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PubMedDate not supplied

Missing data in longitudinal studies.

When observations are made repeatedly over time on the same experimental units, unbalanced patterns of observations are a common occurrence. This complication makes standard analyses more difficult or inappropriate to implement, means loss of efficiency, and may introduce bias into the results as well. Some possible approaches to dealing with missing data include complete case analyses, univariate analyses with adjustments for variance estimates, two-step analyses, and likelihood based approaches. Likelihood approaches can be further categorized as to whether or not an explicit model is introduced for the non-response mechanism. This paper will review the use of likelihood based analyses for longitudinal data with missing responses, both from the point of view of ease of implementation and appropriateness in view of the non-response mechanism. Models for both measured and dichotomous outcome data will be discussed. The appropriateness of some non-likelihood based analyses is briefly considered.

Algorithms↗

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↗

PubMed2005

An appraisal of methods for the analysis of longitudinal categorical data with MAR drop-outs.

A number of methods for analysing longitudinal ordinal categorical data with missing-at-random drop-outs are considered. Two are maximum-likelihood methods (MAXLIK) which employ marginal global odds ratios to model associations. The remainder use weighted or unweighted generalized estimating equations (GEE). Two of the GEE use Cholesky-decomposed standardized residuals to model the association structure, while another three extend methods developed for longitudinal binary data in which the association structures are modelled using either Gaussian estimation, multivariate normal estimating equations or conditional residuals. Simulated data sets were used to discover differences among the methods in terms of biases, variances and convergence rates when the association structure is misspecified. The methods were also applied to a real medical data set. Two of the GEE methods, referred to as Cond and ML-norm in this paper and by their originators, were found to have relatively good convergence rates and mean squared errors for all sample sizes (80, 120, 300) considered, and one more, referred to as MGEE in this paper and by its originators, worked fairly well for all but the smallest sample size, 80.

Biometry↗

PubMedDate not supplied

Assessing drug compliance using longitudinal marker data, with application to AIDS.

The assessment of non-compliance to a study medication is an important issue in the evaluation of clinical trials of self-administered drugs. Traditional methods for evaluating the compliance of subjects include self-reported questionnaires and pharmacologic assays of drug levels in randomly-drawn blood samples, but each of these has important limitations. This paper adapts and extends changepoint methods to assess compliance from longitudinal data on laboratory markers that are affected by the drug. The maximum likelihood estimators for two models are developed and examined. The effect of the drug on the marker process, as well as the spacing of the observations of the marker process relative to the time of non-compliance determine which model parameters are estimable. For the situations examined, the method of maximum likelihood is found to perform well in most cases. However, when non-compliance begins shortly before the last observation of the marker process, these (as well as any other) estimators cannot reliably distinguish non-compliance from compliance. The methods are illustrated with an example from a recent clinical trial of persons infected with HIV.

Acquired Immunodeficiency Syndrome↗

PubMedDate not supplied

Gender differences in language of Alzheimer disease patients revisited.

Results of recent investigations suggest that Alzheimer disease (AD) has a more deleterious effect on language in women than in men. This intriguing finding motivated an analysis of the language performance of probable AD patients, equally divided as to gender, on a variety of language comprehension and production tests. Cross-sectional data were available for 63 probable AD subjects and longitudinal data were available for 26. In addition to analysis of covariance used with the cross-sectional data, effect sizes were calculated. The longitudinal data were analyzed with repeated-measures analyses of covariance. The sum of scores on the orientation items of the Mini-Mental State Examination was used as the covariate in both analyses. No significant differences between the performance scores of male and female subjects were obtained for either the cross-sectional or longitudinal data. All effect sizes of gender were relatively small, with female patients outperforming males on most language tests. Results are discussed in the context of previous findings and comparison of the effect sizes among studies.

Alzheimer Disease↗

PubMed2004

Longitudinal designs, methods and analysis in psychiatric research.

