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Simple pattern-mixture models for longitudinal data with missing observations: analysis of urinary incontinence data.

In longitudinal studies each subject is observed at several different times. Longitudinal studies are rarely balanced and complete due to occurrence of missing data. Little proposed pattern-mixture models for the analysis of incomplete multivariate normal data. Later, Little proposed an approach to modelling the drop-out mechanism based on the pattern-mixture models. We advocate the pattern-mixture models for analysing the longitudinal data with binary or Poisson responses in which the generalized estimating equations formulation of Liang and Zeger is sensible. The proposed method is illustrated with a real data set.

Aged↗

A quality control measure for longitudinal studies with continuous outcomes.

At the time of data acquisition in a longitudinal study a decision needs to be made whether or not the latest measurement of the primary outcome is a potential outlier. If the data point does not fit with the subject's prior data, the patient can be immediately remeasured before he/she leaves the office. From the third visit onwards, a least squares approach can be used to generate prediction intervals for the value of the response at that visit. We propose a Bayesian method for calculating a prediction interval that can incorporate external information about the process that can be used beginning at the first visit. Both the least squares and Bayesian approaches will be used to prospectively clean longitudinal data. An example using longitudinally measured bone density measurements in the elderly will be discussed. In addition, simulation studies will be described which show that both cleaning methods are better than doing nothing and that the Bayesian approach outperforms the least squares method.

Absorptiometry, Photon↗

Blomqvist revisited: how and when to test the relationship between level and longitudinal rate of change.

Longitudinal studies are often interested in assessing the relationship between severity (level) and rate of change (slope). Blomqvist describes an estimator of this relationship that has been used in a variety of contexts. This paper reviews and generalizes the Blomqvist method. Most published applications of the Blomqvist method contain substantial bias because they fail to consider and accommodate confounding due to the pooling of multiple age cohorts in a single analysis. We describe this bias, and present an unbiased algorithm consistent with the intentions of Blomqvist. We also explore when it is appropriate to apply the Blomqvist analysis, and what inferences can be made using this statistic. Aetiological inference about premorbid level of function predicting future rate of decline is often desired, but may not be justified when modelling chronic progressive conditions, since differential progression prior to the start of longitudinal follow-up can induce a relationship between level and rate of decline, even in the absence of an aetiologically relevant association. We conclude that aetiological inference by the Blomqvist analysis is not appropriate in most investigations of chronic progressive disease. Using the model to develop descriptive and predictive equations in these circumstances, however, remains appropriate, as does testing simply for clinical heterogeneity in longitudinal rate of decline.

Aged↗

Linear discriminant models for unbalanced longitudinal data.

This paper discusses statistical methods for the classification of observations into one of two or more groups based on longitudinal observations. Measurements on subjects in longitudinal medical studies are often collected at different times and on a different number of occasions. Classical multivariate methods for linear discriminant analysis are difficult to apply to repeated measurements due to the highly unbalanced structure observed in these data. Linear models for the analysis of longitudinal data proposed by Laird and Ware and non-linear models proposed by Lindstrom and Bates can be used to estimate population parameters for a discriminant model that classifies individuals into distinct predefined groups or populations. An example is presented using data from a study in 150 pregnant women in Santiago, Chile, in order to predict normal versus abnormal pregnancy outcomes.

Abortion, Spontaneous↗

Analysis of longitudinal data from twins.

Longitudinal data from twin pairs may be used to determine how the genetic effects influencing a quantitative trait change with age. Here a model for mixed longitudinal data of Huggins and Loesch [1998] on unrelated individuals is extended to twin studies. The model is fitted using robust statistical methods and a bootstrap procedure is proposed to estimate the percentiles. The method is applied to longitudinal twin data on body mass index in male and female twin pairs aged 5-18 years.

Adolescent↗

Heritability of age at menarche in girls from the Fels Longitudinal Study.

