normal random effects model is adopted, and both likelihood and estimating equation approaches to parameter estimation are studied. A key feature of the proposed approach is that marginal regression parameters are adopted that still permit individual-level predictions or contrasts. An example is presented where scientific interest is in both the mean response and the covariance among repeated measurements.

Biometry↗

PubMed2002

Marginalized transition models and likelihood inference for longitudinal categorical data.

Marginal generalized linear models are now frequently used for the analysis of longitudinal data. Semiparametric inference for marginal models was introduced by Liang and Zeger (1986, Biometrics 73, 13-22). This article develops a general parametric class of serial dependence models that permits likelihood-based marginal regression analysis of binary response data. The methods naturally extend the first-order Markov models of Azzalini (1994, Biometrika 81, 767-775) and prove computationally feasible for long series.

Biometry↗

PubMed2004

Latent pattern mixture models for informative intermittent missing data in longitudinal studies.

A frequently encountered problem in longitudinal studies is data that are missing due to missed visits or dropouts. In the statistical literature, interest has primarily focused on monotone missing data (dropout) with much less work on intermittent missing data in which a subject may return after one or more missed visits. Intermittent missing data have broader applicability that can include the frequent situation in which subjects do not have common sets of visit times or they visit at nonprescheduled times. In this article, we propose a latent pattern mixture model (LPMM), where the mixture patterns are formed from latent classes that link the longitudinal response and the missingness process. This allows us to handle arbitrary patterns of missing data embodied by subjects' visit process, and avoids the need to specify the mixture patterns a priori. One assumption of our model is that the missingness process is assumed to be conditionally independent of the longitudinal outcomes given the latent classes. We propose a noniterative approach to assess this key assumption. The LPMM is illustrated with a data set from a health service research study in which homeless people with mental illness were randomized to three different service packages and measures of homelessness were recorded at multiple time points. Our model suggests the presence of four latent classes linking subject visit patterns to homeless outcomes.

Biometry↗