OBJECTIVE: To outline the strengths and limitations of longitudinal research designs in psychiatry, and to describe different types of longitudinal designs and methods for analyzing longitudinal data. METHOD: Key references on longitudinal methods were reviewed and examples drawn from literature in psychiatry and psychology. RESULTS: Longitudinal studies provide important information regarding the incidence and developmental trajectories of mental disorders. They allow for identification of risk factors and developmental concomitants. Recent developments in statistical methods for analyzing longitudinal data provide efficient estimates of change and predictors of change over time, identification and characteristics of distinct subgroups defined by change pattern, and improved methods for obtaining unbiased population estimates when data are incomplete. CONCLUSION: Longitudinal designs, methods and analysis can contribute to psychiatric studies on risk factors for common mental disorders, studies of early intervention and prevention and treatment outcomes.

Humans↗

PubMedDate not supplied

A research database for improved data management and analysis in longitudinal studies.

We developed a research database for a five-year prospective investigation of the medical, social, and developmental correlates of chronic lung disease during the first three years of life. We used the Ingres database management system and the Statit statistical software package. The database includes records containing 1300 variables each, the results of 35 psychological tests, each repeated five times (providing longitudinal data on the child, the parents, and behavioral interactions), both raw and calculated variables, and both missing and deferred values. The four-layer menu-driven user interface incorporates automatic activation of complex functions to handle data verification, missing and deferred values, static and dynamic backup, determination of calculated values, display of database status, reports, bulk data extraction, and statistical analysis.

Bronchopulmonary Dysplasia↗

PubMed2006

Temporal and spatial analyses of rear-end crashes at signalized intersections.

In this study, the generalized estimating equations with the negative binomial link function were used to model rear-end crash frequencies at signalized intersections to account for the temporal or spatial correlation among the data. The longitudinal data for 208 signalized intersections over 3 years and the spatially correlated data for 476 signalized intersections which are located along different corridors were collected in the state of Florida. The modeling results showed that there are high correlations between the longitudinal or spatially correlated rear-end crashes. Some intersection related variables are identified as significantly influencing rear-end crash occurrences at signalized intersections. Intersections with heavy traffic on the major and minor roadways, having more right and left-turn lanes on the major roadway, having a large number of phases per cycle (indicated by the left-turn protection on the minor roadway), with high speed limits on the major roadway, and in high population areas are correlated with high rear-end crash frequencies. On the other hand, intersections with three legs, having channelized or exclusive right-turn lanes on the minor roadway, with protected left-turning on the major roadway, with medians on the minor roadway, and having longer signal spacing have a lower frequency of rear-end crashes.

Accidents, Traffic↗

PubMed1994

Neuropsychological changes in children with cancer: the treatment of missing data in longitudinal studies.

Researchers conducting longitudinal studies with children or adults are inevitably confronted with problems of attrition and missing data. Missing data in longitudinal studies is frequently handled by excluding from analyses those cases for whom data are incomplete. This approach to missing data is not optimal. On the one hand, if data are missing at random, then dropping incomplete cases ignores information collected on those cases that could be used to improve estimates of population parameters (e.g., means, variances, covariances, and growth rates) and improve the power of significance tests of statistical hypotheses. On the other hand, if data are not missing at random, then dropping incomplete cases leads to biased parameter estimates and hypothesis tests that may be internally and externally invalid. This study uses three years of follow-up data from a longitudinal investigation of neuropsychological outcomes of cancer in children to demonstrate the problems presented by missing data in repeated measures designs and some solutions. In evaluating potential biasing effects of attrition, the study extends previous research on neuropsychological outcomes in pediatric cancer by inclusion of patients whose disease had relapsed, and by comparison of surviving and nonsurviving patients. Although the data presented have specific relevance to the study of neuropsychological outcome in pediatric cancer, the problems of missing data and the solutions presented are relevant to a wide variety of diseases and conditions of interest to researchers in child and adult neuropsychology.

Adolescent↗

PubMed1997

Transitions across various continuing care settings.