Menarche is the hallmark maturational event of female childhood. Many studies indicated a significant genetic contribution to the timing of the onset of menstruation, but most of these studies were limited by the use of retrospective data and by the use of data from only certain types of relatives (i.e., mothers and daughters, sisters, or twin sisters). The primary goal of this study was to use a modern maximum likelihood quantitative genetic method to estimate the heritability (h(2)) of age at menarche, using familial data collected over the course of the 74-year-old Fels Longitudinal Study. The secondary goal was to review earlier studies of the heritability of age at menarche. The study of the heritability of age at menarche presented here is unique for two reasons. First, because of the Fels Longitudinal Study's serial design, age-at-menarche data were collected prospectively from most participants. Second, because the Fels Longitudinal Study is a family study that has been conducted for decades, age-at-menarche data are available from many types of female relatives spanning multiple households and generations. The best-fitting and most parsimonious quantitative genetic model included provision for a secular decrease in age at menarche, and estimated the h(2) of age at menarche to be 0.49+/- 0.13 (95% confidence interval of h(2),=0.24-0.73). The results of this study are in general agreement with the findings of most previous studies of genetic influences on age at menarche, and suggest that it is reasonable to consider it well-established that approximately half the phenotypic variation among girls from developed nations in the timing of menarche is due to genetic factors.

Adolescent↗

Longitudinal study of cerebrospinal fluid levels of tau, A beta1-40, and A beta1-42(43) in Alzheimer's disease: a study in Japan.

To clarify the alterations of tau, amyloid beta protein (A beta) 1-40 and A beta1-42(43) in the cerebrospinal fluid (CSF) that accompany normal aging and the progression of Alzheimer's disease (AD), CSF samples of 93 AD patients, 32 longitudinal subjects among these 93 AD patients, 33 patients with non-AD dementia, 56 with other neurological diseases, and 54 normal control subjects from three independent institutes were analyzed by sensitive enzyme-linked immunosorbent assays. Although the tau levels increased with aging, a significant elevation of tau and a correlation between the tau levels and the clinical progression were observed in the AD patients. A significant decrease of the A beta1-42(43) levels and a significant increase of the ratio of A beta1-40 to A beta1-42(43) were observed in the AD patients. The longitudinal AD study showed continuous low A beta1-42(43) levels and an increase of the ratio of A beta1-40 to A beta1-42(43) before the onset of AD. These findings suggest that CSF tau may increase with the clinical progression of dementia and that the alteration of the CSF level of A beta1-42(43) and the ratio of A beta1-40 to A beta1-42(43) may start at early stages in AD. The assays of CSF tau, A beta1-40, and A beta1-42(43) provided efficient diagnostic sensitivity (71%) and specificity (83%) by using the production of tau levels and the ratio of A beta1-40 to A beta1-42(43), and an improvement in sensitivity (to 91%) was obtained in the longitudinal evaluation.

Aged↗

Description and prediction of physical functional disability in psoriatic arthritis: a longitudinal analysis using a Markov model approach.

OBJECTIVE: To describe the longitudinal course of physical functioning in patients with psoriatic arthritis. METHODS: Between June 1993 and June 2003, 341 patients attending the University of Toronto Psoriatic Arthritis Clinic completed 2 or more Health Assessment Questionnaires (HAQs). At the time of administration of each HAQ, patients were assigned to 1 of 3 physical functional disability states, based on their HAQ score. A Markov model that allowed for transitions to and from these 3 disability states was used to characterize the longitudinal course of physical functioning, as well as to identify factors for both progression and regression of disability. RESULTS: Despite patient variability in the course of physical functioning, the following 3 longitudinal patterns were observed: 1) a stable state of disability throughout the entire study period, with 28%, 12%, and 6% of patients experiencing no, moderate, or severe disability, respectively; 2) a steady improvement or deterioration in disability over time (this pattern was observed in 27% of patients); and 3) a fluctuating state of disability, occurring in 27% of the patients. Sex, age, disease duration, number of actively inflamed joints, and number of deformed joints predicted transitions between disability states. CONCLUSION: Although 28% of patients appeared resistant to becoming disabled over the duration of this study, the remaining patients were observed either to experience enduring disability or to move between disability states.

Arthritis, Psoriatic↗

The genetic contribution to longitudinal changes in knee structure and muscle strength: a sibpair study.

