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PubMedDate not supplied

Longitudinal studies of thigh circumference growth in normal fetuses.

To characterize the growth of the thigh circumference (ThC) in individual fetuses, longitudinal studies of ThC growth were carried out in 20 fetuses between 19 (+/- 1.8) and 38 (+/- 1.5) weeks, menstrual age. Because of measurement uncertainties, analysis of growth patterns was limited to the data collected after 22 weeks. The Rossavik growth model fit the data well [R2: 95.8(+/- 2.9 SD)%], but considerable coefficient variability was seen, particularly for the coefficient k. Use of the coefficient k-value (1.138) derived from a cross-sectional data set reduced the variability of the coefficient c by 95% and made the results of the longitudinal and cross-sectional studies consistent with each other. This k-value was taken as the appropriate one for ThC growth curves. Studies of ThC growth in individual fetuses revealed considerable variability in growth curve shape, although the majority of curves could be approximated by a straight line. No differences between growth curves for males and females could be detected. The average longitudinal ThC growth curve was found to be very similar to the growth curve obtained in a cross-sectional study of ThC growth. ThC growth after 26.1 weeks could be predicted with an accuracy of +/- 15% from growth models derived from the data obtained before 26.1 weeks. These results indicate that ThC growth after 22 weeks (as with other parameters) can be followed in individual fetuses. However, because of the greater inherent variability in growth patterns, using each fetus as its own control may be more important.

Embryonic and Fetal Development↗
PubMed2006

Maximizing follow-up in longitudinal studies of traumatized populations.

Although longitudinal research is essential in understanding the nature and course of posttraumatic mental health problems, high rates of attrition often threaten the internal validity of such studies and make results hard to interpret. C. K. Scott (2004) developed an approach to minimizing attrition in longitudinal studies that consistently yielded retention rates in excess of 90% through to 2-year follow-up. In this article, the authors discuss the interface between trauma exposure and participation in longitudinal research, before describing in detail a model to address those effects. The effectiveness of the model is examined with reference to traumatic stress in a large community sample (N = 887) with eight waves of data over 2 years.

Adult↗
PubMed2005

Reference ranges for umbilical vein blood flow in the second half of pregnancy based on longitudinal data.

OBJECTIVES: To construct new reference ranges for serial measurements of umbilical vein (UV) blood flow. METHODS: Prospective longitudinal study of blood flow velocities and diameter of the UV measured at four-weekly intervals during 19 to 42 weeks' gestation in 130 low-risk singleton pregnancies. Regression models and multilevel modeling were used to construct the reference ranges. RESULTS: On the basis of 511 sets of longitudinal observations, we established new reference percentiles of UV diameter, blood flow velocities, volume flow, and blood flow normalized for fetal weight and abdominal circumference. They reflected some of the developmental patterns of previous cross-sectional studies, but with important differences, particularly near term. The UV blood flow showed a continuous increase until term, whereas the flow normalized per unit fetal weight, a corresponding reduction. Calculating the blood flow on the basis of intensity-weighted mean velocity or 0.5 of the maximum velocity gave almost interchangeable results for most fetuses. CONCLUSION: New reference ranges for UV blood flow based on longitudinal observations appear slightly different from cross-sectional studies, and should be more appropriate for serial evaluation of fetal circulation.

Adolescent↗
PubMed2002

Longitudinal profiles of health care providers.

Provider profiling is the activity of collecting, comparing and reporting quality of care measures for individuals, groups, agencies and institutions that provide health care services. Univariate provider profiles, such as hospital-specific mortality rates, have been constructed using cross-sectional data based on posterior summaries or maximum likelihood estimates. As data continue to be collected over time, the construction and interpretation of longitudinal profiles of health care providers will become increasingly important. Longitudinal series can be used to improve the precision of estimates - a feature that is particularly important for providers who treat a small number of patients per year. We extend and apply hierarchical models to examine and classify provider performance over time using two examples, one in the area of cardiology and the other in mental health. Performance is evaluated using the squared Mahalanobis distance and posterior probabilities based on this distance. By comparing providers based on level and temporal trend simultaneously, conservative but comprehensive assessments of performance are possible. Furthermore, the longitudinal profiles developed are easily interpreted and flexible, making them of practical use to policy-makers.

Cardiovascular Diseases↗
PubMed2003

Pattern mixture models for longitudinal quality of life studies in advanced stage disease.