PURPOSE: to compare cross-nationally the sources and rates of admission and discharge in nursing homes. METHODS: data on admission were used from the Minimum Data Set of the Resident Assessment Instrument as collected in a multi-nation database at the University of Michigan. Additional data containing longitudinal episodes were used from databases in the Netherlands, Switzerland and the USA. RESULTS: the sources and rates of admission and discharge in nursing homes vary widely between countries. In Japan 47.5% of the sample was admitted from another long-term care setting, in Italy and the USA 36% and 42% respectively were admitted directly from hospital, while in Denmark and Iceland more than 60% came from home. The longitudinal data show that in the Netherlands, residents' return to home was much more likely than in Geneva or the USA (27% vs 5% vs 10%) and that in the USA a relatively large number of nursing home residents (>45%) was discharged (intermittently) to a hospital within 180 days after first admission as compared to the Netherlands (10%). CONCLUSIONS: there are large differences between countries in admission and discharge to and from nursing homes. Various policies, payment schemes, care patterns and routine referrals influence this and can be studied with cross-national data now available.

Aged↗

PubMed2006

A marginalized pattern-mixture model for longitudinal binary data when nonresponse depends on unobserved responses.

This paper proposes a method for modeling longitudinal binary data when nonresponse depends on unobserved responses. The proposed method presumes that the target of inference is the marginal distribution of the response at each occasion and its dependence on covariates, and can accommodate both monotone and non-monotone missingness. The approach involves a marginally specified pattern-mixture model that directly parameterizes both the marginal means at each occasion and the dependence of each response on indicators of nonresponse pattern. This formulation readily incorporates a variety of nonresponse processes assumed within a sensitivity analysis. Once identifying restrictions have been made, estimation of model parameters proceeds via solution to a set of modified generalized estimating equations. The proposed method provides an alternative to standard selection and pattern-mixture modeling frameworks, while featuring certain advantages of each. The paper concludes with application of the method to data from a contraceptive clinical trial with substantial dropout.

Amenorrhea↗

PubMed1998

Single women and the dynamics of Medicaid.

OBJECTIVE: To investigate transitions in and out of Medicaid for a cohort of single adult women of childbearing age in order to address questions that arise as policymakers try to encourage transitions from welfare to work. DATA SOURCES: Longitudinal data from Waves 2 through 8 of the 1990 panel of the Survey of Income and Program Participation, a nationally representative survey of American adults covering May 1990-1992. STUDY DESIGN: We estimate a series of discrete-time logit models with duration dependence to obtain transition probabilities among Medicaid, privately insured, and uninsured spells. Explanatory variables in the models include prior insurance history, income limits on Medicaid by state, and important socioeconomic and demographic characteristics. We use these models to characterize insurance spells for a cohort of single women. PRINCIPAL FINDINGS: Most Medicaid spells are relatively short. Over half end in a year or less; only one spell out of seven lasts longer than five years. Two-thirds of Medicaid disenrollees become uninsured. Former welfare recipients are prone to frequent changes in insurance status. In states with more generous income limits for AFDC, women stay on Medicaid longer, but they do not move into the program at a faster rate. CONCLUSIONS: Imposing time limits on Medicaid eligibility would affect only a small proportion of Medicaid spells but would eliminate a significant proportion of the caseload at a point in time. In considering changes in Medicaid that would encourage transitions from welfare to work and would alter the dynamics of Medicaid, policymakers need to consider how transitions both in and out of private insurance and Medicaid would be affected.

Adult↗

PubMedDate not supplied

[Sample survey of persons insured in statutory health insurance institutions in Hessen--concept and realisation of person-related data base].

Statutory health insurance data are being increasingly used for secondary data research. Longitudinal data can be prepared for research in health care, epidemiology or demand planning, in particular through the person-related nature of the data which is a precondition for the creation of inter-sector and inter-period data sets. This application possibility was introduced in a method study "person-related sampling of statutory health insurance data" and is now translated into practice on a larger scale for the first time in the regional sample "Versichertenstichprobe AOK Hessen/KV Hessen". For the collection and use of these data, model procedures were designed which take account of organisational (data access, contractual agreement, advisory board), technical (sampling, collection and storage of data) and confidentiality (data protection concept, pseudonymisation) aspects. The insured person-related sample may thus serve as a basis for the data pool planned for the national health system (Social Security Regulation 303 a-SGB V).

