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PubMed1996

Functional impairment trajectories among persons with HIV disease: a hierarchical linear models approach.

OBJECTIVE: This study investigates the level, time course, and stability of functional impairment in a population of persons with symptomatic HIV disease, and illustrates the application of hierarchical linear modeling (HLM) to trajectories of functional status in unbalanced longitudinal data. STUDY POPULATION: We utilized longitudinal interview data on a demographically diverse cohort of 246 individuals participating in New Jersey's Medicaid waiver program for persons with AIDS or symptomatic HIV disease, with a mean of nine repeated observations per individual. MEASURES AND STATISTICAL METHODS: Impairment in ability to perform 16 activities of daily living (ADL) and instrumental activities of daily living (IADL) was assessed at monthly intervals. To achieve unbiased, efficient estimation of the level and within-individual rate of change of functional status utilizing all observations for each individual, hierarchical linear models were used. Time slopes were compared to those from a single-level model estimated on the pooled observations. Stability of functional status within individuals was also evaluated. PRINCIPAL FINDINGS: A single-level pooled model showed no significant time trend in functional impairment, while the multilevel models did indicate such a trend. In the final HLM model, functional impairment was estimated to increase at a rate of .32 tasks per month. Female gender was associated with impairment in an additional 1.88 tasks and AIDS diagnosis with an additional 1.35 tasks. There was substantial variability within individuals over time, most of which was not explained by time trend. CONCLUSIONS: The multilevel models indicated a significant month-to-month worsening of functional status that was masked in the single-level model by between-person variation. Impairment was found to increase over time, but followed a variable and episodic course rather than a steady or consistent decline. Women appeared to experience special problems in performing ADL and IADL tasks. RELEVANCE/IMPACT: Results demonstrate the need for flexible and responsive systems for authorizing and managing in-home services for persons with HIV disease, systems that can respond to frequent changes in the functional status and level of care needs of these individuals. They suggest further attention to special care needs that may be experienced by women with HIV disease. They illustrate that hierarchical linear modeling can be an important tool in understanding change in functional status over time, providing a multilevel model that disaggregates within-individual and between-individual variation in functional status. This approach can be generalized to a wide variety of problems in health services research in which outcomes are observed over time with unbalanced longitudinal data.

Acquired Immunodeficiency Syndrome↗
PubMed1988

Mixed Poisson likelihood regression models for longitudinal interval count data.

In many longitudinal studies it is desired to estimate and test the rate over time of a particular recurrent event. Often only the event counts corresponding to the elapsed time intervals between each subject's successive observation times, and baseline covariate data, are available. The intervals may vary substantially in length and number between subjects, so that the corresponding vectors of counts are not directly comparable. A family of Poisson likelihood regression models incorporating a mixed random multiplicative component in the rate function of each subject is proposed for this longitudinal data structure. A related empirical Bayes estimate of random-effect parameters is also described. These methods are illustrated by an analysis of dyspepsia data from the National Cooperative Gallstone Study.

Adult↗
PubMed2004

A method for imputing missing data in longitudinal studies.

PURPOSE: In a cohort in which racial data are unknown for some persons, race-specific persons and person-years are imputed using a model-based iterative allocation algorithm (IAA). METHODS: An EM algorithm-based approach to address misclassification in a censored data regression setting can be adapted to estimate the probability that a person of unknown race is white. The corresponding race-specific person-years are obtained as a by-product of the estimation procedure. Variance estimates are computed using the bootstrap. The proposed approach is compared with the proportional allocation method (PAM). RESULTS: In an occupational cohort where racial data were missing for 41% of the workers, the age-time-race-specific person-years were estimated within a relative variation of approximately 20%, using the IAA. The deaths were less reliably estimated. The standardized mortality ratios (SMRs) for all-cause mortality estimated using the IAA and the PAM were more similar for the non-white workers than for a smaller subgroup of white workers. CONCLUSIONS: The IAA provides a method to reliably estimate race-specific person-year denominators in cohort studies with missing racial data. This method is applicable to other incompletely observed non-time-dependent categorical covariates. Internal cohort rates or SMRs can be computed and modeled, with bootstrap confidence intervals that account for the uncertainty in the determination of race.

Adolescent↗
PubMed1986

Life expectancy and health status of the aged.

