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PubMed2005

Quantitative trait locus analysis of longitudinal quantitative trait data in complex pedigrees.

There is currently considerable interest in genetic analysis of quantitative traits such as blood pressure and body mass index. Despite the fact that these traits change throughout life they are commonly analyzed only at a single time point. The genetic basis of such traits can be better understood by collecting and effectively analyzing longitudinal data. Analyses of these data are complicated by the need to incorporate information from complex pedigree structures and genetic markers. We propose conducting longitudinal quantitative trait locus (QTL) analyses on such data sets by using a flexible random regression estimation technique. The relationship between genetic effects at different ages is efficiently modeled using covariance functions (CFs). Using simulated data we show that the change in genetic effects over time can be well characterized using CFs and that including parameters to model the change in effect with age can provide substantial increases in power to detect QTL compared with repeated measure or univariate techniques. The asymptotic distributions of the methods used are investigated and methods for overcoming the practical difficulties in fitting CFs are discussed. The CF-based techniques should allow efficient multivariate analyses of many data sets in human and natural population genetics.

Chromosome Mapping↗
PubMed2006

Games researchers play--extreme-groups analysis and mediation analysis in longitudinal occupational health research.

OBJECTIVES: The study of causal processes using a longitudinal design is often hampered by two methodological problems. First, the lagged effects of a predictor variable on an outcome variable tend to be weak after control for a previous measure of this outcome. One approach that is advocated when effects are weak is to increase the extremeness of the study groups; this step often increases the significance and sizes of effects. Second, causal links are often mediated through third variables, and thus relatively complex mediational analyses are needed to understand the causal processes underlying particular associations. The present paper shows whether and when these two approaches are useful in longitudinal research. METHODS: The two approaches were evaluated using data from a three-wave study among 1251 newcomers from various Western countries (mean age 20.6 years, 59% female). RESULTS: Although the significances and effect sizes indeed increased with increasing extremeness of the study groups, extreme-groups analysis in the context of a longitudinal design may grossly bias findings. Cross-sectional applications of mediation analysis cannot provide evidence for any mediational model. Longitudinal models are better suited for examining mediation. CONCLUSIONS: Rather than using extreme-groups analysis to obtain significant effects across time, researchers should maximize the amount of change in their data by focusing on groups for which change can be expected. Especially multiphase longitudinal data sets offer good opportunities for analyzing mediation models.

Adult↗
PubMed1993

Some conceptual and statistical issues in analysis of longitudinal psychiatric data. Application to the NIMH treatment of Depression Collaborative Research Program dataset.

Longitudinal studies have a prominent role in psychiatric research; however, statistical methods for analyzing these data are rarely commensurate with the effort involved in their acquisition. Frequently the majority of data are discarded and a simple end-point analysis is performed. In other cases, so called repeated-measures analysis of variance procedures are used with little regard to their restrictive and often unrealistic assumptions and the effect of missing data on the statistical properties of their estimates. We explored the unique features of longitudinal psychiatric data from both statistical and conceptual perspectives. We used a family of statistical models termed random regression models that provide a more realistic approach to analysis of longitudinal psychiatric data. Random regression models provide solutions to commonly observed problems of missing data, serial correlation, time-varying covariates, and irregular measurement occasions, and they accommodate systematic person-specific deviations from the average time trend. Properties of these models were compared with traditional approaches at a conceptual level. The approach was then illustrated in a new analysis of the National Institute of Mental Health Treatment of Depression Collaborative Research Program dataset, which investigated two forms of psychotherapy, pharmacotherapy with clinical management, and a placebo with clinical management control. Results indicated that both person-specific effects and serial correlation play major roles in the longitudinal psychiatric response process. Ignoring either of these effects produces misleading estimates of uncertainty that form the basis of statistical tests of hypotheses.

Analysis of Variance↗
PubMed1995

PC program extending the Potthoff-Roy longitudinal data analysis model to allow missing data: Kleinbaum's method.

