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PubMed2002

Age trends in the level of serum testosterone and other hormones in middle-aged men: longitudinal results from the Massachusetts male aging study.

We used longitudinal data from the Massachusetts Male Aging Study, a large population-based random-sample cohort of men aged 40-70 yr at baseline, to establish normative age trends for serum level of T and related hormones in middle-aged men and to test whether general health status affected the age trends. Of 1,709 men enrolled in 1987-1989, 1,156 were followed up 7-10 yr afterward. By repeated-measures statistical analysis, we estimated simultaneously the cross-sectional age trend of each hormone between subjects within the baseline data, the cross-sectional trend between subjects within the follow-up data, and the longitudinal trend within subjects between baseline and follow-up. Total T declined cross-sectionally at 0.8%/yr of age within the follow-up data, whereas both free and albumin-bound T declined at about 2%/yr, all significantly more steeply than within the baseline data. Sex hormone-binding globulin increased cross-sectionally at 1.6%/yr in the follow-up data, similarly to baseline. The longitudinal decline within subjects between baseline and follow-up was considerably steeper than the cross-sectional trend within measurement times for total T (1.6%/yr) and bioavailable T (2-3%/yr). Dehydroepiandrosterone, dehydroepiandrosterone sulfate, cortisol, and estrone showed significant longitudinal declines, whereas dihydrotestosterone, pituitary gonadotropins, and PRL rose longitudinally. Apparent good health, defined as absence of chronic illness, prescription medication, obesity, or excessive drinking, added 10-15% to the level of several androgens and attenuated the cross-sectional trends in T and LH but did not otherwise affect longitudinal or cross-sectional trends. The paradoxical finding that longitudinal age trends were steeper than cross-sectional trends suggests that incident poor health may accelerate the age-related decline in androgen levels.

Adult↗

PubMed1994

Sample size estimation using repeated measurements on biomarkers as outcomes.

The objectives of this paper are to (1) examine methods of using longitudinal data in designing comparative trials and calculating sample sizes or power and (2) show the effect of autocorrelation of repeated measures on the assessment of sample sizes. A statistical model with a simple regression structure for the mean trajectory of the longitudinal data and a two-parameter model for the correlations of within-individual observations given by corr(yt,yt+s) = gamma s theta is used. The methods are illustrated by considering a two-group trial and investigating the effect of different values of the correlation parameters, gamma and theta on the sample size. The results show that taking account of the autocorrelation structure of longitudinal data may lead to more efficient designs. Specifically, the stronger the autocorrelation is, the smaller the sample size that is required.

AIDS Vaccines↗

PubMed2006

The effect of state medicaid case-mix payment on nursing home resident acuity.

OBJECTIVE: To examine the relationship between Medicaid case-mix payment and nursing home resident acuity. DATA SOURCES: Longitudinal Minimum Data Set (MDS) resident assessments from 1999 to 2002 and Online Survey Certification and Reporting (OSCAR) data from 1996 to 2002, for all freestanding nursing homes in the 48 contiguous U.S. states. STUDY DESIGN: We used a facility fixed-effects model to examine the effect of introducing state case-mix payment on changes in nursing home case-mix acuity. Facility acuity was measured by aggregating the nursing case-mix index (NCMI) from the MDS using the Resource Utilization Group (Version III) resident classification system, separately for new admits and long-stay residents, and by an OSCAR-derived index combining a range of activity of daily living dependencies and special treatment measures. DATA COLLECTION/EXTRACTION METHODS: We followed facilities over the study period to create a longitudinal data file based on the MDS and OSCAR, respectively, and linked facilities with longitudinal data on state case-mix payment policies for the same period. PRINCIPAL FINDINGS: Across three acuity measures and two data sources, we found that states shifting to case-mix payment increased nursing home acuity levels over the study period. Specifically, we observed a 2.5 percent increase in the average acuity of new admits and a 1.3 to 1.4 percent increase in the acuity of long-stay residents, following the introduction of case-mix payment. CONCLUSIONS: The adoption of case-mix payment increased access to care for higher acuity Medicaid residents.

