Discussion of “Generalized estimating equations: Notes on the choice of the working correlation matrix”

Objective To discuss generalized estimating equations as an extension of generalized linear models by commenting on the paper of Ziegler and Vens "Generalized Estimating Equations. Notes on the Choice of the Working Correlation Matrix". Methods Inviting an international group of experts to comment on this paper. Results Several perspectives have been taken by the discussants. Econometricians have established parallels to the generalized method of moments (GMM). Statisticians discussed model assumptions and the aspect of missing data Applied statisticians; commented on practical aspects in data analysis. Conclusions In general, careful modeling correlation is encouraged when considering estimation efficiency and other implications, and a comparison of choosing instruments in GMM and generalized estimating equations, (GEE) would be worthwhile. Some theoretical drawbacks of GEE need to be further addressed and require careful analysis of data This particularly applies to the situation when data are missing at random.

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.

Unbiased estimating equations from working correlation models for irregularly timed repeated measures

The method of generalized estimating equation-, (GEEs) has been criticized recently for a failure to protect against misspecification of working correlation models, which in some cases leads to loss of efficiency or infeasibility of solutions. However, the feasibility and efficiency of GEE methods can be enhanced considerably by using flexible families of working correlation models. We propose two ways of constructing unbiased estimating equations from general correlation models for irregularly timed repeated measures to supplement and enhance GEE. The supplementary estimating equations are obtained by differentiation of the Cholesky decomposition of the working correlation, or as score equations for decoupled Gaussian pseudolikelihood. The estimating equations are solved with computational effort equivalent to that required for a first-order GEE. Full details and analytic expressions are developed for a generalized Markovian model that was evaluated through simulation. Large-sample ".sandwich" standard errors for working correlation parameter estimates are derived and shown to have good performance. The proposed estimating functions are further illustrated in an analysis of repeated measures of pulmonary function in children.

Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance

The method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations. We investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods. The asymptotic relative efficiency depends on three-features of the analysis, namely (i) the discrepancy between the working correlation structure and the unobservable true correlation structure, (ii) the method by which the correlation parameters are estimated and (iii) the 'design', by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes. Analytical and numerical studies of realistic data-analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency. Protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a 'Gaussian estimation' pseudolikelihood procedure is used with an AR(1) structure.

A generalized estimating equations approach for analysis of the impact of new technology on a trawl fishery

The article describes a generalized estimating equations approach that was used to investigate the impact of technology on vessel performance in a trawl fishery during 1988-96, while accounting for spatial and temporal correlations in the catch-effort data. Robust estimation of parameters in the presence of several levels of clustering depended more on the choice of cluster definition than on the choice of correlation structure within the cluster. Models with smaller cluster sizes produced stable results, while models with larger cluster sizes, that may have had complex within-cluster correlation structures and that had within-cluster covariates, produced estimates sensitive to the correlation structure. The preferred model arising from this dataset assumed that catches from a vessel were correlated in the same years and the same areas, but independent in different years and areas. The model that assumed catches from a vessel were correlated in all years and areas, equivalent to a random effects term for vessel, produced spurious results. This was an unexpected finding that highlighted the need to adopt a systematic strategy for modelling. The article proposes a modelling strategy of selecting the best cluster definition first, and the working correlation structure (within clusters) second. The article discusses the selection and interpretation of the model in the light of background knowledge of the data and utility of the model, and the potential for this modelling approach to apply in similar statistical situations.