OBJECTIVE: To estimate the heritability of longitudinal changes in knee cartilage volume, chondral defects, subchondral bone size, and lower limb muscle strength. METHODS: A sibpair design was used. Longitudinal changes in lateral and medial tibial cartilage volume and bone size, as well as progression of chondral defects, were determined on serial magnetic resonance images. Radiographs were obtained and scored for individual features of radiographic osteoarthritis (OA) at baseline. Lower limb muscle strength was measured by dynamometry. Heritability was estimated using the SOLAR software package. RESULTS: A total of 115 subjects (55 men and 60 women, mean age 45 years) from 48 families representing 95 sibling pairs were successfully followed up for a mean of 2.4 years. The adjusted heritability estimates for changes in cartilage volume were 73% for the medial compartment (P < 0.01) and 40% for the lateral compartment (P = 0.10). The adjusted heritability estimates for changes in bone size were 62% for the lateral compartment (P = 0.03) and 20% for the medial compartment (P = 0.22). The adjusted heritability estimate for changes in muscle strength was 64% (P = 0.01). The adjusted heritability estimates for progression of chondral defects were 80% for the lateral compartment (P = 0.06) and 98% for the medial compartment (P = 0.03). These estimates changed little after adjusting for each other and for the predominantly mild radiographic OA, with the exception of progression of chondral defects in the lateral compartment. CONCLUSION: Early longitudinal changes in knee structures of relevance to later OA, such as changes in medial tibial cartilage volume, lateral tibial bone size, progression of chondral defects, and muscle strength, have high heritability, most likely reflecting a strong genetic component and suggesting their potential to be studied in quantitative trait linkage and association analysis.

Adult↗

Arthritis onset and worsening self-rated health: a longitudinal evaluation of the role of pain and activity limitations.

OBJECTIVE: To longitudinally explore the hypothesized role of worsening pain and development of activity limitations as mediators in the relationship between arthritis onset and worsening self-rated health (SRH). METHODS: Data was obtained from the 1998/1999 and 2000/2001 cycles of the population-based Canadian longitudinal National Population Health Survey (n = 10,859; ages > or = 18; response rate: time 1 = 81.6%, time 2 = 89.2%). Respondents were asked about chronic conditions, pain, activity limitations, and self-perceived health; change over time was assessed. Change in effect of arthritis onset on worsening SRH upon considering potential mediators was assessed through multivariate logistic regression, controlling for sociodemographic characteristics and onset of other conditions. RESULTS: Worsening pain fully explained the effect of arthritis onset on worsening SRH; a portion of the effect of worsening pain was mediated by the development of activity limitation. Residual direct effect of arthritis onset was statistically insignificant. Worsening pain and development of activity limitations also mediated a portion of the effects of onset of other chronic conditions but to a lesser extent than arthritis onset. CONCLUSION: This is the first study to examine these relationships longitudinally. Identifying the role of mediators is necessary if target areas of prevention and/or management are sought, either at the individual or population level. Our results indicate that the development of arthritis has a significant impact on worsening SRH. Pain and development of activity limitations fully account for the relationship between arthritis onset and worsening SRH. High priority should be placed on prevention and management strategies for pain among people with arthritis.

Activities of Daily Living↗

Lack of association between chondrocalcinosis and increased risk of cartilage loss in knees with osteoarthritis: results of two prospective longitudinal magnetic resonance imaging studies.

OBJECTIVE: To evaluate the relationship between chondrocalcinosis and the progression of knee osteoarthritis (OA) using longitudinal magnetic resonance imaging (MRI) assessments. METHODS: Longitudinal knee MRIs were obtained in the Boston OA Knee Study (BOKS) and in the Health, Aging and Body Composition (Health ABC) Study. Chondrocalcinosis was determined as present or absent on baseline knee radiographs. Cartilage morphology was graded on paired longitudinal MRIs using the Whole-Organ Magnetic Resonance Imaging Score in 5 cartilage subregions of each of the medial and lateral tibiofemoral joints. Cartilage loss in a subregion was defined as an increase in the cartilage score of > or = 1 (0-4 scale). The risk for change in the number of subregions with cartilage loss was assessed using Poisson regression, with generalized estimating equations to account for correlations. Analyses were adjusted for age, sex, body mass index, baseline cartilage score, and presence of damaged menisci. RESULTS: In BOKS, 23 of the 265 included knees (9%) had chondrocalcinosis. In Health ABC, 373 knees were included, of which 69 knees (18.5%) had chondrocalcinosis. In BOKS, knees with chondrocalcinosis had a lower risk of cartilage loss compared with knees without chondrocalcinosis (adjusted risk ratio [RR] 0.4, 95% confidence interval [95% CI] 0.2-0.7) (P = 0.002), and there was no difference in risk in Health ABC (adjusted RR 0.9, 95% CI 0.6-1.5) (P = 0.7). Stratification by intact versus damaged menisci produced similar results within each cohort. CONCLUSION: In knees with OA, the presence of chondrocalcinosis was not associated with increased cartilage loss. These findings do not support the hypothesis that chondrocalcinosis worsens OA progression.

