Sean L. Simpson

Exponential Random Graph Modeling for Complex Brain Networks

Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However, the literature on their use in biological networks (especially brain networks) has remained sparse. Descriptive models based on a specific feature of the graph (clustering coefficient, degree distribution, etc.) have dominated connectivity research in neuroscience. Corresponding generative models have been developed to reproduce one of these features. However, the complexity inherent in whole-brain network data necessitates the development and use of tools that allow the systematic exploration of several features simultaneously and how they interact to form the global network architecture. ERGMs provide a statistically principled approach to the assessment of how a set of interacting local brain network features gives rise to the global structure. We illustrate the utility of ERGMs for modeling, analyzing, and simulating complex whole-brain networks with network data from normal subjects. We also provide a foundation for the selection of important local features through the implementation and assessment of three selection approaches: a traditional p-value based backward selection approach, an information criterion approach (AIC), and a graphical goodness of fit (GOF) approach. The graphical GOF approach serves as the best method given the scientific interest in being able to capture and reproduce the structure of fitted brain networks.

Reproducibility of Graph Metrics in fMRI Networks

The reliability of graph metrics calculated in network analysis is essential to the interpretation of complex network organization. These graph metrics are used to deduce the small-world properties in networks. In this study, we investigated the test-retest reliability of graph metrics from functional magnetic resonance imaging data collected for two runs in 45 healthy older adults. Graph metrics were calculated on data for both runs and compared using intraclass correlation coefficient (ICC) statistics and Bland–Altman (BA) plots. ICC scores describe the level of absolute agreement between two measurements and provide a measure of reproducibility. For mean graph metrics, ICC scores were high for clustering coefficient (ICC = 0.86), global efficiency (ICC = 0.83), path length (ICC = 0.79), and local efficiency (ICC = 0.75); the ICC score for degree was found to be low (ICC = 0.29). ICC scores were also used to generate reproducibility maps in brain space to test voxel-wise reproducibility for unsmoothed and smoothed data. Reproducibility was uniform across the brain for global efficiency and path length, but was only high in network hubs for clustering coefficient, local efficiency, and degree. BA plots were used to test the measurement repeatability of all graph metrics. All graph metrics fell within the limits for repeatability. Together, these results suggest that with exception of degree, mean graph metrics are reproducible and suitable for clinical studies. Further exploration is warranted to better understand reproducibility across the brain on a voxel-wise basis.

Analyzing complex functional brain networks: Fusing statistics and network science to understand the brain

Complex functional brain network analyses have exploded over the last decade, gaining traction due to their profound clinical implications. The application of network science (an interdisciplinary offshoot of graph theory) has facilitated these analyses and enabled examining the brain as an integrated system that produces complex behaviors. While the field of statistics has been integral in advancing activation analyses and some connectivity analyses in functional neuroimaging research, it has yet to play a commensurate role in complex network analyses. Fusing novel statistical methods with network-based functional neuroimage analysis will engender powerful analytical tools that will aid in our understanding of normal brain function as well as alterations due to various brain disorders. Here we survey widely used statistical and network science tools for analyzing fMRI network data and discuss the challenges faced in filling some of the remaining methodological gaps. When applied and interpreted correctly, the fusion of network scientific and statistical methods has a chance to revolutionize the understanding of brain function.

A permutation testing framework to compare groups of brain networks

Brain network analyses have moved to the forefront of neuroimaging research over the last decade. However, methods for statistically comparing groups of networks have lagged behind. These comparisons have great appeal for researchers interested in gaining further insight into complex brain function and how it changes across different mental states and disease conditions. Current comparison approaches generally either rely on a summary metric or on mass-univariate nodal or edge-based comparisons that ignore the inherent topological properties of the network, yielding little power and failing to make network level comparisons. Gleaning deeper insights into normal and abnormal changes in complex brain function demands methods that take advantage of the wealth of data present in an entire brain network. Here we propose a permutation testing framework that allows comparing groups of networks while incorporating topological features inherent in each individual network. We validate our approach using simulated data with known group differences. We then apply the method to functional brain networks derived from fMRI data.

