Efficient parameter estimation in longitudinal data analysis using a hybrid GEE method

The method of generalized estimating equations (GEEs) provides consistent estimates of the regression parameters in a marginal regression model for longitudinal data, even when the working correlation model is misspecified (Liang and Zeger, 1986). However, the efficiency of a GEE estimate can be seriously affected by the choice of the working correlation model. This study addresses this problem by proposing a hybrid method that combines multiple GEEs based on different working correlation models, using the empirical likelihood method (Qin and Lawless, 1994). Analyses show that this hybrid method is more efficient than a GEE using a misspecified working correlation model. Furthermore, if one of the working correlation structures correctly models the within-subject correlations, then this hybrid method provides the most efficient parameter estimates. In simulations, the hybrid method's finite-sample performance is superior to a GEE under any of the commonly used working correlation models and is almost fully efficient in all scenarios studied. The hybrid method is illustrated using data from a longitudinal study of the respiratory infection rates in 275 Indonesian children.

Smooth bootstrap methods for analysis of longitudinal data

In analysis of longitudinal data, the variance matrix of the parameter estimates is usually estimated by the 'sandwich' method, in which the variance for each subject is estimated by its residual products. We propose smooth bootstrap methods by perturbing the estimating functions to obtain 'bootstrapped' realizations of the parameter estimates for statistical inference. Our extensive simulation studies indicate that the variance estimators by our proposed methods can not only correct the bias of the sandwich estimator but also improve the confidence interval coverage. We applied the proposed method to a data set from a clinical trial of antibiotics for leprosy.

A modified pseudolikelihood approach for analysis of longitudinal data

We consider the analysis of longitudinal data when the covariance function is modeled by additional parameters to the mean parameters. In general, inconsistent estimators of the covariance (variance/correlation) parameters will be produced when the "working" correlation matrix is misspecified, which may result in great loss of efficiency of the mean parameter estimators (albeit the consistency is preserved). We consider using different "Working" correlation models for the variance and the mean parameters. In particular, we find that an independence working model should be used for estimating the variance parameters to ensure their consistency in case the correlation structure is misspecified. The designated "working" correlation matrices should be used for estimating the mean and the correlation parameters to attain high efficiency for estimating the mean parameters. Simulation studies indicate that the proposed algorithm performs very well. We also applied different estimation procedures to a data set from a clinical trial for illustration.

Robust estimating functions and bias correction for longitudinal data analysis

Robust methods are useful in making reliable statistical inferences when there are small deviations from the model assumptions. The widely used method of the generalized estimating equations can be "robustified" by replacing the standardized residuals with the M-residuals. If the Pearson residuals are assumed to be unbiased from zero, parameter estimators from the robust approach are asymptotically biased when error distributions are not symmetric. We propose a distribution-free method for correcting this bias. Our extensive numerical studies show that the proposed method can reduce the bias substantially. Examples are given for illustration.

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.

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.

Sponsoring a rival has benefits too: A longitudinal study of changes in fan attitudes toward favored-and opposing-team sponsor brands

A longitudinal field experiment examined sports fans’ attitudes toward favored- and opposing-team sponsors across time. Measurements at five timepoints showed fans’ attitudes were more positive toward their favored-team sponsors, but that attitudes improved across time toward both favored-team sponsors and opposing-team sponsors. This occurred regardless of intensity of fan identification.

Muscle morphometry of the individual hamstring muscles in semi-elite AFL Players: Preliminary findings from a longitudinal study

Hamstring strains in the Australian Football League (AFL) have a high incidence (15%) and recurrence rate (34%) with lateral hamstring injuries most common (83%). Retrospective studies have found significant muscle volume asymmetries ≤23 months post hamstring injury; however examination of the association between hamstring strains and muscle asymmetry has not been investigated prospectively. This study presents baseline data from a longitudinal study focusing on individual hamstring morphometry in uninjured and injured semi-elite AFL players.

Air pollution and fasting blood glucose: A longitudinal study in China

Limited studies have examined the associations between air pollutants [particles with diameters of 10um or less (PM10), sulfur dioxide (SO2), and nitrogen dioxide (NO2)] and fasting blood glucose (FBG). We collected data for 27,685 participants who were followed during 2006 and 2008. Generalized Estimating Equation models were used to examine the effects of air pollutants on FBG while controlling for potential confounders. We found that increased exposure to NO2, SO2 and PM10 was significantly associated with increased FBG levels in single pollutant models (p<0.001). For exposure to 4 days’ average of concentrations, a 100 µg/m3 increase in SO2, NO2, and PM10 was associated with 0.17 mmol/L (95%CI: 0.15–0.19), 0.53 mmol/L (95%CI: 0.42–0.65), and 0.11 mmol/L (95%CI: 0.07–0.15) increase in FBG, respectively. In the multi-pollutant models, the effects of SO2 were enhanced, while the effects of NO2 and PM10 were alleviated. The effects of air pollutants on FBG were stronger in female, elderly, and overweight people than in male, young and underweight people. In conclusion, the findings suggest that air pollution increases the levels of FBG. Vulnerable people should pay more attention on highly polluted days to prevent air pollution-related health issues.

