Effects of variance-function misspecification in analysis of longitudinal data

The approach of generalized estimating equations (GEE) is based on the framework of generalized linear models but allows for specification of a working matrix for modeling within-subject correlations. The variance is often assumed to be a known function of the mean. This article investigates the impacts of misspecifying the variance function on estimators of the mean parameters for quantitative responses. Our numerical studies indicate that (1) correct specification of the variance function can improve the estimation efficiency even if the correlation structure is misspecified; (2) misspecification of the variance function impacts much more on estimators for within-cluster covariates than for cluster-level covariates; and (3) if the variance function is misspecified, correct choice of the correlation structure may not necessarily improve estimation efficiency. We illustrate impacts of different variance functions using a real data set from cow growth.

Criteria for working-correlation-structure selection in GEE: Assessment via simulation

Efficiency of analysis using generalized estimation equations is enhanced when intracluster correlation structure is accurately modeled. We compare two existing criteria (a quasi-likelihood information criterion, and the Rotnitzky-Jewell criterion) to identify the true correlation structure via simulations with Gaussian or binomial response, covariates varying at cluster or observation level, and exchangeable or AR(l) intracluster correlation structure. Rotnitzky and Jewell's approach performs better when the true intracluster correlation structure is exchangeable, while the quasi-likelihood criteria performs better for an AR(l) structure.

Induced smoothing for rank regression with censored survival times

Adaptions of weighted rank regression to the accelerated failure time model for censored survival data have been successful in yielding asymptotically normal estimates and flexible weighting schemes to increase statistical efficiencies. However, for only one simple weighting scheme, Gehan or Wilcoxon weights, are estimating equations guaranteed to be monotone in parameter components, and even in this case are step functions, requiring the equivalent of linear programming for computation. The lack of smoothness makes standard error or covariance matrix estimation even more difficult. An induced smoothing technique overcame these difficulties in various problems involving monotone but pure jump estimating equations, including conventional rank regression. The present paper applies induced smoothing to the Gehan-Wilcoxon weighted rank regression for the accelerated failure time model, for the more difficult case of survival time data subject to censoring, where the inapplicability of permutation arguments necessitates a new method of estimating null variance of estimating functions. Smooth monotone parameter estimation and rapid, reliable standard error or covariance matrix estimation is obtained.

A quasi-likelihood approach for ordered categorical data with overdispersion

Quasi-likelihood (QL) methods are often used to account for overdispersion in categorical data. This paper proposes a new way of constructing a QL function that stems from the conditional mean-variance relationship. Unlike traditional QL approaches to categorical data, this QL function is, in general, not a scaled version of the ordinary log-likelihood function. A simulation study is carried out to examine the performance of the proposed QL method. Fish mortality data from quantal response experiments are used for illustration.

Long-term ambient air pollution exposure and self-reported morbidity in the Australian Longitudinal Study on Women's Health: A cross-sectional study

- Objective We sought to assess the effect of long-term exposure to ambient air pollution on the prevalence of self-reported health outcomes in Australian women. - Design Cross-sectional study - Setting and participants The geocoded residential addresses of 26 991 women across 3 age cohorts in the Australian Longitudinal Study on Women's Health between 2006 and 2011 were linked to nitrogen dioxide (NO2) exposure estimates from a land-use regression model. Annual average NO2 concentrations and residential proximity to roads were used as proxies of exposure to ambient air pollution. - Outcome measures Self-reported disease presence for diabetes mellitus, heart disease, hypertension, stroke, asthma, chronic obstructive pulmonary disease and self-reported symptoms of allergies, breathing difficulties, chest pain and palpitations. - Methods Disease prevalence was modelled by population-averaged Poisson regression models estimated by generalised estimating equations. Associations between symptoms and ambient air pollution were modelled by multilevel mixed logistic regression. Spatial clustering was accounted for at the postcode level. - Results No associations were observed between any of the outcome and exposure variables considered at the 1% significance level after adjusting for known risk factors and confounders. - Conclusions Long-term exposure to ambient air pollution was not associated with self-reported disease prevalence in Australian women. The observed results may have been due to exposure and outcome misclassification, lack of power to detect weak associations or an actual absence of associations with self-reported outcomes at the relatively low annual average air pollution exposure levels across Australia.