Diagnosis-Related Groups↗

PubMed2005

Development and testing of multilevel models for longitudinal craniofacial growth prediction.

INTRODUCTION: The aims of this study were to (1) develop longitudinal growth curves that would allow individual variations to be accurately modeled and (2) use these models to predict craniofacial growth changes in children with varying amounts of longitudinal data available. METHODS: Based on a sample of 159 girls (994 cephalograms) and 128 boys (947 cephalograms), multilevel population models were derived. Polynomial models of the population's growth curve were derived for the measurements MPA, Me-X, Me-theta, Me-Y, and Me-R. Angular and horizontal measures (MPA, Me-X, and Me-theta) were described by simpler, second-order models, and vertical measures (Me-Y and Me-R) were described by more complex, fifth-order models. RESULTS: Decreases in MPA during childhood and increases in Me-theta during adolescence could be explained by the relative contributions of the horizontal (Me-X) and vertical (Me-Y) movements of menton. There was greater anterior movement of menton during childhood and greater inferior movement during the adolescent growth spurt. By using varying numbers of longitudinal cephalograms between 6 and 10 years of age, the models were used to predict subjects' craniofacial growth changes from ages 10 to 15. Based on correlations, root mean squared error, and percent accuracy, individual growth predictions for the various measures were found to be highly accurate on an independent subsample drawn from the larger sample and on an independent validation sample. Correlations between predicted and actual values on the sample used to develop the models ranged from 0.81 to 0.95. Accuracy was best for the measurements that changed the most during the prediction period (Me-Y and Me-R), with accuracies between 83% and 90%. More longitudinal data did not increase the predictive accuracy for all measurements. The models that were least accurate (Me-X, MPA, and Me-theta) showed the greatest improvement in prediction accuracy with more longitudinal data. These improvements ranged from 1.6% to 15%. CONCLUSIONS: Longitudinal growth curves based on multilevel procedures can accurately describe population and individual growth curves, and 5-year predictions with this method are highly accurate and externally valid.

Adolescent↗

PubMed2003

Learning to overeat: maternal use of restrictive feeding practices promotes girls' eating in the absence of hunger.

BACKGROUND: Experimental findings causally link restrictive child-feeding practices to overeating in children. However, longitudinal data are needed to determine the extent to which restrictive feeding practices promote overeating. OBJECTIVES: Our objectives were to determine whether restrictive feeding practices foster girls' eating in the absence of hunger (EAH) and whether girls' weight status moderates the effects of restrictive feeding practices. DESIGN: Longitudinal data were used to create a study design featuring 2 maternal restriction factors (low and high), 2 weight-status factors (nonoverweight and overweight), and 3 time factors (ages 5, 7, and 9 y). RESULTS: Mean EAH increased significantly (P < 0.0001) from 5 to 9 y of age. Higher levels of restriction at 5 y of age predicted higher EAH at 7 y of age (P < 0.001) and at 9 y of age (P < 0.01). Girls who were already overweight at 5 y of age and who received higher levels of restriction had the highest EAH scores at 9 y of age (P < 0.05) and the greatest increases in EAH from 5 to 9 y of age (P < 0.01). CONCLUSIONS: The developmental increase in EAH from 5 to 9 y of age may be especially problematic in obesigenic environments. These longitudinal data provide evidence that maternal restriction can promote overeating. Girls who are already overweight at 5 y of age may be genetically predisposed to be especially responsive to environmental cues. These findings are not expected to be generalized to boys or to other racial and ethnic groups.

Adult↗

PubMed2000

Development of seasonal allergic rhinitis during the first 7 years of life.