A linear exponent AR(1) family of correlation structures.

In repeated measures settings, modeling the correlation pattern of the data can be immensely important for proper analyses. Accurate inference requires proper choice of the correlation model. Optimal efficiency of the estimation procedure demands a parsimonious parameterization of the correlation structure, with sufficient sensitivity to detect the range of correlation patterns that may occur. Many repeated measures settings have within-subject correlation decreasing exponentially in time or space. Among the variety of correlation patterns available for this context, the continuous-time first-order autoregressive correlation structure, denoted AR(1), sees the most utilization. Despite its wide use, the AR(1) structure often poorly gauges within-subject correlations that decay at a slower or faster rate than required by the AR(1) model. To address this deficiency we propose a two-parameter generalization of the continuous-time AR(1) model, termed the linear exponent autoregressive (LEAR) correlation structure, which accommodates much slower and much faster decay patterns. Special cases of the LEAR family include the AR(1), compound symmetry, and first-order moving average correlation structures. Excellent analytic, numerical, and statistical properties help make the LEAR structure a valuable addition to the suite of parsimonious correlation models for repeated measures data. Both medical imaging data concerning neonate neurological development and longitudinal data concerning diet and hypertension [DASH (Dietary Approaches to Stop Hypertension) study] exemplify the utility of the LEAR correlation structure.

Rhinitis associated with pesticide use among private pesticide applicators in the agricultural health study.

Farmers commonly experience rhinitis but the risk factors are not well characterized. The aim of this study was to analyze cross-sectional data on rhinitis in the past year and pesticide use from 21,958 Iowa and North Carolina farmers in the Agricultural Health Study, enrolled 1993–1997, to evaluate pesticide predictors of rhinitis. Polytomous and logistic regression models were used to assess association between pesticide use and rhinitis while controlling for demographics and farm-related exposures. Sixty-seven percent of farmers reported current rhinitis and 39% reported 3 or more rhinitis episodes. The herbicides glyphosate [odds ratio (OR) = 1.09, 95% confidence interval (95% CI) = 1.05–1.13] and petroleum oil (OR = 1.12, 95% CI = 1.05–1.19) were associated with current rhinitis and increased rhinitis episodes. Of the insecticides, four organophosphates (chlorpyrifos, diazinon, dichlorvos, and malathion), carbaryl, and use of permethrin on animals were predictors of current rhinitis. Diazinon was significant in the overall polytomous model and was associated with an elevated OR of 13+ rhinitis episodes (13+ episodes OR = 1.23, 95% CI = 1.09–1.38). The fungicide captan was also a significant predictor of rhinitis. Use of petroleum oil, use of malathion, use of permethrin, and use of the herbicide metolachlor were significant in exposure-response polytomous models. Specific pesticides may contribute to rhinitis in farmers; agricultural activities did not explain these findings.

Changes in brain network efficiency and working memory performance in aging.

Working memory is a complex psychological construct referring to the temporary storage and active processing of information. We used functional connectivity brain network metrics quantifying local and global efficiency of information transfer for predicting individual variability in working memory performance on an n-back task in both young (n = 14) and older (n = 15) adults. Individual differences in both local and global efficiency during the working memory task were significant predictors of working memory performance in addition to age (and an interaction between age and global efficiency). Decreases in local efficiency during the working memory task were associated with better working memory performance in both age cohorts. In contrast, increases in global efficiency were associated with much better working performance for young participants; however, increases in global efficiency were associated with a slight decrease in working memory performance for older participants. Individual differences in local and global efficiency during resting-state sessions were not significant predictors of working memory performance. Significant group whole-brain functional network decreases in local efficiency also were observed during the working memory task compared to rest, whereas no significant differences were observed in network global efficiency. These results are discussed in relation to recently developed models of age-related differences in working memory.

Intraindividual variability in domain-specific cognition and risk of mild cognitive impairment and dementia.

