Selection of working correlation structure and best model in GEE analyses of longitudinal data

The Generalized Estimating Equations (GEE) method is one of the most commonly used statistical methods for the analysis of longitudinal data in epidemiological studies. A working correlation structure for the repeated measures of the outcome variable of a subject needs to be specified by this method. However, statistical criteria for selecting the best correlation structure and the best subset of explanatory variables in GEE are only available recently because the GEE method is developed on the basis of quasi-likelihood theory. Maximum likelihood based model selection methods, such as the widely used Akaike Information Criterion (AIC), are not applicable to GEE directly. Pan (2001) proposed a selection method called QIC which can be used to select the best correlation structure and the best subset of explanatory variables. Based on the QIC method, we developed a computing program to calculate the QIC value for a range of different distributions, link functions and correlation structures. This program was written in Stata software. In this article, we introduce this program and demonstrate how to use it to select the most parsimonious model in GEE analyses of longitudinal data through several representative examples.

Leptin in depressed women : Cross-sectional and longitudinal data from an epidemiologic study

Background There is conflicting evidence regarding levels of leptin in depression. In this study we aimed to investigate the relationship between serum leptin level and depression in a community sample of women using both cross-sectional and longitudinal data.

Methods From among 510 women aged 20–78 yr, 83 were identified with a lifetime history of major depressive disorder or dysthymia, ascertained using the Structured Clinical Interview for DSM-IV-TR Research Version, Non-patient edition (SCID-I/NP). Serum leptin levels were measured by radioimmunoassay. Medication use and lifestyle were self-reported and body mass index (BMI) determined from measures of height and weight.

Results Using multiple linear regression, serum leptin levels were greater among women with a lifetime history of depression compared to women without any history of depression, independent of BMI. Adjusted geometric mean values of serum leptin were 16.37 (95%CI 14.70–18.23) ng/mL for depressed and 14.46 (95%CI 13.79–15.16) ng/mL for non-depressed women (P = 0.039). The hazard ratio (HR) for a de novo depressive disorder over five years increased 2.56-fold for each standard deviation increase in log-transformed serum leptin among non-smokers and this was not explained by differences in BMI, medications or other lifestyle factors (HR = 2.56, 95%CI 1.52-4.30). No association was observed for smokers.

Limitations There is potential for unrecognised confounding, recall bias and transient changes in body composition.

Conclusion Women with a lifetime history of depression have elevated levels of serum leptin, and elevated serum leptin predicts subsequent development of a depressive disorder.

Modeling gene-environment interaction in longitudinal data : risk for neuroticism due to interaction between maternal care and the Dopamine 4 Receptor gene (DRD4)

The purpose of this study was to investigate risk for neuroticism due to the joint action of low maternal care and compromised mesocorticolimbic ‘reward’ system function linked to a variable number tandem repeat (VNTR) in the dopamine 4 receptor gene (DRD4). Data were drawn from the Victorian Adolescent Health Cohort Study, a longitudinal study of the health and well-being of 2,000 young Australians followed from adolescence to young adulthood across 8 waves from 14- to 28-years. Genetic risk was defined by carriage of at least one copy of the 7-repeat allele or derivative alleles 5, 6, and 8 (labeled 7R+). Neuroticism was assessed in adolescence and young adulthood. We observed an approximately fourfold increase in the odds of reporting neurotic symptoms in carriers of the 7R+ disposition who reported low maternal care compared with non-carriers who reported high maternal care. The percentage of risk attributable to mechanisms in which both factors played a role was 35%. Findings are discussed in terms of implications for prevention.

Regulation and wage adjustment patterns : non parametric evidence from longitudinal data

This paper gives a first step toward a methodology to quantify the influences of regulation on short-run earnings dynamics. It also provides evidence on the patterns of wage adjustment adopted during the recent high inflationary experience in Brazil.The large variety of official wage indexation rules adopted in Brazil during the recent years combined with the availability of monthly surveys on labor markets makes the Brazilian case a good laboratory to test how regulation affects earnings dynamics. In particular, the combination of large sample sizes with the possibility of following the same worker through short periods of time allows to estimate the cross-sectional distribution of longitudinal statistics based on observed earnings (e.g., monthly and annual rates of change).The empirical strategy adopted here is to compare the distributions of longitudinal statistics extracted from actual earnings data with simulations generated from minimum adjustment requirements imposed by the Brazilian Wage Law. The analysis provides statistics on how binding were wage regulation schemes. The visual analysis of the distribution of wage adjustments proves useful to highlight stylized facts that may guide future empirical work.