Potthoff and Roy (Biometrika, 51 (1964) 313-326) generalized the multivariate analysis of variance model into a form that is especially useful for the study of longitudinal growth curve data. Applications of this method have, however, been limited by the requirement that each case in the sample be measured at the same set of time points, i.e. there can be no missing data. In this paper we describe, illustrate, and make available a user-friendly, interactive PC program implementing Kleinbaum's (J Mult Anal, 3 (1973) 117-124) extension of the Potthoff-Roy model to allow incomplete measurement sequences. These missing data are permitted to arise either randomly or by design as in mixed longitudinal studies.

Analysis of Variance↗
PubMed2004

Analysis of longitudinal metabolomics data.

MOTIVATION: Metabolomics datasets are generally large and complex. Using principal component analysis (PCA), a simplified view of the variation in the data is obtained. The PCA model can be interpreted and the processes underlying the variation in the data can be analysed. In metabolomics, often a priori information is present about the data. Various forms of this information can be used in an unsupervised data analysis with weighted PCA (WPCA). A WPCA model will give a view on the data that is different from the view obtained using PCA, and it will add to the interpretation of the information in a metabolomics dataset. RESULTS: A method is presented to translate spectra of repeated measurements into weights describing the experimental error. These weights are used in the data analysis with WPCA. The WPCA model will give a view on the data where the non-uniform experimental error is accounted for. Therefore, the WPCA model will focus more on the natural variation in the data. AVAILABILITY: M-files for MATLAB for the algorithm used in this research are available at http://www-its.chem.uva.nl/research/pac/Software/pcaw.zip.

Algorithms↗
PubMed2004

Back and neck pain exhibit many common features in old age: a population-based study of 4,486 Danish twins 70-102 years of age.

STUDY DESIGN: Cross-sectional and longitudinal analysis of data comprising 4486 Danish twins 70-102 years of age. OBJECTIVES: To describe the 1-month prevalence of back pain, neck pain, and concurrent back and neck pain and the development of these over time, associations with other health problems, education, smoking, and physical, and mental functioning. SUMMARY OF BACKGROUND DATA: Back pain and neck pain are prevalent symptoms in the population; however, there is little research addressing these conditions in older age groups. METHODS: Extensive interview data on health, lifestyle, social, and educational factors were collected in a nationwide cohort-sequential study of 70+-year-old Danish twins. Data for back pain, neck pain, lifetime prevalence of a comprehensive list of diseases, education, and self-rated health were based on self-report. Physical and mental functioning were measured using validated performance tests. Data including associated factors were analyzed in a cross-sectional analysis for answers given at entry into the study, and longitudinal analysis was performed for participants in all four surveys. RESULTS: The overall 1-month prevalence for back pain only was 15%, for neck pain only 11%, and for concurrent back and neck pain 11%. The prevalence varied negligibly over time and between the age groups, and 63% of participants in all surveys had no episodes or only one episode of back or neck pain. Back pain and neck pain were associated with a number of other diseases and with poorer self-rated health. Back and neck pain sufferers had significantly lower scores on physical but not cognitive functioning. CONCLUSIONS: Back pain and neck pain are common, intermittent symptoms in old age. Back pain and neck pain are associated with general poor physical health in old age.

Aged↗
PubMed2003

Semiparametric regression analysis of longitudinal data with informative drop-outs.

Informative drop-out arises in longitudinal studies when the subject's follow-up time depends on the unobserved values of the response variable. We specify a semiparametric linear regression model for the repeatedly measured response variable and an accelerated failure time model for the time to informative drop-out. The error terms from the two models are assumed to have a common, but completely arbitrary joint distribution. Using a rank-based estimator for the accelerated failure time model and an artificial censoring device, we construct an asymptotically unbiased estimating function for the linear regression model. The resultant estimator is shown to be consistent and asymptotically normal. A resampling scheme is developed to estimate the limiting covariance matrix. Extensive simulation studies demonstrate that the proposed methods are suitable for practical use. Illustrations with data taken from two AIDS clinical trials are provided.

Child↗
PubMed1990

Simultaneous genetic analysis of longitudinal means and covariance structure using the simplex model: application to repeatedly measured weight in a sample of 164 female twins.

The simultaneous analysis of means and covariance structures is applied to longitudinal twin data. Body weight was measured on six occasions in a sample of young female MZ and DZ twins. When average body weight at the first measurement occasion, as well as the increments in weight at later occasions, are specified in the genetic part of the model that also adequately explains the covariance structure, a good fit is obtained. In this application the increase in body weight at each occasion is weighted by the square root of the genetic variance innovation terms that represent the new genetic variance entering into the process.