Inverse Correlation between Vitamin D and C-Reactive Protein in Newborns

Some studies suggested that adequate vitamin D might reduce inflammation in adults. However, little is known about this association in early life. We aimed to determine the relationship between cord blood 25-hydroxyvitamin D (25(OH)D) and C-reactive protein (CRP) in neonates. Cord blood levels of 25(OH)D and CRP were measured in 1491 neonates in Hefei, China. Potential confounders including maternal sociodemographic characteristics, perinatal health status, lifestyle, and birth outcomes were prospectively collected. The average values of cord blood 25(OH)D and CRP were 39.43 nmol/L (SD = 20.35) and 6.71 mg/L (SD = 3.07), respectively. Stratified by 25(OH)D levels, per 10 nmol/L increase in 25(OH)D, CRP decreased by 1.42 mg/L (95% CI: 0.90, 1.95) among neonates with 25(OH)D <25.0 nmol/L, and decreased by 0.49 mg/L (95% CI: 0.17, 0.80) among neonates with 25(OH)D between 25.0 nmol/L and 49.9 nmol/L, after adjusting for potential confounders. However, no significant association between 25(OH)D and CRP was observed among neonates with 25(OH)D ≥50 nmol/L. Cord blood 25(OH)D and CRP levels showed a significant seasonal trend with lower 25(OH)D and higher CRP during winter-spring than summer-autumn. Stratified by season, a significant linear association of 25(OH)D with CRP was observed in neonates born in winter-spring (adjusted β = −0.11, 95% CI: −0.13, −0.10), but not summer-autumn. Among neonates born in winter-spring, neonates with 25(OH)D <25 nmol/L had higher risk of CRP ≥10 mg/L (adjusted OR = 3.06, 95% CI: 2.00, 4.69), compared to neonates with 25(OH)D ≥25 nmol/L. Neonates with vitamin D deficiency had higher risk of exposure to elevated inflammation at birth.

Spectral analysis of pair-correlation bandwidth: Application to cell biology images

Images from cell biology experiments often indicate the presence of cell clustering, which can provide insight into the mechanisms driving the collective cell behaviour. Pair-correlation functions provide quantitative information about the presence, or absence, of clustering in a spatial distribution of cells. This is because the pair-correlation function describes the ratio of the abundance of pairs of cells, separated by a particular distance, relative to a randomly distributed reference population. Pair-correlation functions are often presented as a kernel density estimate where the frequency of pairs of objects are grouped using a particular bandwidth (or bin width), Δ>0. The choice of bandwidth has a dramatic impact: choosing Δ too large produces a pair-correlation function that contains insufficient information, whereas choosing Δ too small produces a pair-correlation signal dominated by fluctuations. Presently, there is little guidance available regarding how to make an objective choice of Δ. We present a new technique to choose Δ by analysing the power spectrum of the discrete Fourier transform of the pair-correlation function. Using synthetic simulation data, we confirm that our approach allows us to objectively choose Δ such that the appropriately binned pair-correlation function captures known features in uniform and clustered synthetic images. We also apply our technique to images from two different cell biology assays. The first assay corresponds to an approximately uniform distribution of cells, while the second assay involves a time series of images of a cell population which forms aggregates over time. The appropriately binned pair-correlation function allows us to make quantitative inferences about the average aggregate size, as well as quantifying how the average aggregate size changes with time.

A quantitative-trait genome-wide association study of alcoholism risk in the community: findings and implications

BACKGROUND Given moderately strong genetic contributions to variation in alcoholism and heaviness of drinking (50% to 60% heritability) with high correlation of genetic influences, we have conducted a quantitative trait genome-wide association study (GWAS) for phenotypes related to alcohol use and dependence. METHODS Diagnostic interview and blood/buccal samples were obtained from sibships ascertained through the Australian Twin Registry. Genome-wide single nucleotide polymorphism (SNP) genotyping was performed with 8754 individuals (2062 alcohol-dependent cases) selected for informativeness for alcohol use disorder and associated quantitative traits. Family-based association tests were performed for alcohol dependence, dependence factor score, and heaviness of drinking factor score, with confirmatory case-population control comparisons using an unassessed population control series of 3393 Australians with genome-wide SNP data. RESULTS No findings reached genome-wide significance (p = 8.4 x 10(-8) for this study), with lowest p value for primary phenotypes of 1.2 x 10(-7). Convergent findings for quantitative consumption and diagnostic and quantitative dependence measures suggest possible roles for a transmembrane protein gene (TMEM108) and for ANKS1A. The major finding, however, was small effect sizes estimated for individual SNPs, suggesting that hundreds of genetic variants make modest contributions (1/4% of variance or less) to alcohol dependence risk. CONCLUSIONS We conclude that: - 1) meta-analyses of consumption data may contribute usefully to gene discovery; - 2) translation of human alcoholism GWAS results to drug discovery or clinically useful prediction of risk will be challenging, and; - 3) through accumulation across studies, GWAS data may become valuable for improved genetic risk differentiation in research in biological psychiatry (e.g., prospective high-risk or resilience studies).