Analysis of beef cattle longitudinal data applying a nonlinear model

The objective of this work was to evaluate the Nelore beef cattle, growth curve parameters using the Von Bertalanffy function in a nested Bayesian procedure that allowed estimation of the joint posterior distribution of growth curve parameters, their (co)variance components, and the environmental and additive genetic components affecting them. A hierarchical model was applied; each individual had a growth trajectory described by the nonlinear function, and each parameter of this function was considered to be affected by genetic and environmental effects that were described by an animal model. Random samples of the posterior distributions were drawn using Gibbs sampling and Metropolis-Hastings algorithms. The data set consisted of a total of 145,961 BW recorded from 15,386 animals. Even though the curve parameters were estimated for animals with few records, given that the information from related animals and the structure of systematic effects were considered in the curve fitting, all mature BW predicted were suitable. A large additive genetic variance for mature BW was observed. The parameter a of growth curves, which represents asymptotic adult BW, could be used as a selection criterion to control increases in adult BW when selecting for growth rate. The effect of maternal environment on growth was carried through to maturity and should be considered when evaluating adult BW. Other growth curve parameters showed small additive genetic and maternal effects. Mature BW and parameter k, related to the slope of the curve, presented a large, positive genetic correlation. The results indicated that selection for growth rate would increase adult BW without substantially changing the shape of the growth curve. Selection to change the slope of the growth curve without modifying adult BW would be inefficient because their genetic correlation is large. However, adult BW could be considered in a selection index with its corresponding economic weight to improve the overall efficiency of beef cattle production.

Bayesian longitudinal data analysis with mixed models and thick-tailed distributions using MCMC

Linear mixed effects models are frequently used to analyse longitudinal data, due to their flexibility in modelling the covariance structure between and within observations. Further, it is easy to deal with unbalanced data, either with respect to the number of observations per subject or per time period, and with varying time intervals between observations. In most applications of mixed models to biological sciences, a normal distribution is assumed both for the random effects and for the residuals. This, however, makes inferences vulnerable to the presence of outliers. Here, linear mixed models employing thick-tailed distributions for robust inferences in longitudinal data analysis are described. Specific distributions discussed include the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted, and the Gibbs sampler and the Metropolis-Hastings algorithms are used to carry out the posterior analyses. An example with data on orthodontic distance growth in children is discussed to illustrate the methodology. Analyses based on either the Student-t distribution or on the usual Gaussian assumption are contrasted. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process for modelling distributions of the random effects and of residuals in linear mixed models, and the MCMC implementation allows the computations to be performed in a flexible manner.

Wage differentials between the public and private sectors in Chile: Evidence from longitudinal data

Includes bibliography.

Competing regression models for longitudinal data

The choice of an appropriate family of linear models for the analysis of longitudinal data is often a matter of concern for practitioners. To attenuate such difficulties, we discuss some issues that emerge when analyzing this type of data via a practical example involving pretestposttest longitudinal data. In particular, we consider log-normal linear mixed models (LNLMM), generalized linear mixed models (GLMM), and models based on generalized estimating equations (GEE). We show how some special features of the data, like a nonconstant coefficient of variation, may be handled in the three approaches and evaluate their performance with respect to the magnitude of standard errors of interpretable and comparable parameters. We also show how different diagnostic tools may be employed to identify outliers and comment on available software. We conclude by noting that the results are similar, but that GEE-based models may be preferable when the goal is to compare the marginal expected responses.

Longitudinal data on telomere length in leukocytes from newborn baboons support a marked drop in stem cell turnover around 1 year of age

Stem cells of various tissues are typically defined as multipotent cells with 'self-renewal' properties. Despite the increasing interest in stem cells, surprisingly little is known about the number of times stem cells can or do divide over a lifetime. Based on telomere-length measurements of hematopoietic cells, we previously proposed that the self-renewal capacity of hematopoietic stem cells is limited by progressive telomere attrition and that such cells divide very rapidly during the first year of life. Recent studies of patients with aplastic anemia resulting from inherited mutations in telomerase genes support the notion that the replicative potential of hematopoietic stem cells is directly related to telomere length, which is indirectly related to telomerase levels. To revisit conclusions about stem cell turnover based on cross-sectional studies of telomere length, we performed a longitudinal study of telomere length in leukocytes from newborn baboons. All four individual animals studied showed a rapid decline in telomere length (approximately 2-3 kb) in granulocytes and lymphocytes in the first year after birth. After 50-70 weeks the telomere length appeared to stabilize in all cell types. These observations suggest that hematopoietic stem cells, after an initial phase of rapid expansion, switch at around 1 year of age to a different functional mode characterized by a markedly decreased turnover rate.