There are several research issues which need further exploration if we are to better understand the implications of what appears to be increased levels of morbidity. Three general areas require additional research: the time of onset of chronic illness, the progression rate of illness, and the overlap and interaction between chronic and non-chronic conditions as well as multiple chronic conditions in a single individual. A major reason for the present uncertainty about morbidity is that information is unavailable regarding the incidence of chronic illness. However, incidence of chronic disease is difficult to measure unless there are either clear clinical indications or functional limitations. Work by survey researchers in defining initial reports of functional limitations associated with chronic illness would be very helpful. Furthermore, an understanding of incidence is necessary to further our understanding of the rate of progression of illness. The concept of a progression rate of illness makes sense only if we can have agreed upon measures of the onset of the illness. Both of these issues clearly require the use of longitudinal data. In fact any serious attempt to predict changes in health status over time as well as to relate changing patterns of mortality with changing patterns of morbidity will require a longitudinal data base. The difficulty in establishing a longitudinal data base is not only the time and expense of follow given set of individuals over a prolonged period of time, but also the problem of having a sample large enough to include individuals with specific chronic conditions of illness. One way to resolve the problem of sufficient sample size may be to do a combined survey which includes both a national probability sample of individuals as well as a sample of individuals with specific chronic diseases. Monitoring a group of individuals known to have specific chronic conditions would provide information about the progression and impact of the disease over time. Including a national probability sample of the entire population would provide information on the impact over time of changing health conditions for the entire population. While screening for specific conditions is an expensive procedure, it is likely to be far cheaper than including a sample size large enough to provide reliable estimates for specific conditions based on a national probability sample. Because the effects of postponed social security benefit eligibility will not be felt for many years, the opportunity for fruitful research is great. For now, we will summarize what we know from current research.

Adolescent↗
PubMed2006

Successful aging in health care institutions.

OBJECTIVES: This article explores factors associated with positive self-perceived health among Canadian seniors who live in health care institutions. DATA SOURCE: Cross-sectional and longitudinal data are from the institutional and household files of the National Population Health Survey (NPHS). ANALYTICAL TECHNIQUES: Prevalence rates of positive self-perceived health were estimated using 1996/97 cross-sectional data from the NPHS. Logistic regression models were used to identify factors associated with positive self-perceived health. With four cycles of longitudinal data, the relationship between positive self-perceived health and mortality was explored using survival analysis. MAIN RESULTS: In 1996/97, 43% of the institutional population aged 65 or older reported positive self-perceived health. Institutional residents with positive self-perceived health had a lower risk of mortality. The odds of positive self-perceived health were higher for those who were usually free of pain and were independent. Participation in social and recreational activities and having a close relationship with at least one staff member of the institution were associated with positive self-perceived health.

Aged↗
PubMed2001

Bayesian analyses of longitudinal binary data using Markov regression models of unknown order.

We present non-homogeneous Markov regression models of unknown order as a means to assess the duration of autoregressive dependence in longitudinal binary data. We describe a subject's transition probability evolving over time using logistic regression models for his or her past outcomes and covariates. When the initial values of the binary process are unknown, they are treated as latent variables. The unknown initial values, model parameters, and the order of transitions are then estimated using a Bayesian variable selection approach, via Gibbs sampling. As a comparison with our approach, we also implement the deviance information criterion (DIC) for the determination of the order of transitions. An example addresses the progression of substance use in a community sample of n = 242 American Indian children who were interviewed annually four times. An extension of the Markov model to account for subject-to-subject heterogeneity is also discussed.

Adolescent↗
PubMed2001

Bilateral medial temporal lobe damage does not affect lexical or grammatical processing: evidence from amnesic patient H.M.

In the most extensive investigation to date of language in global amnesia, we acquired data from experimental measures and examined longitudinal data from standardized tests, to determine whether language function was preserved in the amnesic patient H.M. The experimental measures indicated that H.M. performed normally on tests of lexical memory and grammatical function, relative to age- and education-matched control participants. Longitudinal data from four Wechsler subtests (Information, Comprehension, Similarities, and Vocabulary), that H.M. had taken 20 times between 1953 (preoperatively) and 2000, indicated consistent performance across time, and provided no evidence of a lexical memory decrement. We conclude that medial temporal lobe structures are not critical for retention and use of already acquired lexical information or for grammatical processing. They are, however, required for acquisition of lexical information, as evidenced in previous studies revealing H.M.'s profound impairment at learning new words.

Adult↗
PubMed1981

Longitudinal models for chronic disease risk: an evaluation of logistic multiple regression and alternatives.

The logistic multiple regression model is often used in the analysis of the relation between chronic disease risk and selected risk factors in longitudinal data. Unfortunately, the logistic function has certain properties that make it inappropriate as a mode of risk analysis for longitudinal studies. The consequences of applying the logistic function to longitudinal data is that the numerical values of logistic regression coefficients cannot be meaningfully compared between studies of different durations. Sample calculations are presented to illustrate the magnitude of the problem for a range of relative study lengths and levels of risk. Two solutions are offered for the problem. First, a series of approximations are derived which permit such comparisons if the studies are not greatly dissimilar in length. Second, if comparisons of the risk coefficients are to be made across studies of greatly dissimilar duration, it is necessary to model risk via an appropriate statistical model. Criteria for assessing the appropriateness of risk functions for the analysis of longitudinal data are proposed and alternatives evaluated.