Aged↗

Predictors of contact difficulty and refusal in a longitudinal study.

BACKGROUND: Attrition presents a serious problem to researchers collecting longitudinal data. Participant loss threatens both the internal and external validity of research findings. This study sought to examine predictors related to contact difficulty and refusals in a longitudinal study. METHOD: Data for this paper came from the Developmental Trends Study, a longitudinal study investigating the development of disruptive behaviour disorders in a sample of 177 clinic-referred boys. Annual follow-up assessments were conducted, ages for the periods examined ranged from 11 to 19 years. The predictor domains during project years 1-4 included demographics, child functioning, parental functioning, parenting skills and participant dispersion. RESULTS: These indicated that participant's older age, low socioeconomic status, the presence of callous and un-emotional behaviours, and having a father with antisocial personality disorder predicted contact difficulty, while participant's older age, living in a rural environment and attention deficit hyperactivity disorder were predictive of refusals. Participant dispersion was not significantly related to either contact difficulty or refusal status. CONCLUSIONS: Investigating a broader range of variables may better allow researchers to identify participants who may be at risk of attrition. Early identification of 'difficult' participants enables development of retention strategies to minimize attrition.

Adolescent↗

The longitudinal case study: from Schön's model to self-directed learning.

BACKGROUND: Rapid changes observed in information technologies, medical practice, and learning methods encourage physicians to develop new updating strategies. To test its feasibility and to help physicians devise new learning and updating strategies, the knowing-in-action model developed by Schön was applied in planning and evaluating an interactive workshop. Acquisition of knowledge was tested. METHODS: The office and hospital charts of a family physician were reviewed. They were used to prepare a longitudinal case study, based on the real-life story of a hypertensive patient followed by her doctor over a period of 15 years. The clinician's approach to solving clinical problems was triangulated for credibility with general practitioners, specialists, and the information available in the literature. This longitudinal case study was used to develop an interactive educational workshop. The workshop was presented to physicians who had registered in an accredited continuing medical education event. Changes in pre- and postevent knowledge among the participants were assessed using touch pad technology to evaluate the effectiveness of this approach on the acquisition of knowledge related to management of arterial hypertension and associated clinical problems. RESULTS: A comparison of pre- and post-test data showed a significant improvement in knowledge for participants who answered all questions on both questionnaires (n = 8/37). The average score of these participants increased from 5.5 of 10 before the workshop to 8.3 of 10 after the workshop (p < .05). Participants reported a high satisfaction rate for the event. FINDINGS: A workshop using the longitudinal case study enables physicians to perceive their daily practice through a continuing education activity in which they experience the processes of reflection in action and reflection on action described by Schön. It also increases awareness of the gap between current practice and experts' recommendations and provides an opportunity to evaluate the means for bridging or closing this gap. It sensitizes the physician to patients' changing needs and prompts the clinician to reflect on the who, what, when, where, and how of learning.

Education, Medical, Continuing↗

Longitudinal data analysis in pedigree studies.

Longitudinal family studies provide a valuable resource for investigating genetic and environmental factors that influence long-term averages and changes over time in a complex trait. This paper summarizes 13 contributions to Genetic Analysis Workshop 13, which include a wide range of methods for genetic analysis of longitudinal data in families. The methods can be grouped into two basic approaches: 1) two-step modeling, in which repeated observations are first reduced to one summary statistic per subject (e.g., a mean or slope), after which this statistic is used in a standard genetic analysis, or 2) joint modeling, in which genetic and longitudinal model parameters are estimated simultaneously in a single analysis. In applications to Framingham Heart Study data, contributors collectively reported evidence for genes that affected trait mean on chromosomes 1, 2, 3, 5, 8, 9, 10, 13, and 17, but most did not find genes affecting slope. Applications to simulated data suggested that even for a gene that only affected slope, use of a mean-type statistic could provide greater power than a slope-type statistic for detecting that gene. We report on the results of a small experiment that sheds some light on this apparently paradoxical finding, and indicate how one might form a more powerful test for finding a slope-affecting gene. Several areas for future research are discussed.

Cardiovascular Diseases↗

Consistency of genetic analyses in longitudinal data: observations from the GAW13 Framingham Heart Study data.

