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PubMed2005

A nonparametric approach to the analysis of longitudinal data via a set of level crossing problems with application to the analysis of microarray time course experiments.

Here we develop a completely nonparametric method for comparing two groups on a set of longitudinal measurements. No assumptions are made about the form of the mean response function, the covariance structure or the distributional form of disturbances around the mean response function. The solution proposed here is based on the realization that every longitudinal data set can also be thought of as a collection of survival data sets where the events of interest are level crossings. The method for testing for differences in the longitudinal measurements then is as follows: for an arbitrarily large set of levels, for each subject determine the first time the subject has an upcrossing and a downcrossing for each level. For each level one then computes the log rank statistic and uses the maximum in absolute value of all these statistics as the test statistic. By permuting group labels we obtain a permutation test of the hypothesis that the joint distribution of the measurements over time does not depend on group membership. Simulations are performed to investigate the power and it is applied to the area that motivated the method-the analysis of microarrays. In this area small sample sizes, few time points and far too many genes to consider genuine gene level longitudinal modeling have created a need for a simple, model free test to screen for interesting features in the data.

Computer Simulation↗
PubMed1997

Age-associated changes in blood pressure in a longitudinal study of healthy men and women.

BACKGROUND: Current knowledge of age-associated increases in blood pressure is based primarily on unscreened population studies that may not be representative of healthy men and women. We examined longitudinal patterns of change in blood pressure in healthy male and female volunteers from the Baltimore Longitudinal Study of Aging (BLSA). METHODS: Longitudinal mixed-effects regression models are used to estimate the age-associated changes in blood pressure in 1307 men (age 17-97) and 333 women (age 18-93) who have been followed for up to 32 years (mean: 8.4 years for men and 3.4 years for women) and who have been screened for health problems or medications that affect blood pressure. RESULTS: On average, systolic pressure is relatively stable in men and women until approximately age 45, increases at 5-8 mm Hg per decade in middle age, then accelerates in men and stabilizes in women. Diastolic pressure increases at 1 mm Hg per decade at all ages in men, whereas in women the rate of change in diastolic pressure increases in middle age and then plateaus and may decline after age 70. Additional findings include: (a) BLSA cross-sectional and longitudinal findings are more similar than has been observed in studies of unscreened samples; (b) there is no evidence of a gender cross-over in this group of healthy men and women; and (c) compared to previous studies of unscreened samples, healthy BLSA men and women show a weaker association between baseline blood pressure and subsequent rate of blood pressure change. CONCLUSIONS: These findings suggest that several previously described age-associated patterns of blood pressure change partially reflect the effects of hypertension and its treatment, rather than intrinsic age changes in the blood pressure of healthy individuals.

Adolescent↗
PubMed1998

Comparison of cross-sectional and longitudinal designs in the study of aging of upper extremity performance.

The purpose of the study was to compare two research designs, namely the cross-sectional design and the longitudinal design, in the context of upper extremity performance and age-related changes. Upper extremity performance of 360 randomly recruited healthy, community-dwelling elderly persons was evaluated with reliable and valid sensori-motor tests. Three years later, survivors (n = 264) were reevaluated with the same tests. In many tests, cross-sectional and longitudinal designs were comparable for estimating the changes in upper extremity performance with age. However, in some tests, the decline with age using a cross-sectional design was underestimated. The upper extremity performance decline observed with the longitudinal design was larger than the decline predicted with the cross-sectional design. The withdrawal and survivor biases related to the longitudinal design and the cohort bias associated with the cross-sectional design may, in part, explain these results.

Aged↗
PubMed1992

A longitudinal approach to modeling outcomes in a nursing home study.

Recent developments in longitudinal statistical methodology have improved our ability to model dynamic processes such as adaptation to nursing homes. Longitudinal observations provide information on individual patterns of change and factors affecting them. However, longitudinal analyses are often complicated by unequal periods of observation and individual variability in patterns of change. This paper demonstrates the use of a linear mixed-effects model to study adaptation in a longitudinal nursing home study with different numbers of repeated measurements for each individual because of discharges, transfers, and mortality.

Adaptation, Psychological↗
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↗
PubMed2005

Covariance components models for longitudinal family data.