Chronic Disease↗
PubMedDate not supplied

Some general methods for the analysis of categorical data in longitudinal studies.

This paper is concerned with the analysis of multivariate categorical data from epidemiologic and clinical studies with longitudinal designs. An expository discussion of pertinent hypotheses for such situations is provided within the context of two relevant data sets. Appropriate large-sample tests of these hypotheses are developed through the application of weighted least squares to generate Wald statistics. These procedures are illustrated with extensive analyses of one of these data sets. In some situations, the resulting cross-classification of the response variables leads to extremely sparse frequency data, especially when the number of subjects is not large. For such repeated measurement designs in which a single variable is measured repeatedly over time, this paper considers the use of a generalized Mantel-Haenszel strategy for tests of marginal homogeneity (symmetry). These randomization model methods are illustrated for data in which the repeated measurement variable is reported on an ordinal scale. This paper also focuses on the available computing software to implement these methods within the version 5 release of the SAS system. The randomization model approach can be implemented within the FREQ procedure and a broad range of models and hypotheses can be investigated within the CATMOD procedure.

Animals↗
PubMed1990

Some covariance models for longitudinal count data with overdispersion.

A family of covariance models for longitudinal counts with predictive covariates is presented. These models account for overdispersion, heteroscedasticity, and dependence among repeated observations. The approach is a quasi-likelihood regression similar to the formulation given by Liang and Zeger (1986, Biometrika 73, 13-22). Generalized estimating equations for both the covariate parameters and the variance-covariance parameters are presented. Large-sample properties of the parameter estimates are derived. The proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures.

Analysis of Variance↗
PubMed2004

Dental nomograms for benchmarking based on the study of health in Pomerania data set.

AIM: Benchmarking is a means of setting goals or targets. On an oral health level, it denotes retaining more teeth and/or improving the quality of life. The goal of this pilot investigation was to assess whether the data generated by a population-based study (SHIP 0) can be used as a benchmark data set to characterize different practice profiles. MATERIAL AND METHODS: The data collected in the population-based study SHIP (n=4310) in eastern Germany were used to generate nomograms of tooth loss, attachment loss, and probing depth. The nomograms included twelve 5-year age strata (20-79 years) presented as quartiles, and additional percentiles of the dental parameters for each age group. Cross-sectional data from a conventional dental office (n=186) and from a periodontology unit (n=130, Greifswald) in the study region as well as longitudinal data set of a another periodontology unit (n=135, Kiel) were utilized in order to verify whether the given practice profile was accurately reflected by the nomogram. RESULTS: In terms of tooth loss, the data from the conventional dental office agree with the median from the nomogram. For attachment loss and probing depth, some age groups yielded slight but not uniform deviations from the median. Cross-sectional data from the periodontology unit Greifswald showed attachment loss higher than the median in younger but not in older age groups. The probing depth was uniformly less than the median and tended toward the 25th percentile with increasing age. The longitudinal data of the Unit of Periodontology in Kiel showed a pronounced trend towards higher percentiles of residual teeth, meaning that the patients retained more teeth. CONCLUSION: The profile of the Pomeranian dental office does not deviate noticeably from the population-based nomograms. The higher attachment loss of the Unit of Periodontology in Greifswald in younger age strata clearly reflects their selection because of periodontal disease; the combination of higher attachment loss and decreased probing depth may reflect the success of the treatment. The tendency of attachment loss towards the median with increasing age may indicate that the Unit of Periodontology in Greifswald does not fulfill its function as a special care unit in the older subjects. The longitudinal data set of the Unit of Periodontology in Kiel impressively reflects the potential of population-based data sets as a means for benchmarking. Thus, nomograms can help to determine the practice profile, potentially yielding benefits for the dentist, health insurance company, or--as in the case of the special care unit--public health research.

Adult↗
PubMed1989

Commentary on Gracia et al.: diagnostic entity or dynamic processes?