Analyses of longitudinal quality of life (QOL) for patients with advanced stage disease are frequently plagued by problems of non-random drop-out attributable to deteriorating health and/or death. As an example, Moinpour et al. cite specific challenges which limited their report and assessment of QOL for patients treated for advanced stage colorectal cancer in a clinical trial of several chemotherapeutic regimes performed by the Southwest Oncology Group. A particular source of confusion that arises in studies of advanced stage disease is whether or not to differentiate loss of follow-up due to death from drop-out where the patient is still alive but has dropped from the study. In this paper we examine exploratory data techniques for longitudinal QOL data with non-random missingness due to drop-out and censorship by death. We propose a pattern mixture model for longitudinal QOL, time of drop-out and survival, which allows for straightforward implementation of sensitivity analyses and explicit comparisons to the raw data. Our method is illustrated in the context of analysing the data and addressing the challenges posed by Moinpour et al.

Antimetabolites, Antineoplastic↗
PubMed2003

Comparing longitudinal binary outcomes in an observational oral health study.

Observational studies continue to be recognized as viable alternatives to randomized trials when making treatment group comparisons, in spite of drawbacks due mainly to selection bias. Sample selection models have been proposed in the economics literature, and more recently in the medical literature, as a method to adjust for selection bias due to observed and unobserved confounders in observational studies. Application of these models has been limited to cross-sectional observational data and to outcomes that are continuous in nature. In this paper we extend application of these models to include longitudinal studies and binary outcomes. We apply a two-stage probit model using GEE to account for correlated longitudinal binary chewing difficulty outcomes. Chewing difficulty was measured every six months during a 24-month period between two groups of subjects: those either receiving or not receiving dental care. Dental care use was measured at six-month intervals as well. Results from our proposed model are compared to results using a standard GEE model that ignores the potential selection bias introduced by unobserved confounders. In this application, accounting for selection bias made a major difference in the substantive conclusions about the outcomes of interest. This is due in part to an adverse selection phenomenon in which those most in need of treatment (and consequently most likely to benefit from it) are actually the ones least likely to seek treatment. Our application of sample selection models to binary longitudinal observational outcome data should serve as impetus for increased utilization of this promising set of models to other health outcomes studies.

Dental Health Services↗
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↗
PubMed2004

Multivariate longitudinal models for complex change processes.

Longitudinal studies offer us an opportunity to develop detailed descriptions of the process of growth and development or of the course of progression of chronic diseases. Most longitudinal analyses focus on characterizing change over time in a single outcome variable and identifying predictors of growth or decline. Both growth and degenerative diseases, however, are complex processes with multiple markers of change, so that it may be important to model more than one outcome measure and to understand their relationship over time. We consider random effects models for the association between the trajectories of two outcomes over time, and then compare their properties to approaches based on separate ordinary least-squares estimates of change. We then illustrate with an example from the Religious Orders Study, a longitudinal cohort study of more than 900 members of Catholic religious orders who have had up to eight annual clinical examinations.

Aged↗
PubMed2004

Handling drop-out in longitudinal studies.

Drop-out is a prevalent complication in the analysis of data from longitudinal studies, and remains an active area of research for statisticians and other quantitative methodologists. This tutorial is designed to synthesize and illustrate the broad array of techniques that are used to address outcome-related drop-out, with emphasis on regression-based methods. We begin with a review of important assumptions underlying likelihood-based and semi-parametric models, followed by an overview of models and methods used to draw inferences from incomplete longitudinal data. The majority of the tutorial is devoted to detailed analysis of two studies with substantial rates of drop-out, designed to illustrate the use of effective methods that are relatively easy to apply: in the first example, we use both semi-parametric and fully parametric models to analyse repeated binary responses from a clinical trial of smoking cessation interventions; in the second, pattern mixture models are used to analyse longitudinal CD4 counts from an observational cohort study of HIV-infected women. In each example, we describe exploratory analyses, model formulation, estimation methodology and interpretation of results. Analyses of incomplete data requires making unverifiable assumptions, and these are discussed in detail within the context of each application. Relevant SAS code is provided.

Biometry↗
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↗
PubMed2005

Estimating treatment efficacy over time: a logistic regression model for binary longitudinal outcomes.