BACKGROUND: Against the background of the controversial discussion about an increase in allergic rhinitis in recent years, intraindividual longitudinal data is lacking for IgE-mediated seasonal allergic rhinitis (SAR). Little is known about the development of SAR in terms of prevalence and incidence rates from birth to school age. OBJECTIVE: In a prospective birth cohort, we investigated the development of sensitization and symptoms of SAR. SAR should be defined with high specificity, and associated risk factors should be determined. METHODS: Annual longitudinal data about seasonal allergic symptoms and sensitization was available for 587 children from birth to their seventh birthday. The definition of SAR was based on a combination of exposure-related symptoms and sensitization. RESULTS: Up to 7 years of age, SAR developed in 15% of the children. Incidence and prevalence of symptoms and sensitization were low during early childhood (<2%) and increased steadily with age. Children in which SAR had already developed in the second year all were born in spring or early summer, resulting in at least two seasons of pollen exposure before manifestation of SAR. Risk factors assessed by multiple logistic regression analysis were male sex (odds ratio [OR] = 2.4), atopic mothers (OR = 2.6) and fathers (OR = 3.6) having allergic rhinitis themselves, first-born child (OR = 2.0), early sensitization to food (OR = 3.3), and atopic dermatitis (OR = 2.5), whereas early wheezing was not associated with SAR. CONCLUSION: The development of SAR is characterized by a marked increase in prevalence and incidence after the second year of life. Our longitudinal data further indicate that in combination with the risk of allergic predisposition, at least 2 seasons of pollen allergen exposure are needed before allergic rhinitis becomes clinically manifest.

Age Factors↗

PubMed1996

Intention-to-treat analyses for incomplete repeated measures data.

In a randomized longitudinal clinical trial designed to evaluate two or more rival treatments, an intent-to-treat analysis requires inclusion of all randomized patients, regardless of whether they remain on protocol for the duration of the study. We propose a piecewise linear random effects model for analyzing longitudinal data where the multivariate outcome can depend upon time spent on treatment. The model assumes that data are available on a random sample of subjects after treatment is terminated, and allows either a pragmatic or explanatory analysis (as defined by Schwartz and Lellouch, 1967, Journal of Chronic Diseases 20, 637-648). Full maximum likelihood estimation of the model parameters is carried out using widely available statistical software for repeated measures with missing data and for nonparametric survival curve estimation. Data from a national, multicenter pediatric AIDS clinical trial are analyzed to illustrate implementation and interpretation of the model.

Acquired Immunodeficiency Syndrome↗

PubMed2003

Genome-wide linkage analysis of systolic blood pressure: a comparison of two approaches to phenotype definition.

Problem 1 of the Genetic Analysis Workshop 13(GAW13) contains longitudinal data of cardiovascular measurements from 330 pedigrees. The longitudinal data complicates the phenotype definition because multiple measurements are taken on each individual. To address this complication, we propose an approach that uses generalized estimating equations to obtain residuals for each time point for each person. The mean residual is then taken as the new phenotype with which to use in a variance components linkage analysis. We compare our phenotype definition approach to an approach that first reduces the multiple measurements to a single measurement and then models these summary statistics as regression terms in a variance components analysis. For each approach, multipoint linkage analysis was performed using the residuals and the SOLAR computer program. Our results show little difference between the methods based on the LOD scores.

Adult Children↗

PubMed1991

Rao's polynomial growth curve model for unequal-time intervals: a menu-driven GAUSS program.

For lack of alternatives, longitudinal data are often analyzed with cross-sectional statistical methods, for instance, t-tests, ANOVA and ordinary least-squares regression. Appropriate statistical software has been generally unavailable to investigators using serial records to study growth and development or treatment effects. In an earlier paper (Schneiderman and Kowalski, Am. J. Phys. Anthropol., 67 (1985) 323-333.) we described a suitable method, Rao's polynomial growth curve model (Rao, Biometrika, 46 (1959) 49-58), and provided an SAS computer program for the analysis of a single sample of complete longitudinal data. This method included the computation of an average polynomial growth curve, its 95% confidence band, its coefficients and corresponding confidence intervals. The present paper extends this method to accommodate a sample with observations made at unequal time-intervals. Significant improvements in the accessibility, operation and user-friendliness of the program have been made, facilitated by recent advances in microcomputer technology. This stand-alone GAUSS program (no compiler necessary) runs on PC-compatibles and is available at a nominal cost. In this report we provide an overview of the statistical model, the general structure of the program, and give an example in which a developmental variable (human upper incisor angulation) is analyzed. Ease of installation and use, speed of execution and color graphic displays of growth curves and confidence bands, and most importantly, suitability to longitudinal data, make this method/program a potentially valuable tool for those interested in growth, development, and treatment effects in humans and other species. Some areas in which this method will have immediate applications are orthodontics, maxillofacial surgery and pediatrics.