Nine year changes in sitting time in young and mid-aged Australian women: Findings from the Australian longitudinal study for women's health

- Objective To examine changes in sitting time (ST) in women over nine years and to identify associations between life events and these changes. - Methods Young (born 1973–78, n = 5215) and mid-aged (born 1946–51, n = 6973) women reported life events and ST in four surveys of the Australian Longitudinal Study on Women's Health between 2000 and 2010. Associations between life events and changes in ST between surveys (decreasers ≥ 2 h/day less, increasers ≥ 2 h/day more) were estimated using generalized estimating equations. - Results Against a background of complex changes there was an overall decrease in ST in young women (median change − 0.48 h/day, interquartile range [IQR] = − 2.54, 1.50) and an increase in ST in mid-aged women (median change 0.43 h/day; IQR = − 1.29, 2.0) over nine years. In young women, returning to study and job loss were associated with increased ST, while having a baby, beginning work and decreased income were associated with decreased ST. In mid-aged women, changes at work were associated with increased ST, while retiring and decreased income were associated with decreased ST. - Conclusions ST changed over nine years in young and mid-aged Australian women. The life events they experienced, particularly events related to work and family, were associated with these changes.

IMPOSE (IMProving Outcomes after Sepsis)—the effect of a multidisciplinary follow-up service on health-related quality of life in patients postsepsis syndromes—a double-blinded randomised controlled trial: protocol

Introduction Patients post sepsis syndromes have a poor quality of life and a high rate of recurring illness or mortality. Follow-up clinics have been instituted for patients postgeneral intensive care but evidence is sparse, and there has been no clinic specifically for survivors of sepsis. The aim of this trial is to investigate if targeted screening and appropriate intervention to these patients can result in an improved quality of life (Short Form 36 health survey (SF36V.2)), decreased mortality in the first 12 months, decreased readmission to hospital and/or decreased use of health resources. Methods and analysis 204 patients postsepsis syndromes will be randomised to one of the two groups. The intervention group will attend an outpatient clinic two monthly for 6 months and receive screening and targeted intervention. The usual care group will remain under the care of their physician. To analyse the results, a baseline comparison will be carried out between each group. Generalised estimating equations will compare the SF36 domain scores between groups and across time points. Mortality will be compared between groups using a Cox proportional hazards (time until death) analysis. Time to first readmission will be compared between groups by a survival analysis. Healthcare costs will be compared between groups using a generalised linear model. Economic (health resource) evaluation will be a within-trial incremental cost utility analysis with a societal perspective. Ethics and dissemination Ethical approval has been granted by the Royal Brisbane and Women’s Hospital Human Research Ethics Committee (HREC; HREC/13/QRBW/17), The University of Queensland HREC (2013000543), Griffith University (RHS/08/14/HREC) and the Australian Government Department of Health (26/2013). The results of this study will be submitted to peer-reviewed intensive care journals and presented at national and international intensive care and/or rehabilitation conferences.

Robust fixed order lateral H-2 controller for micro air vehicle

This paper presents a robust fixed order H-2 controller design using Strengthened discrete optimal projection equations, which approximate the first order necessary optimality condition. The novelty of this work is the application of the robust H-2 controller to a micro aerial vehicle named Sarika2 developed in house. The controller is designed in discrete domain for the lateral dynamics of Sarika2 in the presence of low frequency atmospheric turbulence (gust) and high frequency sensor noise. The design specification includes simultaneous stabilization, disturbance rejection and noise attenuation over the entire flight envelope of the vehicle. The resulting controller performance is comprehensively analyzed by means of simulation.

Robust Fixed Order Lateral H2 Controller for Micro Air Vehicle

This paper presents a robust fixed order H2controller design using strengthened discrete optimal projection equations, which approximate the first order necessary optimality condition. The novelty of this work is the application of the robust H2controller to a micro aerial vehicle named Sarika2 developed in house. The controller is designed in discrete domain for the lateral dynamics of Sarika2 in the presence of low frequency atmospheric turbulence (gust) and high frequency sensor noise. The design specification includes simultaneous stabilization, disturbance rejection and noise attenuation over the entire flight envelope of the vehicle. The resulting controller performance is comprehensively analyzed by means of simulation

Additional information on the length-weight relationship of skipjack tuna from the Eastern Tropical Pacific Ocean