Susceptibility locus on chromosome 1q23-25 for a schizophrenia subtype resembling deficit schizophrenia identified by latent class analysis

Context: Identifying susceptibility genes for schizophrenia may be complicated by phenotypic heterogeneity, with some evidence suggesting that phenotypic heterogeneity reflects genetic heterogeneity. Objective: To evaluate the heritability and conduct genetic linkage analyses of empirically derived, clinically homogeneous schizophrenia subtypes. Design: Latent class and linkage analysis. Setting: Taiwanese field research centers. Participants: The latent class analysis included 1236 Han Chinese individuals with DSM-IV schizophrenia. These individuals were members of a large affected-sibling-pair sample of schizophrenia (606 ascertained families), original linkage analyses of which detected a maximum logarithm of odds (LOD) of 1.8 (z = 2.88) on chromosome 10q22.3. Main Outcome Measures: Multipoint exponential LOD scores by latent class assignment and parametric heterogeneity LOD scores. Results: Latent class analyses identified 4 classes, with 2 demonstrating familial aggregation. The first (LC2) described a group with severe negative symptoms, disorganization, and pronounced functional impairment, resembling “deficit schizophrenia.” The second (LC3) described a group with minimal functional impairment, mild or absent negative symptoms, and low disorganization. Using the negative/deficit subtype, we detected genome-wide significant linkage to 1q23-25 (LOD = 3.78, empiric genome-wide P = .01). This region was not detected using the DSM-IV schizophrenia diagnosis, but has been strongly implicated in schizophrenia pathogenesis by previous linkage and association studies.Variants in the 1q region may specifically increase risk for a negative/deficit schizophrenia subtype. Alternatively, these results may reflect increased familiality/heritability of the negative class, the presence of multiple 1q schizophrenia risk genes, or a pleiotropic 1q risk locus or loci, with stronger genotype-phenotype correlation with negative/deficit symptoms. Using the second familial latent class, we identified nominally significant linkage to the original 10q peak region. Conclusion: Genetic analyses of heritable, homogeneous phenotypes may improve the power of linkage and association studies of schizophrenia and thus have relevance to the design and analysis of genome-wide association studies.

Step based physical activity guidelines for preschool-aged children

OBJECTIVE Public health organizations recommend that preschool-aged children accumulate at least 3h of physical activity (PA) daily. Objective monitoring using pedometers offers an opportunity to measure preschooler's PA and assess compliance with this recommendation. The purpose of this study was to derive step-based recommendations consistent with the 3h PA recommendation for preschool-aged children. METHOD The study sample comprised 916 preschool-aged children, aged 3 to 6years (mean age=5.0+/-0.8years). Children were recruited from kindergartens located in Portugal, between 2009 and 2013. Children wore an ActiGraph GT1M accelerometer that measured PA intensity and steps per day simultaneously over a 7-day monitoring period. Receiver operating characteristic (ROC) curve analysis was used to identify the daily step count threshold associated with meeting the daily 3hour PA recommendation. RESULTS A significant correlation was observed between minutes of total PA and steps per day (r=0.76, p<0.001). The optimal step count for >/=3h of total PA was 9099 steps per day (sensitivity (90%) and specificity (66%)) with area under the ROC curve=0.86 (95% CI: 0.84 to 0.88). CONCLUSION Preschool-aged children who accumulate less than 9000 steps per day may be considered Insufficiently Active.

Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering

The family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. The family nests as particular cases several important asymmetric distributions like the Generalized Hyperbolic distribution. The Generalized Hyperbolic distribution in turn nests many other well known distributions such as the Normal Inverse Gaussian. In a multivariate setting, an extension of the standard location and scale mixture concept is proposed into a so called multiple scaled framework which has the advantage of allowing different tail and skewness behaviours in each dimension with arbitrary correlation between dimensions. Estimation of the parameters is provided via an EM algorithm and extended to cover the case of mixtures of such multiple scaled distributions for application to clustering. Assessments on simulated and real data confirm the gain in degrees of freedom and flexibility in modelling data of varying tail behaviour and directional shape.