Community Participation↗

PubMed2005

Maternal perspectives on children's health-related quality of life during the first year after pediatric hematopoietic stem cell transplant.

OBJECTIVE: To assess the longitudinal health-related quality of life (HRQL) of children receiving hematopoietic stem cell transplantation (HSCT). METHODS: Mothers (N = 160) of HSCT recipients aged 5-20 at six US transplant centers completed the Child Health Ratings Inventories (CHRIs), the Disease Impairment Inventory (DSII)-HSCT module, and the Short Form (SF)-36 at baseline, 3, 6, and 12 months. RESULTS: HRQL domain scores at baseline varied by recipient age and program site. Longitudinal data over the first year post-HSCT revealed lowest functioning at baseline and 3 months, with largest improvement in functioning between the 3 and 6-months assessments and continued improvement from 6 to 12 months. Recipients of unrelated donor transplants had steepest declines in functioning at 3 months and great HSCT-specific issues at 3 and 6 months. Among children who survived the first year, functioning at 12 months was similar across transplant types and surpassed baseline scores. Children who did not survive the first year exhibited deterioration in HRQL in the months before death and trajectories were strikingly different than for survivors. CONCLUSIONS: This study offers the first glimpse of the 12-month trajectory of HRQL following pediatric HSCT from mothers' perspectives. This study also highlights the importance of and approaches to addressing missing data in longitudinal research.

Activities of Daily Living↗

PubMed2004

Effective HIV treatment and the employment of HIV(+) adults.

OBJECTIVE: To examine whether highly active antiretroviral therapy (HAART) helps HIV-infected patients return to work, remain employed, and maintain hours of work. DATA SOURCE: Longitudinal data from a national probability sample of HIV+ patients older than 18 years old who made at least one visit in the contiguous United States in early 1996. STUDY DESIGN: We consider the effect of HAART on three employment outcomes: (1) returning to work within six months of treatment, conditional on not working pretreatment; (2) remaining employed within six months of treatment, conditional on working pretreatment; (3) hours of work conditional on working at the second follow-up survey. We use a bivariate probit model to jointly model employment and treatment with HAART for the first two outcomes and the two-stage least squares method for hours of work. State policies regarding prescription drug coverage are used as instrumental variables for HAART to account for a key source of potential bias-the more severely ill tend to have the most difficulty working, but are also the most likely to be on HAART. PRINCIPAL FINDINGS: Our results indicate that HAART increases the probability of remaining employed by HIV patients and hours of work for those working within six months of treatment. In the case of remaining employed, the employment effect (an increase from 58 percent to 94 percent in the probability of remaining employed) is statistically significant and the related incremental income is sizable compared to the incremental costs of HAART. Sensitivity analyses demonstrate that the results are robust to different specifications for insurance coverage. CONCLUSIONS: Patients who are working are more likely to remain employed because of treatment with HAART. HAART prescribed to patients in less advanced stages of the infection may lead to the greatest gain in employment.

Adult↗

PubMed2005

The role of fiber-matrix interactions in a nonlinear fiber-reinforced strain energy model of tendon.

The objective of this study was to develop a nonlinear and anisotropic three-dimensional mathematical model of tendon behavior in which the structural components of fibers, matrix, and fiber-matrix interactions are explicitly incorporated and to use this model to infer the contributions of these structures to tendon mechanical behavior. We hypothesized that this model would show that: (i) tendon mechanical behavior is not solely governed by the isotropic matrix and fiber stretch, but is also influenced by fiber-matrix interactions; and (ii) shear fiber-matrix interaction terms will better describe tendon mechanical behavior than bulk fiber-matrix interaction terms. Model versions that did and did not include fiber-matrix interaction terms were applied to experimental tendon stress-strain data in longitudinal and transverse orientations, and the R2 goodness-of-fit was evaluated. This study showed that models that included fiber-matrix interaction terms improved the fit to longitudinal data (R2(toe) = 0.88, R2(Lin) = 0.94) over models that only included isotropic matrix and fiber stretch terms (R2(Toe) = 0.36, R2(Lin) = 0.84). Shear fiber-matrix interaction terms proved to be responsible for the best fit to data and to contribute to stress-strain nonlinearity. The mathematical model of tendon behavior developed in this study showed that fiber-matrix interactions are an important contributor to tendon behavior The more complete characterization of mechanical behavior afforded by this mathematical model can lead to an improved understanding of structure-function relationships in soft tissues and, ultimately, to the development of tissue-engineered therapies for injury or degeneration.