The case of Mr. G is a fascinating and beautifully presented, although sad, history of a patient. The clarity of the presentation and the discussion are particularly impressive in this example of the use of longitudinal data for descriptive diagnosis and conceptualization. The report exemplifies current trends in descriptive psychiatry, which focus on diagnosing an illness as a whole. The illness itself is considered a relatively static entity, even if it includes changes within its course. From this perspective, longitudinal data provide information for deciding what type of illness is being described. In my commentary, I would like to focus on a different way of using longitudinal data from that employed by the authors--a different type of longitudinal perspective, one that does not have the primary goal of defining a type of disorder diagnostically. I would like instead to focus on understanding this patient in terms of longitudinal processes rather than as someone afflicted with a persisting diagnostic entity. Attention to longitudinal processes can raise different questions and suggest what further information would be needed to understand these processes and plan optimal treatment. This more dynamic approach to understanding processes is not mutually exclusive with the static approach to diagnosis, but the two orientations provide very different perspectives on assessment, conceptualization and treatment.

Adult↗
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↗
PubMed2001

The APOE-E4 allele and the risk of functional decline in a community sample of African American and white older adults.

BACKGROUND: Given previous findings of adverse health outcomes associated with the E4 allele, data from a biracial community sample of older adults were used to determine whether functional decline is associated with the apolipoprotein E (APOE) E4 allele. METHODS: In 1986, a stratified random household sample of community residents 65 years of age and older (n = 4162) formed the Duke Established Populations for Epidemiologic Studies of the Elderly. Of those available 6 years later, 78.4% (n = 1999) were genotyped, providing "baseline" data at this time. The available survivors (n = 1529) provided longitudinal data 4 years later. Using longitudinal data from this sample, a combination of measures assessing self-care capability, instrumental activities of daily living (IADL), and mobility was obtained at baseline and 4 years later (n = 1529) to determine the extent to which the E4 allele affected change in functional status. Functional status was assessed using items from a modified Katz Activities of Daily Living (ADL) Scale, the Older American Resources and Services IADL scale, and the Rosow-Breslau physical health scale. Control measures included demographic characteristics, depression, health status, arthritis, and cognitive status. APOE was coded as E4 present versus absent. RESULTS: APOE E4 was not associated with decline in functional status in either bivariate or multivariate analyses as a main effect. There were, however, statistically significant interactions of the E4 allele with gender and baseline functional status, with greater functional decline in women with the E4 allele, whereas those with poorer baseline functioning who had the E4 allele were less likely to decline. No significant racial differences were found. CONCLUSIONS: Despite the documented association of the E4 allele of APOE with adverse health outcomes, the E4 allele was not associated with a decline in functional status as a main effect. Interactions of E4 with gender (being female) and baseline functional status, however, did predict functional decline.

Activities of Daily Living↗
PubMed2001

On the evaluation of drug benefits policy changes with longitudinal claims data: the policy maker's versus the clinician's perspective.

Cost containment in pharmaceutical-benefit plans are often controversially debated for their potential of unintended consequences on health and overall expenditures. Thorough evaluations are needed but hypotheses and design considerations are complex. Our objective is to provide a structured framework for the evaluation of drug-benefit changes using longitudinal claims data. Differential cost sharing (DCS) will serve as a recent example. Benefit-plan managers are mainly interested in the overall performance of their plan. In a policy model, any observed policy-related effects may be compared with what would have happened had the intervention not been implemented by extrapolating the pre-policy trend from the same patients. These estimates will reflect the global consequences of the policy maker's decision. However, such estimates represent summary effects of benefits and harms, separately identifiable in those complying with the intended policy and those not complying. Results from a policy model apply only to a specific policy implementation and tend to underestimate effects when non-compliance is high. Clinical-decision makers and patients, by contrast, are interested in the consequences of patients' actual compliance to the policy. A clinical model assesses the effects of DCS depending on the actual treatment in contrast to the treatment intended by the policy. However, this model must sometimes make, unprovable assumptions about the appropriate control of selection factors. In conclusion, both policy and clinical models should be tested with a clear understanding of their perspectives, hypotheses, and interpretations, using quasi-experimental time-series designs to evaluate the effects of drug cost-containment policies.

Attitude of Health Personnel↗
PubMed1998

Gibbs sampler for the logistic model in the analysis of longitudinal binary data.

Logistic mixed-effects models constitute a natural framework to study longitudinal binary response variables when the question addressed with the data is related to covariate effects within persons. However, the computations of the likelihoods are generally tedious and require the resolution of integrals which have no analytical solution. In this paper, we study a logistic mixed-effects model in a Bayesian framework and use the Gibbs sampler to overcome the current computational limitations. From a study of side-effects occurring during plasma exchanges, we explore the issues of bayesian formulation, model parametrization, choice of the prior distributions, diagnosing convergence, comparison between models and model adequacy. Finally, we show that a Bayesian random-effects model is useful to facilitate prediction.

Bayes Theorem↗
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↗