Intraindividual variability among cognitive domains may predict dementia independently of interindividual differences in cognition. A multidomain cognitive battery was administered to 2305 older adult women (mean age 74 years) enrolled in an ancillary study of the Womens Health Initiative. Women were evaluated annually for probable dementia and mild cognitive impairment (MCI) for an average of 5.3 years using a standardized protocol. Proportional hazards regression showed that lower baseline domain-specific cognitive scores significantly predicted MCI (N = 74), probable dementia (N = 45), and MCI or probable dementia combined (N = 101) and that verbal and figural memory predicted each outcome independently of all other cognitive domains. The baseline intraindividual standard deviation across test scores (IAV Cognitive Domains) significantly predicted probable dementia and this effect was attenuated by interindividual differences in verbal episodic memory. Slope increases in IAV Cognitive Domains across measurement occasions (IAV Time) explained additional risk for MCI and MCI or probable dementia, beyond that accounted for by interindividual differences in multiple cognitive measures, but risk for probable dementia was attenuated by mean decreases in verbal episodic memory slope. These findings demonstrate that within-person variability across cognitive domains both at baseline and longitudinally independently accounts for risk of cognitive impairment and dementia in support of the predictive utility of within-person variability.

Off-hours admission to pediatric intensive care and mortality

BACKGROUND: Critically ill patients are admitted to the pediatric ICU at all times, while staffing and other factors may vary by day of the week or time of day. The purpose of this study was to evaluate whether admission during off-hours is independently associated with mortality in PICUs. METHODS: A retrospective cohort study of admissions of patients <18 years of age to PICUs was performed using the Virtual PICU Systems (VPS, LLC) database. “Off-hours” was defined as nighttime (7:00 pm to 6:59 am) or weekend (Saturday or Sunday any time). Mixed-effects multivariable regression was performed by using Pediatric Index of Mortality 2 (PIM2) to adjust for severity of illness. Primary outcome was death in the pediatric ICU. RESULTS: Data from 234 192 admissions to 99 PICUs from January 2009 to September 2012 were included. When compared with regular weekday admissions, off-hours admissions were less likely to be elective, had a higher risk for mortality by PIM2, and had a higher observed ICU mortality (off-hours 2.7% vs weekdays 2.2%; P < .001). Multivariable regression revealed that, after adjustment for other significant factors, off-hours admission was associated with lower odds of mortality (odds ratio, 0.91; 95% confidence interval, 0.85–0.97; P = .004). Post hoc multivariable analysis revealed that admission during the morning period 6:00 am to 10:59 am was independently associated with death (odds ratio, 1.27; 95% confidence interval, 1.16–1.39; P < .0001). CONCLUSIONS: Off-hours admission does not independently increase odds of death in the PICU. Admission from 6:00 am to 10:59 am is associated with increased risk for death and warrants further investigation in the PICU population.

Kronecker Product Linear Exponent AR(1) Correlation Structures for Multivariate Repeated Measures

Longitudinal imaging studies have moved to the forefront of medical research due to their ability to characterize spatio-temporal features of biological structures across the lifespan. Credible models of the correlations in longitudinal imaging require two or more pattern components. Valid inference requires enough flexibility of the correlation model to allow reasonable fidelity to the true pattern. On the other hand, the existence of computable estimates demands a parsimonious parameterization of the correlation structure. For many one-dimensional spatial or temporal arrays, the linear exponent autoregressive (LEAR) correlation structure meets these two opposing goals in one model. The LEAR structure is a flexible two-parameter correlation model that applies to situations in which the within-subject correlation decreases exponentially in time or space. It allows for an attenuation or acceleration of the exponential decay rate imposed by the commonly used continuous-time AR(1) structure. We propose the Kronecker product LEAR correlation structure for multivariate repeated measures data in which the correlation between measurements for a given subject is induced by two factors (e.g., spatial and temporal dependence). Excellent analytic and numerical properties make the Kronecker product LEAR model a valuable addition to the suite of parsimonious correlation structures for multivariate repeated measures data. Longitudinal medical imaging data of caudate morphology in schizophrenia illustrates the appeal of the Kronecker product LEAR correlation structure.