Animals↗

PubMed2004

The effect of parity-induced copayment reductions on adolescent utilization of substance use services.

OBJECTIVE: The purpose of this study was to determine if the reduction in copayment amount by a large self-insured state employer increased utilization of adolescent services. Specifically, the study sought to discover if the number of unique adolescent users of substance use outpatient services increased as a result of reductions in cost-sharing arrangements. METHOD: The data utilized in this study were 31,585 records from administrative claims data on utilization of mental health and substance abuse services from members of a state indemnity plan fromJuly 1998 through December 2001, translating to 36 months of pre-intervention data and 6 months of postintervention data. Monthly longitudinal data before and after benefit design change were analyzed using a quasi-experimental time series design, using Box and Jenkins' autoregressive, integrated, moving-average time-series modeling methods. The primary outcome measure was the number of unique users of services. RESULTS: The hypothesis that service utilization would increase following the implementation of a reduction in copayment amount (the intervention) was supported in these analyses for adolescents' substance use service utilization. A significant increase in the number of unique adolescent users of substance use services was detected in the month following the intervention (p < .01). CONCLUSIONS: The results of this study suggest that a reduction in adolescents' substance use service copayment requirements to a level equal to those for general medical services may be a step toward assuring full parity between such types of services. These findings provide potentially important information regarding the possible effects of broader policy changes, as parity in benefit design is a common component of laws that attempt to ensure "full parity."

Adolescent↗

PubMed1992

Randomized comparison of metabolic control achieved by intraperitoneal insulin infusion with implantable pumps versus intensive subcutaneous insulin therapy in type I diabetic patients.

OBJECTIVE: To compare intraperitoneal implantable insulin infusion (IP) to subcutaneous (SC) intensive insulin therapy. RESEARCH DESIGN AND METHODS: Twenty-one insulin-dependent (type I) diabetic patients aged 24-61 yr underwent a 3-mo treatment optimization using multiple SC daily injections or external pumps. Patients were then randomized (time 0 mo) to IP infusion using Infusaid-programmable pumps or continuation on SC intensive insulin for 6 mo. RESULTS: No differences were noted between study and control group data. However, longitudinal within-group comparisons from baseline showed that glycosylated hemoglobin improved to near-normal in both groups: IP, 9.0 +/- 0.5 vs. 7.8 +/- 0.6% (P less than 0.05) and SC, 8.4 +/- 0.5 vs. 7.5 +/- 0.3% (P less than 0.5) at 0 and 4 mo, respectively (normal less than 6.9%). The percentage of blood glucose tests greater than 11 mM at 0 and 6 mo was 28 +/- 5 vs. 16 +/- 4% in the IP group (P less than 0.05) and 22 +/- 5 vs. 24 +/- 7% in the SC group (NS). At 0 and 6 mo, the standard deviation of blood glucose values, an index of glycemic fluctuations, was 4.3 +/- 0.4 vs. 3.2 +/- 0.5 mM in the IP group (P less than 0.05) and 3.7 +/- 0.3 vs. 4.0 +/- 0.4 mM in the SC group (NS). Weight, insulin dosages, circulating lipid levels, and the frequency of severe hypoglycemic reactions and biochemical hypoglycemias were similar and did not change in the two groups. CONCLUSIONS: IP-implantable pumps compared with SC intensive insulin therapy have similar effects on most metabolic variables and are equally effective at achieving near-normal glycemic levels. Only longitudinal data suggest that IP treatment may be more effective at limiting glycemic fluctuations.

Adult↗