Crude oil and agricultural futures: An analysis of correlation dynamics

Correlations between oil and agricultural commodities have varied over previous decades, impacted by renewable fuels policy and turbulent economic conditions. We estimate smooth transition conditional correlation models for 12 agricultural commodities and WTI crude oil. While a structural change in correlations occurred concurrently with the introduction of biofuel policy, oil and food price levels are also key influences. High correlation between biofuel feedstocks and oil is more likely to occur when food and oil price levels are high. Correlation with oil returns is strong for biofuel feedstocks, unlike with other agricultural futures, suggesting limited contagion from energy to food markets.

Factors influencing hospital readmission and length of stay of Vietnamese patients with type 2 diabetes and cardiac disease

Background: Increased hospital readmission and longer stays in the hospital for patients with type 2 diabetes and cardiac disease can result in higher healthcare costs and heavier individual burden. Thus, knowledge of the characteristics and predictive factors for Vietnamese patients with type 2 diabetes and cardiac disease, at high risk of hospital readmission and longer stays in the hospital, could provide a better understanding on how to develop an effective care plan aimed at improving patient outcomes. However, information about factors influencing hospital readmission and length of stay of patients with type 2 diabetes and cardiac disease in Vietnam is limited. Aim: This study examined factors influencing hospital readmission and length of stay of Vietnamese patients with both type 2 diabetes and cardiac disease. Methods: An exploratory prospective study design was conducted on 209 patients with type 2 diabetes and cardiac disease in Vietnam. Data were collected from patient charts and patients' responses to self-administered questionnaires. Descriptive statistics, bivariate correlation, logistic and multiple regression were used to analyse the data. Results: The hospital readmission rate was 12.0% among patients with both type 2 diabetes and cardiac disease. The average length of stay in the hospital was 9.37 days. Older age (OR= 1.11, p< .05), increased duration of type 2 diabetes (OR= 1.22, p< .05), less engagement in stretching/strengthening exercise behaviours (OR= .93, p< .001) and in communication with physician (OR= .21, p< .001) were significant predictors of 30-dayhospital readmission. Increased number of additional co-morbidities (β= .33, p< .001) was a significant predictor of longer stays in the hospital. High levels of cognitive symptom management (β= .40, p< .001) significantly predicted longer stays in the hospital, indicating that the more patients practiced cognitive symptom management, the longer the stay in hospital. Conclusions: This study provides some evidence of factors influencing hospital readmission and length of stay and argues that this information may have significant implications for clinical practice in order to improve patients' health outcomes. However, the findings of this study related to the targeted hospital only. Additionally, the investigation of environmental factors is recommended for future research as these factors are important components contributing to the research model.

Aircraft trajectory clustering techniques using circular statistics

This paper presents a statistical aircraft trajectory clustering approach aimed at discriminating between typical manned and expected unmanned traffic patterns. First, a resampled version of each trajectory is modelled using a mixture of Von Mises distributions (circular statistics). Second, the remodelled trajectories are globally aligned using tools from bioinformatics. Third, the alignment scores are used to cluster the trajectories using an iterative k-medoids approach and an appropriate distance function. The approach is then evaluated using synthetically generated unmanned aircraft flights combined with real air traffic position reports taken over a sector of Northern Queensland, Australia. Results suggest that the technique is useful in distinguishing between expected unmanned and manned aircraft traffic behaviour, as well as identifying some common conventional air traffic patterns.

Testing against changing correlation

A test for time-varying correlation is developed within the framework of a dynamic conditional score (DCS) model for both Gaussian and Student t-distributions. The test may be interpreted as a Lagrange multiplier test and modified to allow for the estimation of models for time-varying volatility in the individual series. Unlike standard moment-based tests, the score-based test statistic includes information on the level of correlation under the null hypothesis and local power arguments indicate the benefits of doing so. A simulation study shows that the performance of the score-based test is strong relative to existing tests across a range of data generating processes. An application to the Hong Kong and South Korean equity markets shows that the new test reveals changes in correlation that are not detected by the standard moment-based test.