This paper presents a case study in longitudinal data analysis where the goal is to estimate the efficacy of a new drug for treatment of a severe chronic constipation. Data consist of long sequences of binary outcomes (relief/no relief) on each of a large number of patients randomized to treatment (low and high dose) or placebo. Data characteristics indicate: (1) the treatment effects vary non-linearly with time; (2) there is substantial heterogeneity across subjects in their responses to treatment; and (3) there is a high proportion of subjects who never experience any relief (the non-responders). To overcome these challenges, we develop a hierarchical model for binary longitudinal data with a mixture distribution on the probability of response to account for the high frequency of non-responders. While the model is specified conditionally on subject-specific latent variables, we also draw inferences on key population-average parameters for the assessment of the treatments' efficacy in a population. In addition we employ a model-checking method to compare the goodness-of-fit for our model against simpler modelling approaches for aggregated counts, such as the zero-inflated Poisson and zero-inflated negative binomial models. We estimate subject-specific and population-average rate ratios of relief for the treatment with respect to the placebo as functions of time (RR(t)), and compare them with the rate ratios estimated from the models for aggregated counts. We find that: (1) the treatment is effective with respect to the placebo with higher efficacy at the beginning of the study; (2) the estimated rate ratios from the models for aggregated counts appear to be similar to the average across time of the population-average rate ratios estimated under our model; and (3) model-checking suggests that the hierarchical and zero-inflated negative binomial model fit the data best. If we are mainly interested to establish the overall efficacy (or safety) of a new drug, it is appropriate to aggregate the longitudinal data over time and analyse the count data by use of standard statistical methods. However, the models for aggregated counts cannot capture time trend of treatment such as the initial treatment benefit or the development of tolerance during the early stage of the treatment which may be important information to physicians to predict the treatment effects for their patients.

Biometry↗
PubMed2006

Pseudo-likelihood methods for longitudinal binary data with non-ignorable missing responses and covariates.

In this paper we consider longitudinal studies in which the outcome to be measured over time is binary, and the covariates of interest are categorical. In longitudinal studies it is common for the outcomes and any time-varying covariates to be missing due to missed study visits, resulting in non-monotone patterns of missingness. Moreover, the reasons for missed visits may be related to the specific values of the response and/or covariates that should have been obtained, i.e. missingness is non-ignorable. With non-monotone non-ignorable missing response and covariate data, a full likelihood approach is quite complicated, and maximum likelihood estimation can be computationally prohibitive when there are many occasions of follow-up. Furthermore, the full likelihood must be correctly specified to obtain consistent parameter estimates. We propose a pseudo-likelihood method for jointly estimating the covariate effects on the marginal probabilities of the outcomes and the parameters of the missing data mechanism. The pseudo-likelihood requires specification of the marginal distributions of the missingness indicator, outcome, and possibly missing covariates at each occasions, but avoids making assumptions about the joint distribution of the data at two or more occasions. Thus, the proposed method can be considered semi-parametric. The proposed method is an extension of the pseudo-likelihood approach in Troxel et al. to handle binary responses and possibly missing time-varying covariates. The method is illustrated using data from the Six Cities study, a longitudinal study of the health effects of air pollution.

Air Pollutants↗
PubMed2007

Functional regression analysis using an F test for longitudinal data with large numbers of repeated measures.

Longitudinal data sets from certain fields of biomedical research often consist of several variables repeatedly measured on each subject yielding a large number of observations. This characteristic complicates the use of traditional longitudinal modelling strategies, which were primarily developed for studies with a relatively small number of repeated measures per subject. An innovative way to model such 'wide' data is to apply functional regression analysis, an emerging statistical approach in which observations of the same subject are viewed as a sample from a functional space. Shen and Faraway introduced an F test for linear models with functional responses. This paper illustrates how to apply this F test and functional regression analysis to the setting of longitudinal data. A smoking cessation study for methadone-maintained tobacco smokers is analysed for demonstration. In estimating the treatment effects, the functional regression analysis provides meaningful clinical interpretations, and the functional F test provides consistent results supported by a mixed-effects linear regression model. A simulation study is also conducted under the condition of the smoking data to investigate the statistical power for the F test, Wilks' likelihood ratio test, and the linear mixed-effects model using AIC.

Behavior Therapy↗
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↗
PubMedDate not supplied

An overview of methods for the analysis of longitudinal data.

This paper reviews statistical methods for the analysis of discrete and continuous longitudinal data. The relative merits of longitudinal and cross-sectional studies are discussed. Three approaches, marginal, transition and random effects models, are presented with emphasis on the distinct interpretations of their coefficients in the discrete data case. We review generalized estimating equations for inferences about marginal models. The ideas are illustrated with analyses of a 2 x 2 crossover trial with binary responses and a randomized longitudinal study with a count outcome.

Cross-Sectional Studies↗
PubMed2001

A comparison of generalized linear mixed model procedures with estimating equations for variance and covariance parameter estimation in longitudinal studies and group randomized trials.