A longitudinal family study is an epidemiological design that involves repeated measurements over time in a sample that includes families. Such studies, that may also include relative pairs and unrelated individuals, allow closer investigation of not only the factors that cause a disease to arise, but also the genetic and environmental determinants that modulate the subsequent progression of that disease. Knowledge of such determinants may pay high dividends in terms of prognostic assessment and in the development of new treatments that may be tailored to the prognostic profile of individual patients. Unfortunately longitudinal family studies are difficult to analyse. They conflate the complex within-family correlation structure of a cross-sectional family study with the correlation over time that is intrinsic to longitudinal repeated measures. Here we describe an approach to analysis that is relatively straightforward to implement, yet is flexible in its application. It represents a natural extension of a Gibbs-sampling-based approach to the analysis of cross-sectional family studies that we have described previously. The approach can be applied to pedigrees of arbitrary complexity. It is applicable to continuous traits, repeated binary disease states, and repeated counts or rates with a Poisson distribution. It not only supports the analysis of observed determinants, including measured genotypes, but also allows decomposition of the correlation structure, thereby permitting conclusions to be drawn about the effect of unobserved genes and environment on key features of disease progression, and hence to estimate the heritability of these features. We demonstrate the efficacy of our methods using a range of simulated data analyses, and illustrate its practical application to longitudinal blood pressure data measured in families from the Framingham Heart Study.

Blood Pressure↗
PubMed1990

Longitudinal and cross-sectional estimates of pulmonary function decline in never-smoking adults.

This paper describes methods for simultaneous cross-sectional and longitudinal analysis of repeated measurements obtained in cohort studies with regular examination schedules, then uses these methods to describe age-related changes in pulmonary function level among nonsmoking participants in the Six Cities Study, a longitudinal study of air pollution and respiratory health conducted between 1974 and 1983 in Watertown, Massachusetts; Kingston and Harriman, Tennessee; St. Louis, Missouri; Steubenville, Ohio; Portage, Wisconsin; and Topeka, Kansas. The subjects, initially aged 25-74, were examined on three occasions at 3-year intervals. Individual rates of loss increased more rapidly with age than predicted from the cross-sectional model. For example, for a male of height 1.75 m, the cross-sectional model predicted an increase in the annual rate of loss of FEV1 from 23.7 ml/yr at age 25 to 39.0 ml/yr at age 75, while the longitudinal model gave rates of loss increasing from 12.9 ml/yr at age 25 to 58.2 ml/yr at age 75. These results contrast with those of other studies comparing longitudinal and cross-sectional estimates of pulmonary function loss.

Adult↗
PubMed1991

Longitudinal research strategies: advantages, problems, and prospects.

The single-cohort, long-term longitudinal survey has many advantages in comparison with a cross-sectional survey in advancing knowledge about offending and other types of psychopathology, notably in providing information about onset and desistance, about continuity and prediction, and about within-individual change. However, the longitudinal survey also has significant problems, notably in confounding aging and period effects, delayed results, achieving continuity in funding and research direction, and cumulative attrition. This paper suggests the use of a multiple-cohort sequential strategy (the "accelerated longitudinal design") as a way of achieving the benefits of the longitudinal method while minimizing the problems in advancing knowledge about the natural history, causes, prevention, and treatment of psychopathological disorders.

Adolescent↗
PubMed2000

Longitudinal changes in physical activity in a biracial cohort during adolescence.

PURPOSE: This report describes the development and use of two self-report methods and an objective measure to assess longitudinal changes in physical activity in a large biethnic cohort of young girls from childhood through adolescence. METHODS: The NHLBI Growth and Health Study (NGHS) is a multicenter study of obesity development in 2379 black and white girls followed from ages 9-10 yr to 18-19 yr (NGHS years 1-10). A Caltrac activity monitor was used to objectively quantify activity levels in years 3-5. A 3-d diary (AD) and a habitual patterns questionnaire (HAQ) were administered annually and biannually, respectively, to subjectively quantify physical activity levels. The changing pattern of activities as the girls matured during the 10-yr study period necessitated periodic form changes. Empirical analytic approaches were developed to help distinguish between true longitudinal changes in activity levels from potential numerical artifacts resulting from modifications in forms. RESULTS: The longitudinal activity data indicate a steep decline in the level of reported activity from baseline to year 10 as indicated by AD scores (446.8 to 292.1 MET-min x d(-1), 35%) as well as by HAQ scores (29.3 to 4.9 MET-times x wk(-1), 83%). This parallel trend in the pattern of the decline in activity among the two self-report methods was mirrored by a similar decline using the Caltrac method of physical activity assessment. From years 3 to 5, the AD decreased by 22%, whereas both the HAQ and Caltrac declined by 21%. CONCLUSION: The longitudinal data on physical activity collected in the NGHS cohort further confirm a dramatic decrease in the overall level of physical activity during the transition from childhood to adolescence. The consistency among the three methods indicate that both the AD and HAQ are useful tools for the assessment of activity levels in adolescent girls.