Adolescent↗

PubMed2005

Regression analysis of longitudinal binary data with time-dependent environmental covariates: bias and efficiency.

Generalized estimating equations (Liang and Zeger, 1986) is a widely used, moment-based procedure to estimate marginal regression parameters. However, a subtle and often overlooked point is that valid inference requires the mean for the response at time t to be expressed properly as a function of the complete past, present, and future values of any time-varying covariate. For example, with environmental exposures it may be necessary to express the response as a function of multiple lagged values of the covariate series. Despite the fact that multiple lagged covariates may be predictive of outcomes, researchers often focus interest on parameters in a 'cross-sectional' model, where the response is expressed as a function of a single lag in the covariate series. Cross-sectional models yield parameters with simple interpretations and avoid issues of collinearity associated with multiple lagged values of a covariate. Pepe and Anderson (1994), showed that parameter estimates for time-varying covariates may be biased unless the mean, given all past, present, and future covariate values, is equal to the cross-sectional mean or unless independence estimating equations are used. Although working independence avoids potential bias, many authors have shown that a poor choice for the response correlation model can lead to highly inefficient parameter estimates. The purpose of this paper is to study the bias-efficiency trade-off associated with working correlation choices for application with binary response data. We investigate data characteristics or design features (e.g. cluster size, overall response association, functional form of the response association, covariate distribution, and others) that influence the small and large sample characteristics of parameter estimates obtained from several different weighting schemes or equivalently 'working' covariance models. We find that the impact of covariance model choice depends highly on the specific structure of the data features, and that key aspects should be examined before choosing a weighting scheme.

Air Pollutants↗

PubMed2004

Evaluation of visual impairment in Usher syndrome 1b and Usher syndrome 2a.

PURPOSE: To evaluate visual impairment in Usher syndrome 1b (USH1b) and Usher syndrome 2a (USH2a). METHODS: We carried out a retrospective study of 19 USH1b patients and 40 USH2a patients. Cross-sectional regression analyses of the functional acuity score (FAS), functional field score (FFS) and functional vision score (FVS) related to age were performed. Statistical tests relating to regression lines and Student's t-test were used to compare between (sub)groups of patients. Parts of the available individual longitudinal data were used to obtain individual estimates of progressive deterioration and compare these to those obtained with cross-sectional analysis. Results were compared between subgroups of USH2a patients pertaining to combinations of different types of mutations. RESULTS: Cross-sectional analyses revealed significant deterioration of the FAS (0.7% per year), FFS (1.0% per year) and FVS (1.5% per year) with advancing age in both patient groups, without a significant difference between the USH1b and USH2a patients. Individual estimates of the deterioration rates were substantially and significantly higher than the cross-sectional estimates in some USH2a cases, including values of about 5% per year (or even higher) for the FAS (age 35-50 years), 3-4% per year for the FFS and 4-5% per year for the FVS (age > 20 years). There was no difference in functional vision score behaviour detected between subgroups of patients pertaining to different biallelic combinations of specific types of mutations. CONCLUSIONS: The FAS, FFS and FVS deteriorated significantly by 0.7-1.5% per year according to cross-sectional linear regression analysis in both USH1b and USH2a patients. Higher deterioration rates (3-5% per year) in any of these scores were attained, according to longitudinal data collected from individual USH2a patients. Score behaviour was similar across the patient groups and across different biallelic combinations of various types of mutations. However, more elaborate studies, preferably covering longitudinal data, are needed to obtain conclusive evidence.

Adolescent↗

PubMed2006

Neural networks for longitudinal studies in Alzheimer's disease.