Emotional intelligence development in student radiation therapists: A longitudinal pilot study

Emotional intelligence (EI) is defined as “the ability to recognise, understand and manage emotions in ourselves and others” [1]. Initially identified as a concept applied to leadership and management, EI is now recognised as an important skill in a number of areas, including healthcare [2]. Empathy (the ability to see the world through someone else’s eyes) is known to play an important role in the therapeutic relationship with patients [3]. As EI has been shown to improve empathy [4], it is clear that developing the EI of student health professionals should benefit patients in the long term. It is not surprising, then, that a number of studies have investigated the role of EI in medical, dental and nursing students, however there is little reported evidence relating to EI development in pre-registration radiation therapy (RT) students.

Emotional intelligence development in radiation therapy students: A longitudinal study

Purpose: Emotional intelligence (EI) is an increasingly important aspect of a health professional’s skill set. It is strongly associated with empathy, reflection and resilience; all key aspects of radiotherapy practice. Previous work in other disciplines has formed contradictory conclusions concerning development of EI over time. This study aimed to determine the extent to which EI can develop during a radiotherapy undergraduate course and identify factors affecting this. Methods and materials: This study used anonymous coded Likert-style surveys to gather longitudinal data from radiotherapy students relating to a range of self-perceived EI traits during their 3-year degree. Data were gathered at various points throughout the course from the whole cohort. Results: A total of 26 students provided data with 14 completing the full series of datasets. There was a 17·2% increase in self-reported EI score with a p-value<0·0001. Social awareness and relationship skills exhibited the greatest increase in scores compared with self-awareness. Variance of scores decreased over time; there was a reduced change in EI for mature students who tended to have higher initial scores. EI increase was most evident immediately after clinical placements. Conclusions: Radiotherapy students increase their EI scores during a 3-year course. Students reported higher levels of EI immediately after their clinical placement; radiotherapy curricula should seek to maximise on these learning opportunities.

Shaping (reflexive) professional identities across an undergraduate degree programme: A longitudinal case study

In our complex and incongruous professional worlds, where there is no blueprint for dealing with unpredictable people and events, it is imperative that individuals develop reflexive approaches to professional identity building. Notwithstanding the importance of disciplinary knowledge and skills, higher education has a crucial role to play in guiding students to examine and mediate self in relation to context for effective decision-making and action. This paper reports on a small-scale longitudinal project that investigated the ways in which ten undergraduate students over the course of a three-year Radiation Therapy degree shaped their professional identities. Theories of reflexivity and methods of discourse analysis are utilised to understand the ways in which individuals accounted for their professional identity projects at university. The findings suggest that, across time, the participants negotiated professional ‘becoming’ through four distinct kinds of reflexive modalities. These findings have implications for teaching strategies and curriculum design in undergraduate programs.

Emotional intelligence development in student radiation therapists: A longitudinal pilot study

Emotional intelligence (EI) is defined as “the ability to recognise, understand and manage emotions in ourselves and others”. Initially identified as a concept applied to leadership and management, EI is now recognised as an important skill in a number of areas, including healthcare [2]. Empathy (the ability to see the world through someone else’s eyes) is known to play an important role in the therapeutic relationship with patients [3]. As EI has been shown to improve empathy [4], it is clear that developing the EI of student health professionals should benefit patients in the long term. It is not surprising, then, that a number of studies have investigated the role of EI in medical, dental and nursing students, however there is little reported evidence relating to EI development in pre-registration radiation therapy (RT) students.

Risk factors associated with corneal nerve alteration in type 1 diabetes in the absence of neuropathy: A longitudinal in vivo corneal confocal microscopy study

Purpose The aim of this study was to determine alterations to the corneal subbasal nerve plexus (SNP) over four years using in vivo corneal confocal microscopy (IVCM) in participants with type 1 diabetes and to identify significant risk factors associated with these alterations. Methods A cohort of 108 individuals with type 1 diabetes and no evidence of peripheral neuropathy at enrollment underwent laser-scanning IVCM, ocular screening, and health and metabolic assessment at baseline and the examinations continued for four subsequent annual visits. At each annual visit, eight central corneal images of the SNP were selected and analyzed to quantify corneal nerve fiber density (CNFD), branch density (CNBD) and fiber length (CNFL). Linear mixed model approaches were fitted to examine the relationship between risk factors and corneal nerve parameters. Results A total of 96 participants completed the final visit and 91 participants completed all visits. No significant relationships were found between corneal nerve parameters and time, sex, duration of diabetes, smoking, alcohol consumption, blood pressure or BMI. However, CNFD was negatively associated with HbA1c (β=-0.76, P<0.01) and age (β=-0.13, P<0.01) and positively related to high density lipids (HDL) (β=2.01, P=0.03). Higher HbA1c (β=-1.58, P=0.04) and age (β=-0.23, P<0.01) also negatively impacted CNBD. CNFL was only affected by higher age (β=-0.06, P<0.01). Conclusions Glycemic control, HDL and age have significant effects on SNP structure. These findings highlight the importance of diabetic management to prevent corneal nerve damage as well as the capability of IVCM for monitoring subclinical alterations in the corneal SNP in diabetes.

Research update: LANDMark study: Longitudinal assessment of neuropathy in diabetes using novel ophthalmic MARKers

The eye is a simple, non-invasive location for screening, diagnosing and follow up of diabetic peripheral neuropathy.