Adolescent↗
PubMedDate not supplied

Relation between the longitudinal development of personality characteristics and biological and lifestyle risk factors for coronary heart disease.

OBJECTIVE: This study was undertaken to assess the stability of personality characteristics (ie, inadequacy, rigidity, dominance, self-sufficiency, and social inadequacy) over a 15-year period covering adolescence and young adulthood and to analyze the longitudinal relationships between personality characteristics and both biological (ie, lipoproteins, blood pressure, and body fatness) and lifestyle (ie, physical activity, dietary intake, smoking, and alcohol consumption) risk factors for coronary heart disease (CHD). METHODS: The data were derived from the Amsterdam Growth and Health Study, an observational longitudinal study in which, over a period from 13 to 27 years of age, six repeated measurements were performed on 181 subjects. Both the stability analysis and the analysis of the longitudinal relationships were performed by generalized estimating equations (GEE). This method is suitable for both continuous and dichotomous outcome variables, by using all available longitudinal data. RESULTS: Stability coefficients for the personality characteristics varied between 0.39 for self-sufficiency and dominance and 0.53 for social inadequacy. Self-sufficiency was inversely related to total serum cholesterol (only male subjects) and body fatness; inadequacy was inversely related to systolic blood pressure. Dominance (female subjects) was positively related to body fatness and social inadequacy (male subjects) was positively related to total serum cholesterol. Furthermore, inadequacy was positively related to smoking behavior. Social inadequacy and rigidity were inversely related to smoking behavior. Self-sufficiency was inversely related to alcohol consumption. CONCLUSIONS: Over a period of 15 years, personality characteristics showed marginal stability. Weak relationships were found between personality characteristics and both biological and lifestyle CHD risk factors.

Adolescent↗
PubMed1994

The significance of the cervical soft disc herniation in the ossification of the posterior longitudinal ligament.

The significance and role of cervical soft disc hernia in ossification of the posterior longitudinal ligament were investigated based on 54 surgical cases. The types of ossification of the posterior longitudinal ligament were divided into three sub-types: segmental, continuous, and mixed types. In the current series, there were 29 segmental type, 12 continuous type, and 13 mixed type. In the 29 segmental type, 23 patients had accompanying cervical disc hernias (79%). In the 12 continuous type, only 2 patients (17%), and in the 13 mixed type, 5 patients (33%), had accompanying disc hernias. According to the current study, an essential difference exists between the segmental type and the continuous or mixed types. In addition, the current result seems to indicate that, at least in the segmental type, disc herniation is not the promoting or initiating factor of ossification of the posterior longitudinal ligament, but that, in these cases, the fragility of the posterior longitudinal ligament may increase the chance of a disc hernia.

Adult↗
PubMed1998

Magnetic resonance imaging of the spinal cord in cervical ossification of the posterior longitudinal ligament. Can it predict surgical outcome?

STUDY DESIGN: Magnetic resonance imaging findings of an increased signal in the cervical cord in patients undergoing surgery for ossification of the posterior longitudinal ligament were analyzed to determined whether an increased signal on T2-weighted images correlated with a poorer outcome. OBJECTIVES: To clarify whether preoperative magnetic resonance imaging findings of a high signal in the cord constitute a poor prognostic factor. SUMMARY OF BACKGROUND DATA: The importance of a high, T2-weighted, intramedullary signal on preoperative magnetic resonance studies in patients undergoing surgery for ossification of the posterior longitudinal ligament requires further clarification. METHODS: Of 91 patients having cervical surgery for ossification of the posterior longitudinal ligament, 26 had a history of minor trauma. High, T2-weighted signals in the cord were noted in 23 patients who had sustained trauma and in 39 patients who had no history of trauma. Patients were divided into four groups according to the presence or absence of a high cord signal and/or a trauma history. Pre- and postoperative Japanese Orthopaedic Association scores and recovery ratios then were evaluated. RESULTS: The pre- and postoperative Japanese Orthopaedic Association scores and recovery ratios of the patients with a high signal and a trauma history were significantly less than those with no high signal but with a trauma history. Among the patients with no history of trauma, however, there were no significant differences in the pre- and postoperative JOA scores and recovery ratios between the patients with a high signal and those with no high signal. CONCLUSION: A high preoperative cord signal on T2-weighted magnetic resonance images for patients undergoing surgery for ossification of the posterior longitudinal ligament constitutes a poor prognostic factor, when trauma has played a role.