OBJECTIVE: Alzheimer's disease affects a growing population of elderly people today. The predictions about the course of the disease is a key component of health care decision making for patients with Alzheimer's. The physician's prognosis and predicted trajectory of cognitive decline often form the basis of treatment and health care decisions taken by patients and their families. These predictions are difficult to make because of the high variability and non-linearity exhibited by individual patterns of cognitive decline. This paper presents a new method of predicting the course of a disease using longitudinal data collected through multiple clinic visits. Longitudinal databases are similar to temporal databases, with some important differences--data is collected at irregular time intervals that are patient specific and also a varying number of observations are made for each patient, depending upon the number of times the patient visited the clinic. We propose a new type of neural network called the mixed effects neural network (MENN) model that can incorporate this type of longitudinal information. MATERIAL AND METHODS: We have used longitudinal data on 704 subjects enrolled at the Layton aging and research center (LAARC) at Oregon Health and Science University. A back-propagation algorithm, modified for longitudinal data is used to obtain the weight parameters of the MENN. The modified back-propagation algorithm is further embedded in an iterative procedure that estimates the noise variance and the parameters that capture the longitudinal (temporal) correlation structure. RESULTS: We have compared the performance of the MENN with linear mixed effects models and standard neural networks (NN). MENN show better performance (misclassification rate = 0.13 and relative MSE = 0.35) as compared to standard NN (misclassification rate = 0.34 and relative MSE = 2.74) and linear mixed effects models (misclassification rate = 0.14 and relative MSE = 0.4). CONCLUSION: The results show that this method can be a useful tool for predicting non-linear disease trajectories and uncovering significant prognostic factors in longitudinal databases.

Aged↗

PubMed2003

A local influence approach applied to binary data from a psychiatric study.

Recently, a lot of concern has been raised about assumptions needed in order to fit statistical models to incomplete multivariate and longitudinal data. In response, research efforts are being devoted to the development of tools that assess the sensitivity of such models to often strong but always, at least in part, unverifiable assumptions. Many efforts have been devoted to longitudinal data, primarily in the selection model context, although some researchers have expressed interest in the pattern-mixture setting as well. A promising tool, proposed by Verbeke et al. (2001, Biometrics 57, 43-50), is based on local influence (Cook, 1986, Journal of the Royal Statistical Society, Series B 48, 133-169). These authors considered the Diggle and Kenward (1994, Applied Statistics 43, 49-93) model, which is based on a selection model, integrating a linear mixed model for continuous outcomes with logistic regression for dropout. In this article, we show that a similar idea can be developed for multivariate and longitudinal binary data, subject to nonmonotone missingness. We focus on the model proposed by Baker, Rosenberger, and DerSimonian (1992, Statistics in Medicine 11, 643-657). The original model is first extended to allow for (possibly continuous) covariates, whereafter a local influence strategy is developed to support the model-building process. The model is able to deal with nonmonotone missingness but has some limitations as well, stemming from the conditional nature of the model parameters. Some analytical insight is provided into the behavior of the local influence graphs.

Antidepressive Agents, Tricyclic↗

PubMed2002

Multivariate cubic spline smoothing in multiple prediction.

Given longitudinal data for several variables, including a given outcome variable, it is desired to predict the outcome for a specific individual, or more generally experimental unit, in such a way that the predicted value is both accurate and resistant (i.e. has good cross-validation). There are certain data-analytic difficulties associated with long-term multivariate longitudinal data that must be overcome in the prediction process. This paper provides a program written in the Statistical Analysis System (SAS) programming language, based generally on the Roche-Wainer-Thissen stature prediction model, that enables the researcher to overcome these difficulties.

Computer Simulation↗

PubMed1999

Body composition of healthy 7-and 8-year-old children and a comparison with the 'reference child'.