ENGLISH: Results of a study of the length-weight relationships of yellowfin (Neothunnus macropterus) and skipjack (Katsuwonus pelamis) tuna from several fishing areas of the Eastern Tropical Pacific Ocean have been published by Chatwin (1959). In that report, a very low exponential value of 2.6261 was obtained for skipjack from Area 14 (off northern Chile, see Chatwin, Figure 1). It was pointed out, however, that this estimate was based on two samples of fish with a very narrow range of total lengths, not representative of the range in the catch, and that it would be desirable to obtain a further estimate based on a larger range of total lengths. In addition, there proved to be significantly large differences among exponents for the areas sampled, precluding use of a single regression equation for all areas. Two important fishing areas remained unsampled (Areas 10 and 13, see Chatwin, Figure 1), and it appeared desirable to collect length-weight measurement data from them, so that estimating equations would be available for all areas. Subsequent to publication of Chatwin's study, samples of skipjack length-weight measurements were obtained from the desired areas. Estimates derived from these data, and their effects on the previous analysis are presented herein. SPANISH:Los resultados de un estudio sobre las relaciones entre la longitud y el peso del atún aleta amarilla (Neothunnus macropterus) y del barrilete (Katsuwonus pelamis) de las diferentes áreas de pesca en el Pacífico Oriental Tropical ya han sido publicados por Chatwin (1959). En ese informe se obtuvo un valor exponencial muy bajo de 2.626 para el barrilete del Area 14 (frente a la costa norte de Chile, ver Chatwin, Figura 1). Se hizo hincapié, sin embargo, en que esta estimación se basaba en dos muestras de peces con una amplitud muy estrecha de longitudes totales, no representativa de la amplitud en la pesca, y que sería deseable obtener una estimación adicional basada en una amplitud mayor de longitudes totales. Además, se comprobó que habian diferencias significativamente grandes entre los exponentes de las áreas muestreadas lo que impedía el usa de una sola ecuación de regresión para todas las áreas. Se quedaron sin muestrear dos importantes áreas de pesca (Areas 10 y 13, ver Chatwin, Figura 1) y pareció deseable recolectar datos de medidas de longitud y peso de estas áreas, de tal manera que hubiesen disponibles ecuaciones estimadoras para todas las áreas. Después de la publicación del estudio de Chatwin, so obtuvieron muestras de medidas de longitud y peso de barriletes de las áreas deseadas. Las estimaciones derivadas de estos datos y sus efectos sabre el análisis previo se dan en el presente informe.

Framingham Heart Study 100K project: genome-wide associations for cardiovascular disease outcomes

BACKGROUND:Cardiovascular disease (CVD) and its most common manifestations - including coronary heart disease (CHD), stroke, heart failure (HF), and atrial fibrillation (AF) - are major causes of morbidity and mortality. In many industrialized countries, cardiovascular disease (CVD) claims more lives each year than any other disease. Heart disease and stroke are the first and third leading causes of death in the United States. Prior investigations have reported several single gene variants associated with CHD, stroke, HF, and AF. We report a community-based genome-wide association study of major CVD outcomes.METHODS:In 1345 Framingham Heart Study participants from the largest 310 pedigrees (54% women, mean age 33 years at entry), we analyzed associations of 70,987 qualifying SNPs (Affymetrix 100K GeneChip) to four major CVD outcomes: major atherosclerotic CVD (n = 142; myocardial infarction, stroke, CHD death), major CHD (n = 118; myocardial infarction, CHD death), AF (n = 151), and HF (n = 73). Participants free of the condition at entry were included in proportional hazards models. We analyzed model-based deviance residuals using generalized estimating equations to test associations between SNP genotypes and traits in additive genetic models restricted to autosomal SNPs with minor allele frequency [greater than or equal to]0.10, genotype call rate [greater than or equal to]0.80, and Hardy-Weinberg equilibrium p-value [greater than or equal to] 0.001.RESULTS:Six associations yielded p <10-5. The lowest p-values for each CVD trait were as follows: major CVD, rs499818, p = 6.6 x 10-6; major CHD, rs2549513, p = 9.7 x 10-6; AF, rs958546, p = 4.8 x 10-6; HF: rs740363, p = 8.8 x 10-6. Of note, we found associations of a 13 Kb region on chromosome 9p21 with major CVD (p 1.7 - 1.9 x 10-5) and major CHD (p 2.5 - 3.5 x 10-4) that confirm associations with CHD in two recently reported genome-wide association studies. Also, rs10501920 in CNTN5 was associated with AF (p = 9.4 x 10-6) and HF (p = 1.2 x 10-4). Complete results for these phenotypes can be found at the dbgap website http://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?id=phs000007.CONCLUSION:No association attained genome-wide significance, but several intriguing findings emerged. Notably, we replicated associations of chromosome 9p21 with major CVD. Additional studies are needed to validate these results. Finding genetic variants associated with CVD may point to novel disease pathways and identify potential targeted preventive therapies.