Analysis of Variance↗
PubMed2003

Longitudinal genetic analysis of childhood IQ in 6- and 7-year-old Russian twins.

Using a longitudinal twin study of Moscow children, we have studied the development of psychometric intelligence during the transition from preschool (age 6) to school (age 7). Children were tested using the Wechsler Intelligence Scale for Children (WISC). Simplex models were applied to explore the relationship of different sources of phenotypic variance. The following sources of variation were considered: genetic effects, common or shared family environment and unique environment. At age 6, genetic influences were much greater than those of shared environment but the magnitude of genetic influences decreased and the magnitude of shared environment influences increased substantially by age 7.

Child↗
PubMed1989

Statistical methods for the analysis of longitudinal data from school-based smoking prevention studies.

The features which make longitudinal data obtained from school-based smoking prevention studies well-suited for efficient analysis by survival analysis methods are discussed. Survival analysis methods, in particular relative risk regression models, are described and illustrated through an example involving data from the Waterloo Smoking Prevention Project--Study 1. Indications of some of the possible applications for these techniques in the evaluation of interventions to prevent smoking and the study of the smoking onset process are provided.

Adolescent↗
PubMed2005

Directly parameterized regression conditioning on being alive: analysis of longitudinal data truncated by deaths.

For observational longitudinal studies of geriatric populations, outcomes such as disability or cognitive functioning are often censored by death. Statistical analysis of such data may explicitly condition on either vital status or survival time when summarizing the longitudinal response. For example a pattern-mixture model characterizes the mean response at time t conditional on death at time S = s (for s > t), and thus uses future status as a predictor for the time t response. As an alternative, we define regression conditioning on being alive as a regression model that conditions on survival status, rather than a specific survival time. Such models may be referred to as partly conditional since the mean at time t is specified conditional on being alive (S > t), rather than using finer stratification (S = s for s > t). We show that naive use of standard likelihood-based longitudinal methods and generalized estimating equations with non-independence weights may lead to biased estimation of the partly conditional mean model. We develop a taxonomy for accommodation of both dropout and death, and describe estimation for binary longitudinal data that applies selection weights to estimating equations with independence working correlation. Simulation studies and an analysis of monthly disability status illustrate potential bias in regression methods that do not explicitly condition on survival.

Activities of Daily Living↗
PubMed1999

Longitudinal phenotypic analysis of human immunodeficiency virus type 1-specific cytotoxic T lymphocytes: correlation with disease progression.

Few studies have examined longitudinal changes in human immunodeficiency virus type 1 (HIV)-specific cytotoxic T lymphocytes (CTL). To more closely define the natural history of HIV-specific CTL, we used HLA-peptide tetrameric complexes to study the longitudinal CD8(+) T-cell response evolution in 16 A*0201-positive untreated individuals followed clinically for up to 14 years. As early as 1 to 2 years after seroconversion, we found a significant association between high frequencies of A*0201-restricted p17(Gag/Pol) tetramer-binding cells and slower disease progression (P < 0.01). We observed that responses could remain stable over many months, but any longitudinal changes that occurred were typically accompanied by reciprocal changes in RNA viral load. Phenotypic analysis with markers CD45RO, CD45RA, and CD27 identified distinct subsets of antigen-specific cells and the preferential loss of CD27(+) CD45RO(+) cells during periods of rapid decline in the frequency of tetramer-binding cells. In addition we were unable to confirm previous studies showing a consistent selective loss of HIV-specific cells in the context of sustained Epstein-Barr virus-specific cell frequencies. Overall, these data support a role of HIV-specific CTL in the control of disease progression and suggest that the ultimate loss of such CTL may be preferentially from the CD27(+) CD45RO(+) subset.

Disease Progression↗
PubMed2003

Quantitative trait linkage analysis of longitudinal change in body weight.