Response data in longitudinal studies and group randomized trials are gathered on units that belong to clusters, within which data are usually positively correlated. Therefore, estimates and confidence intervals for intraclass correlation or variance components are helpful when designing a longitudinal study or group randomized trial. Data simulated from both study designs are used to investigate the estimation of variance and covariance parameters from the following procedures: for continuous outcomes, restricted maximum likelihood (REML) and estimating equations (EE); for binary outcomes, restricted pseudo-likelihood (REPL) and estimating equations (EE). We evaluate these procedures to see which provide valid and precise estimates as well as correct standard errors for the intraclass correlation coefficient or variance components. REML seems the better choice for estimating terms related to correlation for models with normal outcomes, especially in group randomized trial situations. Results for REML and EE are mixed when outcomes are continuous and non-normal. With binary outcomes neither REPL nor EE provides satisfactory estimation or inference in longitudinal study situations, while REPL is preferable for group randomized trials.

Cluster Analysis↗
PubMed2006

Longitudinal reference ranges for ductus venosus flow velocities and waveform indices.

OBJECTIVES: Serial Doppler measurements of the ductus venosus are used increasingly for monitoring fetuses at risk of hemodynamic compromise, but existing reference ranges are based on cross-sectional studies and thus are less suitable for comparison with serial measurements. We aimed to establish longitudinal reference ranges for ductus venosus flow velocities and waveform indices and to provide the necessary terms for calculating conditional reference ranges for serial measurements. METHODS: This was a longitudinal study of 160 low-risk pregnancies. Pulsed Doppler ultrasound was used to record ductus venosus blood flow velocities at 4-week intervals from 20-22 weeks of gestation onwards. RESULTS: With a success rate of 93%, 547 measurements (four or five in each fetus) were used to establish reference ranges. The time-averaged maximum velocity was 50 cm/s at 21 weeks of gestation, increased to 60 cm/s at 32 weeks, and remained so until term. Similarly, the peak systolic velocity increased from 59 cm/s at 21 weeks to 71 cm/s at 31 weeks and remained so until term. The end-diastolic velocity showed a continuous increase from 31 cm/s at 21 weeks to 43 cm/s at 40 weeks. The pulsatility index for veins decreased from 0.57 at 21 weeks to 0.44 at 40 weeks. When conditioned by a previous measurement, the reference ranges for the next observation became narrower and commonly shifted compared with those of the entire population. CONCLUSION: The new longitudinal reference ranges presented here reflect the development of the ductus venosus flow velocities and velocity indices and are thus appropriate for serial measurements, particularly if conditional terms are included.

Adult↗
PubMed1997

A longitudinal study of human age-related chromosomal analysis in skin fibroblasts.

Previous chromosomal analyses related to human aging used mainly cross-sectional data on metaphase chromosomes. However, it is difficult to directly relate the cross-sectional results to the specific type(s) of chromosomal mutations possibly occurring within a specific individual with advancing age, because the unique genetic endowment of each individual for longevity might be a modulating factor. We therefore have performed, for the first time, a longitudinal study of both numerical and structural chromosome analyses of skin fibroblasts at interphase and at metaphase derived from eight donors participating in the Baltimore Longitudinal Study. We have used the FISH method with chromosome-specific DNA probes and the data on total aneuploidy of 17 different chromosomes in each of the 16 cell cultures (2 from each of eight individuals) indicate that significantly higher percentages of aneuploid cells are detected at interphase than at metaphase. Mostly, the levels of chromosome-specific aneuploidy increase with the donor's advancing age and, in most individuals, chromosomes 1, 4, 6, 8, 10, and 15 show significantly higher frequencies of aneuploidy at interphase than those of the 11 other chromosomes studied. Although the significance of relatively higher levels of aneuploidy of certain chromosomes with aging remains unclear, it is intriguing to note that some of these chromosomes, such as 1, 4, and 6, have already been assigned to harbor senescence genes and chromosome 8 is known to house the gene for Werner Syndrome (progeroid syndrome), which shows very limited proliferative capacity of fibroblasts. It is conceivable that the degree and/or type of chromosome-specific aneuploidy might have some gene dosage effects in the control of cellular proliferation and selection during aging. We also show that a combination of both interphase and metaphase aneuploidy analyses provides more comprehensive and insightful information on intraindividual cellular dynamics and chromosomal aneuploidy as a function of age. Occasionally, very small proportions of cells in two individuals showed age-related structural chromosome aberrations, such as an acentric fragment derived from an X chromosome and an achromatic gap in chromosome 7. Thus, a comparative analysis of both intra- and interindividual longitudinal studies is very useful in detecting the pattern(s) of chromosome-specific alterations with increasing age.

Adult↗