BACKGROUND: There are few longitudinal data on body composition in healthy children. This has prompted a reliance on notional standards such as the 'reference child', to validate new methods of determining body composition and comparing cross-sectional height, weight and fatness data. OBJECTIVES: These were twofold-to provide normative longitudinal data on changes in body composition in healthy pre-pubertal children, and to compare measures of growth and body composition with the appropriate age-specific reference child. DESIGN: A sample of healthy Scottish children aged 7-8y (n = 257) was recruited during 1991/1992. Data on height, weight, skinfold thickness and resistance from bioelectrical impedance analysis were collected twice, 12 months apart. Percentage body fat was estimated from both skinfolds and bioelectrical impedance. RESULTS: Fat and fat-free mass, but not body mass index, differed between boys and girls. All measurements increased significantly over the 12 month period except percentage body fat from skinfolds in boys. The reference child comparison revealed that our sample was taller, heavier and fatter and gained weight and fat mass at a greater rate than the Fomon standards. CONCLUSIONS: Data from the children in this study suggest that the reference child has a body composition which is now out of date. This may have important implications for body composition methodology. New references for height and weight may be required, but an upgrading of the body fat reference may conflict with public health aims to reduce obesity.

Body Composition↗

PubMedDate not supplied

[Longitudinal studies: concepts and particularities].

In this review the definition of "longitudinal study" is analysed. Most current textbooks on epidemiology do not define a longitudinal study, whereas statistical textbooks do. It is more common to talk about longitudinal data than about longitudinal studies. A longitudinal study implies the existence of repeated measurements (more than two) across follow-up. According to these ideas, a longitudinal study can be considered a subtype of cohort study that, in contrast with life-table cohort studies, allows inference to the subject level, to analyze changes in variables (exposures and outcomes) and transitions among different health states. The characteristics of this design force to paid special attention to quality control during data collection, losses during follow-up, and missing data in some measurements. The statistical analysis should take repeated measures into account, and it is what finally gives the longitudinal character to a study with repeated measurements.

Biomedical Research↗

PubMed2003

Genetic analyses of longitudinal phenotype data: a comparison of univariate methods and a multivariate approach.

BACKGROUND: We explored three approaches to heritability and linkage analyses of longitudinal total cholesterol levels (CHOL) in the Genetic Analysis Workshop 13 simulated data without knowing the answers. The first two were univariate approaches and used 1) baseline measure at exam one or 2) summary measures such as mean and slope from multiple exams. The third method was a multivariate approach that directly models multiple measurements on a subject. A variance components model (SOLAR) was employed in the univariate approaches. A mixed regression model with polynomials was employed in the multivariate approach and implemented in SAS/IML. RESULTS: Using the baseline measure at exam 1, we detected all baseline or slope genes contributing a substantial amount (0.08) of variance (LOD > 3). Compared to the baseline measure, the mean measures yielded slightly higher LOD at the slope genes, and a lower LOD at the baseline genes. The slope measure produced a somewhat lower LOD for the slope gene than did the mean measure. Descriptive information on the pattern of changes in gene effects with age was estimated for three linked loci by the third approach. CONCLUSION: We found simple univariate methods may be effective to detect genes affecting longitudinal phenotypes but may not fully reveal temporal trends in gene effects. The relative efficiency of the univariate methods to detect genes depends heavily on the underlying model. Compared with the univariate approaches, the multivariate approach provided more information on temporal trends in gene effects at the cost of more complicated modelling and more intense computations.

Adult↗

PubMed1993

A test of the missing data mechanism for repeated categorical data.

Due to the occurrence of missing observations, longitudinal data are rarely balanced and complete. Weighted least squares analyses described by Grizzle, Starmer, and Koch (1969, Biometrics 25, 489-504) have been developed for the analysis of incomplete longitudinal categorical data [Stanish, Gillings, and Koch (1978, Biometrics 34, 305-317); Woolson and Clarke (1984, Journal of the Royal Statistical Society, Series A 147, 87-99)]. However, all these analyses have assumed that missing observations are missing completely at random in the sense of Rubin (1976, Biometrika 63, 581-592). When the occurrence of missing observations is related to the unobserved response values, these analyses may result in biased results. In this paper, we develop a simple and practical test of the missing mechanism in incomplete repeated categorical data. The proposed test is an extension of the test of Little (1988, Journal of the American Statistical Association 83, 1198-1202) and uses a test criterion given in general form by Wald. The test is illustrated using data from a longitudinal investigation of obesity in school-age children.

Adolescent↗