Adult↗
PubMed2000

Atlantoaxial subluxation associated with ossification of posterior longitudinal ligament of the cervical spine.

STUDY DESIGN: Two case reports. OBJECTIVE: To demonstrate two rare cases of atlantoaxial subluxation associated with ossification of the posterior longitudinal ligament of the cervical spine, in which spastic quadriplegia developed. SUMMARY OF BACKGROUND DATA: There are only two reports of an association of diffuse idiopathic skeletal hyperostosis with atlantoaxial subluxation. This condition often accompanies ossification of the posterior longitudinal ligament of the cervical spine, but there is nothing in the literature about the association of ossification of the posterior longitudinal ligament with atlantoaxial subluxation. METHODS: Clinical and radiographic findings of these two cases were demonstrated. In both cases laminoplasty of the cervical spine was performed with occipitoaxial arthrodesis. RESULTS: The spastic quadriplegia of these two patients caused by myelocompression improved after surgical intervention. CONCLUSION: Ossification of the posterior longitudinal ligament of the cervical spine may cause atlantoaxial subluxation.

Aged↗
PubMed2004

Collecting longitudinal data through childhood, adolescence, and young adulthood: methodological challenges.

This article presents the proceedings of a workshop at the 2003 Research Society on Alcoholism meeting in Fort Lauderdale, Florida. The organizers and chairs were Vivian Faden and Nancy Day. The presentations were (1) Lessons Learned From the Lives Across Time Longitudinal Study, by Michael Windle and Rebecca Windle; (2) Methodological Issues in Longitudinal Surveys With Children and Adolescents, by Joel Grube; (3) The Pittsburgh ADHD Longitudinal Study: Methodological and Conceptual Challenges, by Brooke Molina, William Pelham, Elizabeth Gnagy, and Tracey Wilson; and (4) Lessons learned in Conducting Longitudinal Research on Alcohol Involvement: If Only I Had Known Before Hand! by Kristina Jackson and Kenneth Sher.

Adolescent↗
PubMed2004

Clinical value of longitudinal free-to-total prostate specific antigen ratio slope to diagnosis of prostate cancer.

PURPOSE: Free and total serum prostate specific antigen (PSA) levels are frequently used for early prostate cancer detection in men with a total PSA in the 2.6 to 10 ng/ml range. Results from a longitudinal study suggested that the free-to-total PSA ratio (F/T PSA), declining the decade before prostate cancer diagnosis, is the earliest serum marker predicting a subsequent diagnosis of prostate cancer. Other than this study, there are limited data on the predictive value of longitudinal F/T PSA measurements for subsequent cancer. To evaluate the clinical importance of a decreasing F/T PSA, we compared longitudinal F/T PSA in volunteers in a prostate cancer screening study. MATERIALS AND METHODS: We evaluated 657 volunteers in a screening study with a total PSA of 2.6 to 10 ng/ml but whose initial biopsies were either negative for cancer or were waived. To obtain meaningful F/T PSA slopes, the patients have been followed with at least 3 F/T PSA levels measured for 3 or greater years (mean 3.5, median 3.5, range 3 to 5.3). Of these men 22 subsequently were diagnosed with prostate cancer. We calculated the F/T PSA slope as the last F/T PSA minus the first F/T PSA divided by the interval between the measurements. The F/T PSA slopes of the patients with and without cancer were compared using chi-square analysis. RESULTS: Mean F/T PSA slope for the patients with cancer was -0.06 (median -0.03, range -0.63 to 0.22) compared to mean slope of -0.02 (median -0.01, range -0.57 to 0.69) for patients without cancer (p = 0.21). Of the patients with cancer 61% had a negative slope compared with 54% of patients without cancer (p = 0.59). The positive predictive value of a negative F/T PSA slope for subsequent cancer detection to date is only 4%. CONCLUSIONS: A decreasing F/T PSA during a 3 to 5-year interval has little value in predicting subsequent diagnosis of prostate cancer. Further followup of a larger number of patients will be required to determine the value of longitudinal F/T PSA measurements in early prostate cancer detection.