Genome-wide association study for subclinical atherosclerosis in major arterial territories in the NHLBI's Framingham Heart Study

INTRODUCTION:Subclinical atherosclerosis (SCA) measures in multiple arterial beds are heritable phenotypes that are associated with increased incidence of cardiovascular disease. We conducted a genome-wide association study (GWAS) for SCA measurements in the community-based Framingham Heart Study.METHODS:Over 100,000 single nucleotide polymorphisms (SNPs) were genotyped (Human 100K GeneChip, Affymetrix) in 1345 subjects from 310 families. We calculated sex-specific age-adjusted and multivariable-adjusted residuals in subjects tested for quantitative SCA phenotypes, including ankle-brachial index, coronary artery calcification and abdominal aortic calcification using multi-detector computed tomography, and carotid intimal medial thickness (IMT) using carotid ultrasonography. We evaluated associations of these phenotypes with 70,987 autosomal SNPs with minor allele frequency [greater than or equal to] 0.10, call rate [greater than or equal to] 80%, and Hardy-Weinberg p-value [greater than or equal to] 0.001 in samples ranging from 673 to 984 subjects, using linear regression with generalized estimating equations (GEE) methodology and family-based association testing (FBAT). Variance components LOD scores were also calculated.RESULTS:There was no association result meeting criteria for genome-wide significance, but our methods identified 11 SNPs with p < 10-5 by GEE and five SNPs with p < 10-5 by FBAT for multivariable-adjusted phenotypes. Among the associated variants were SNPs in or near genes that may be considered candidates for further study, such as rs1376877 (GEE p < 0.000001, located in ABI2) for maximum internal carotid artery IMT and rs4814615 (FBAT p = 0.000003, located in PCSK2) for maximum common carotid artery IMT. Modest significant associations were noted with various SCA phenotypes for variants in previously reported atherosclerosis candidate genes, including NOS3 and ESR1. Associations were also noted of a region on chromosome 9p21 with CAC phenotypes that confirm associations with coronary heart disease and CAC in two recently reported genome-wide association studies. In linkage analyses, several regions of genome-wide linkage were noted, confirming previously reported linkage of internal carotid artery IMT on chromosome 12. All GEE, FBAT and linkage results are provided as an open-access results resource at http://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?id=phs000007.CONCLUSION:The results from this GWAS generate hypotheses regarding several SNPs that may be associated with SCA phenotypes in multiple arterial beds. Given the number of tests conducted, subsequent independent replication in a staged approach is essential to identify genetic variants that may be implicated in atherosclerosis.

A genome-wide association study for blood lipid phenotypes in the Framingham Heart Study