One of the great strengths of the Framingham Heart Study data, provided for the Genetic Analysis Workshop 13, is the long-term survey of phenotypic data. We used this unique data to create new phenotypes representing the pattern of longitudinal change of the provided phenotypes, especially systolic blood pressure and body weight. We performed a linear regression of body weight and systolic blood pressure on age and took the slopes as new phenotypes for quantitative trait linkage analysis using the SOLAR package. There was no evidence for heritability of systolic blood pressure change. Heritability was estimated as 0.15 for adult life "body weight change", measured as the regression slope, and "body weight gain" (including only individuals with a positive regression slope), and as 0.22 for body weight "change up to 50" (regression slope of weight on age up to an age of 50). With multipoint analysis, two regions on the long arm of chromosome 8 showed the highest LOD scores of 1.6 at 152 cM for "body weight change" and of >1.9 around location 102 cM for "body weight gain" and "change up to 50". The latter two LOD scores almost reach the threshold for suggestive linkage. We conclude that the chromosome 8 region may harbor a gene acting on long-term body weight regulation, thereby contributing to the development of the metabolic syndrome.

Adult↗
PubMed2006

Shared parameter models for the joint analysis of longitudinal data and event times.

Longitudinal studies often gather joint information on time to some event (survival analysis, time to dropout) and serial outcome measures (repeated measures, growth curves). Depending on the purpose of the study, one may wish to estimate and compare serial trends over time while accounting for possibly non-ignorable dropout or one may wish to investigate any associations that may exist between the event time of interest and various longitudinal trends. In this paper, we consider a class of random-effects models known as shared parameter models that are particularly useful for jointly analysing such data; namely repeated measurements and event time data. Specific attention will be given to the longitudinal setting where the primary goal is to estimate and compare serial trends over time while adjusting for possible informative censoring due to patient dropout. Parametric and semi-parametric survival models for event times together with generalized linear or non-linear mixed-effects models for repeated measurements are proposed for jointly modelling serial outcome measures and event times. Methods of estimation are based on a generalized non-linear mixed-effects model that may be easily implemented using existing software. This approach allows for flexible modelling of both the distribution of event times and of the relationship of the longitudinal response variable to the event time of interest. The model and methods are illustrated using data from a multi-centre study of the effects of diet and blood pressure control on progression of renal disease, the modification of diet in renal disease study.

Blood Pressure↗
PubMed2001

Analysis of longitudinally observed irregularly timed multivariate outcomes: regression with focus on cross-component correlation.

Components of repeatedly observed multivariate outcomes (for example, the two components of blood pressure measures (SBP(it), DBP(it)), obtained on subject i at arbitrarily spaced times t) are often analysed separately. We present a unified approach to regression analysis of such irregularly timed multivariate longitudinal data, with particular attention to assessment of the magnitude and durability of cross-component correlation. Maximum likelihood estimates are presented for component-specific regression parameters and autocorrelation and cross-correlation functions. The component-specific autocorrelation function has the 'damped exponential' form [see text], which generalizes the AR(1), MA(1) and random intercept models for univariate longitudinal outcomes. The cross-component correlation function (CCCF) has an analogous form, allowing damped-exponential decay of cross-component correlation as time between repeated measures elapses. Finite sample performance is assessed through simulation studies. The methods are illustrated through blood pressure modelling and construction of multivariate prediction regions.

Adult↗
PubMed2002

Comparison of alternative strategies for analysis of longitudinal trials with dropouts.

PROBLEM: Patients may withdraw from longitudinal clinical trials for many reasons. Methods for handling the problem presented by missing data of patients who withdraw before reaching the time point of the primary measurement include carrying the last observation forward (LOCF), data as observed analysis (DAO), mixed model approaches, and pattern mixture models. METHOD: We evaluate a multiple imputation (MI) approach that has the flexibility to adjust inferences about the treatment effect for the withdrawn patients relative to currently used alternatives. Sensitivity analyses are performed under a collection of scenarios that include many circumstances that may arise in practice, including different assumptions about treatment effects post-withdrawal and about the missing data mechanism. Simulations are used to compare the results of analyses based on the MI approach with those based on the LOCF, DAO, and the mixed model approaches. RESULTS: The LOCF and DAO approaches cannot be recommended as strategies for handling missing responses, at least for these scenarios, because they provide biased estimates of treatment effects and biased tests of the null hypothesis of no treatment effect. Application of the various approaches to the analysis of clinical data from a longitudinal trial confirms the underestimation of the variability when the LOCF approach is used.

Analysis of Variance↗