Aged↗
PubMed2002

Parameter estimation in longitudinal studies with outcome-dependent follow-up.

In many observational studies, individuals are measured repeatedly over time, although not necessarily at a set of prespecified occasions. Instead, individuals may be measured at irregular intervals, with those having a history of poorer health outcomes being measured with somewhat greater frequency and regularity; i.e., those individuals with poorer health outcomes may have more frequent follow-up measurements and the intervals between their repeated measurements may be shorter. In this article, we consider estimation of regression parameters in models for longitudinal data where the follow-up times are not fixed by design but can depend on previous outcomes. In particular, we focus on general linear models for longitudinal data where the repeated measures are assumed to have a multivariate Gaussian distribution. We consider assumptions regarding the follow-up time process that result in the likelihood function separating into two components: one for the follow-up time process, the other for the outcome process. The practical implication of this separation is that the former process can be ignored when making likelihood-based inferences about the latter; i.e., maximum likelihood (ML) estimation of the regression parameters relating the mean of the longitudinal outcomes to covariates does not require that a model for the distribution of follow-up times be specified. As a result, standard statistical software, e.g., SAS PROC MIXED (Littell et al., 1996, SAS System for Mixed Models), can be used to analyze the data. However, we also demonstrate that misspecification of the model for the covariance among the repeated measures will, in general, result in regression parameter estimates that are biased. Furthermore, results of a simulation study indicate that the potential bias due to misspecification of the covariance can be quite considerable in this setting. Finally, we illustrate these results using data from a longitudinal observational study (Lipshultz et al., 1995, New England Journal of Medicine 332, 1738-1743) that explored the cardiotoxic effects of doxorubicin chemotherapy for the treatment of acute lymphoblastic leukemia in children.

Adolescent↗
PubMed2002

A semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data.

Joint models for a time-to-event (e.g., survival) and a longitudinal response have generated considerable recent interest. The longitudinal data are assumed to follow a mixed effects model, and a proportional hazards model depending on the longitudinal random effects and other covariates is assumed for the survival endpoint. Interest may focus on inference on the longitudinal data process, which is informatively censored, or on the hazard relationship. Several methods for fitting such models have been proposed, most requiring a parametric distributional assumption (normality) on the random effects. A natural concern is sensitivity to violation of this assumption; moreover, a restrictive distributional assumption may obscure key features in the data. We investigate these issues through our proposal of a likelihood-based approach that requires only the assumption that the random effects have a smooth density. Implementation via the EM algorithm is described, and performance and the benefits for uncovering noteworthy features are illustrated by application to data from an HIV clinical trial and by simulation.

Anti-HIV Agents↗
PubMed2004

Marginal analysis of incomplete longitudinal binary data: a cautionary note on LOCF imputation.

In recent years there has been considerable research devoted to the development of methods for the analysis of incomplete data in longitudinal studies. Despite these advances, the methods used in practice have changed relatively little, particularly in the reporting of pharmaceutical trials. In this setting, perhaps the most widely adopted strategy for dealing with incomplete longitudinal data is imputation by the "last observation carried forward" (LOCF) approach, in which values for missing responses are imputed using observations from the most recently completed assessment. We examine the asymptotic and empirical bias, the empirical type I error rate, and the empirical coverage probability associated with estimators and tests of treatment effect based on the LOCF imputation strategy. We consider a setting involving longitudinal binary data with longitudinal analyses based on generalized estimating equations, and an analysis based simply on the response at the end of the scheduled follow-up. We find that for both of these approaches, imputation by LOCF can lead to substantial biases in estimators of treatment effects, the type I error rates of associated tests can be greatly inflated, and the coverage probability can be far from the nominal level. Alternative analyses based on all available data lead to estimators with comparatively small bias, and inverse probability weighted analyses yield consistent estimators subject to correct specification of the missing data process. We illustrate the differences between various methods of dealing with drop-outs using data from a study of smoking behavior.

Adolescent↗