BACKGROUND:Blood lipid levels including low-density lipoprotein cholesterol (LDL-C), high-density lipoprotein cholesterol (HDL-C), and triglycerides (TG) are highly heritable. Genome-wide association is a promising approach to map genetic loci related to these heritable phenotypes.METHODS:In 1087 Framingham Heart Study Offspring cohort participants (mean age 47 years, 52% women), we conducted genome-wide analyses (Affymetrix 100K GeneChip) for fasting blood lipid traits. Total cholesterol, HDL-C, and TG were measured by standard enzymatic methods and LDL-C was calculated using the Friedewald formula. The long-term averages of up to seven measurements of LDL-C, HDL-C, and TG over a ~30 year span were the primary phenotypes. We used generalized estimating equations (GEE), family-based association tests (FBAT) and variance components linkage to investigate the relationships between SNPs (on autosomes, with minor allele frequency [greater than or equal to]10%, genotypic call rate [greater than or equal to]80%, and Hardy-Weinberg equilibrium p [greater than or equal to] 0.001) and multivariable-adjusted residuals. We pursued a three-stage replication strategy of the GEE association results with 287 SNPs (P < 0.001 in Stage I) tested in Stage II (n ~1450 individuals) and 40 SNPs (P < 0.001 in joint analysis of Stages I and II) tested in Stage III (n~6650 individuals).RESULTS:Long-term averages of LDL-C, HDL-C, and TG were highly heritable (h2 = 0.66, 0.69, 0.58, respectively; each P < 0.0001). Of 70,987 tests for each of the phenotypes, two SNPs had p < 10-5 in GEE results for LDL-C, four for HDL-C, and one for TG. For each multivariable-adjusted phenotype, the number of SNPs with association p < 10-4 ranged from 13 to 18 and with p < 10-3, from 94 to 149. Some results confirmed previously reported associations with candidate genes including variation in the lipoprotein lipase gene (LPL) and HDL-C and TG (rs7007797; P = 0.0005 for HDL-C and 0.002 for TG). The full set of GEE, FBAT and linkage results are posted at the database of Genotype and Phenotype (dbGaP). After three stages of replication, there was no convincing statistical evidence for association (i.e., combined P < 10-5 across all three stages) between any of the tested SNPs and lipid phenotypes.CONCLUSION:Using a 100K genome-wide scan, we have generated a set of putative associations for common sequence variants and lipid phenotypes. Validation of selected hypotheses in additional samples did not identify any new loci underlying variability in blood lipids. Lack of replication may be due to inadequate statistical power to detect modest quantitative trait locus effects (i.e., < 1% of trait variance explained) or reduced genomic coverage of the 100K array. GWAS in FHS using a denser genome-wide genotyping platform and a better-powered replication strategy may identify novel loci underlying blood lipids.

Trends in anemia management in US hemodialysis patients 2004-2010.

BACKGROUND: There have been major changes in the management of anemia in US hemodialysis patients in recent years. We sought to determine the influence of clinical trial results, safety regulations, and changes in reimbursement policy on practice. METHODS: We examined indicators of anemia management among incident and prevalent hemodialysis patients from a medium-sized dialysis provider over three time periods: (1) 2004 to 2006 (2) 2007 to 2009, and (3) 2010. Trends across the three time periods were compared using generalized estimating equations. RESULTS: Prior to 2007, the median proportion of patients with monthly hemoglobin >12 g/dL for patients on dialysis 0 to 3, 4 to 6 and 7 to 18 months, respectively, was 42%, 55% and 46% declined to 41%, 54%, and 40% after 2007, and declined more sharply in 2010 to 34%, 41%, and 30%. Median weekly Epoeitin alpha doses over the same periods were 18,000, 12,400, and 9,100 units before 2007; remained relatively unchanged from 2007 to 2009; and decreased sharply in the patients 3-6 and 6-18 months on dialysis to 10,200 and 7,800 units, respectively in 2010. Iron doses, serum ferritin, and transferrin saturation levels increased over time with more pronounced increases in 2010. CONCLUSION: Modest changes in anemia management occurred between 2007 and 2009, followed by more dramatic changes in 2010. Studies are needed to examine the effects of declining erythropoietin use and hemoglobin levels and increasing intravenous iron use on quality of life, transplantation rates, infection rates and survival.

Mesoscale fronts as foraging habitats: composite front mapping reveals oceanographic drivers of habitat use for a pelagic seabird

The oceanographic drivers of marine vertebrate habitat use are poorly understood yet fundamental to our knowledge of marine ecosystem functioning. Here, we use composite front mapping and high-resolution GPS tracking to determine the significance of mesoscale oceanographic fronts as physical drivers of foraging habitat selection in northern gannets Morus bassanus. We tracked 66 breeding gannets from a Celtic Sea colony over 2 years and used residence time to identify area-restricted search (ARS) behaviour. Composite front maps identified thermal and chlorophyll-a mesoscale fronts at two different temporal scales—(i) contemporaneous fronts and (ii) seasonally persistent frontal zones. Using generalized additive models (GAMs), with generalized estimating equations (GEE-GAMs) to account for serial autocorrelation in tracking data, we found that gannets do not adjust their behaviour in response to contemporaneous fronts. However, ARS was more likely to occur within spatially predictable, seasonally persistent frontal zones (GAMs). Our results provide proof of concept that composite front mapping is a useful tool for studying the influence of oceanographic features on animal movements. Moreover, we highlight that frontal persistence is a crucial element of the formation of pelagic foraging hotspots for mobile marine vertebrates.