This paper examines the consistency of genetic analyses across time, both in the context of replicating results from one data collection point to the next, and from the perspective of modeling longitudinal processes. This summary originates from the examination of findings from nine papers from Genetic Analysis Workshop (GAW) 13 that reported on analyses of longitudinal data of a variety of traits from the Framingham Heart Study. These analyses include both assessments of consistency of aggregate genetic effects, in the form of estimation of heritability and relative risk of disease, as well as localization of quantitative trait loci (QTLs) by genome-wide linkage screens. Consistency varied widely by trait, possibly reflecting differences in measurement error, secular trends, or underlying biological features such as genotype x age interaction. Quantitatively, comparing magnitudes of estimates across age or time, heritability estimates showed greater consistency than LOD scores. However, qualitatively, the same regions of interest were often identified in genome scans from different time points or different ages. Estimates of sibling recurrence risk, on the other hand, showed little consistency. Heritabilities were greater when participants were matched by age than when they were matched by date of examination. Multivariate approaches, either in use of multiple traits or in use of multiple measures of the same trait, appeared to provide stronger genetic signals both for relative risk and for linkage. Finally, modeling of longitudinal processes provided evidence for genotype x age interactions that may partially explain variation in results of genetic analyses across time or age.

Age Factors↗

Psychological wellbeing in later life: the longitudinal effects of marriage, widowhood and marital status change.

AIM: The study examined cross-sectionally and longitudinally psychological wellbeing in the context of marital status, gender, and age. METHOD: Measures were taken eight years apart for three groups: married at both interviews; widowed at both interviews; and married at first interview but widowed at third. Data were analysed using multiple regression models: dependent variables were morale and social engagement; independent variables were marital status, gender and age. RESULTS: Cross-sectionally significant differences were found for marital status and age for both morale and social engagement. Both widowed and newly widowed participants reported lower morale and social engagement than their married counterparts. In the longitudinal model, when prior levels of morale were taken into account, only age and being newly widowed contributed significantly to the variance (R2). The same pattern of results was found for social engagement. Gender was never significant. CONCLUSION: The results illustrate the value of modelling both cross-sectional and longitudinal data. The latter demonstrated that the size of the effect differed between those who had recently widowed and those who had been widowed for longer. The study shows that age needs to be taken into account when examining widowhood.

Aged↗

Impact of race and baseline PSA on longitudinal PSA.

There is an increasing debate regarding the frequency of prostate-specific antigen (PSA) testing and the current primary screening modality used to detect prostate cancer. The purpose of this study is to determine whether PSA screening intervals should be based on initial PSA. Our study explores longitudinal changes of PSA levels in black and white males separately. Study participants were 768 white and 450 black males attending an annual prostate cancer screening. We fit a longitudinal repeated measures model separately for blacks and whites and estimated the probability of PSA converting to greater than 4.0 ng/ml at a follow-up year given baseline PSA range among males without an abnormal DRE. Black and white males with a baseline PSA between 0 and 1.0 ng/ml, with a healthy or enlarged prostate, have a less than 1% chance that their PSA will increase above 4.0 ng/ml over the following 5 years. Black and white males with a PSA between 1.0 and 1.9 ng/ml have a less than 1% chance of PSA conversion to greater than 4.0 ng/ml over the next year. Our findings further support that annual screening for prostate cancer may not be necessary, specifically males with a baseline PSA less than 2.0 may not need to undergo annual screening. Our results suggest that race does not affect the longitudinal trend of PSA enough to warrant setting screening intervals based on race.

Aged↗

Comparison of cross-sectional and longitudinal measurements of age-related changes in bone mineral content.

Age-related, postmenopausal bone loss was examined among a cohort of Japanese-American women living in Hawaii. None of the women were using estrogens or thiazides. Cross-sectional and longitudinal measurements of bone mineral content were compared at the calcaneus, the proximal radius, and the distal radius. Cross-sectional measurements were also available for the lumbar spine. The longitudinal data showed a slowing rate of bone loss with increasing age at the radius sites. By contrast, the cross-sectional data suggested constant rates of bone loss for all ages at both radius sites and the spine. The calcaneus demonstrated a complex pattern of bone loss in both cross-sectional and longitudinal analyses. The loss rates among women in their fifties were greater than for those in their sixties. From the middle sixties onward calcaneal bone loss remained essentially constant. Because of the sustained bone loss, however, women in their seventies were actually losing greater percentages of their calcaneal bone mineral than they had in their sixties.

Aged↗