Mixed Effects Models for Resampled Network Statistics Improves Statistical Power to Find Differences in Multi-Subject Functional Connectivity

Abstract

Many complex brain disorders, such as autism spectrum disorders, exhibit a wide range of symptoms and disability. To understand how brain communication is impaired in such conditions, functional connectivity studies seek to understand individual differences in brain network structure in terms of covariates that measure symptom severity. In practice, however, functional connectivity is not observed but estimated from complex and noisy neural activity measurements. Imperfect subject network estimates can compromise subsequent efforts to detect covariate effects on network structure. We address this problem in the case of Gaussian graphical models of functional connectivity, by proposing novel two-level models that treat both subject level networks and population level covariate effects as unknown parameters. To account for imperfectly estimated subject level networks when fitting these models, we propose two related approaches-R 2 based on resampling and random effects test statistics, and R 3 that additionally employs random adaptive penalization. Simulation studies using realistic graph structures reveal that R 2 and R 3 have superior statistical power to detect covariate effects compared to existing approaches, particularly when the number of within subject observations is comparable to the size of subject networks. Using our novel models and methods to study parts of the ABIDE dataset, we find evidence of hypoconnectivity associated with symptom severity in autism spectrum disorders, in frontoparietal and limbic systems as well as in anterior and posterior cingulate cortices.

Statistical Approaches for the Study of Cognitive and Brain Aging

“…For testing the brain network differences between groups such as young vs. older, there are three levels of tests including the edge-level, node-level, and subgraph-level (Nichols and Holmes, 2002 ; Kim et al, 2014 , 2015 ; Narayan and Allen, 2016 ). The edge-level testing approach first tests the group differences at the edges one by one, then applies multiple correction for the p -values such as FDR correction.…”

Statistical testing and power analysis for brain-wide association study

“…Third, the estimation of subject-level functional network is based on the Pearson correlation between pairwise BOLD signal time series in the current framework, which may be suboptimal [Westfall and Yarkoni, 2016;Bellec et al, 2008;Sahib et al, 2016]. Therefore, a better approach for constructing a functional network at the voxel level should be designed and validated in the future [Narayan and Allen, 2016;Bickel and Levina, 2008]. Fourth, with the higher volume of available data, statistical methods for combining BWAS results from multiple imaging centers are needed.…”

Edgewise and subgraph‐level tests for brain networks

“…Random sampling of the subjects such as bootstrap or subsample without replacement is often used to generate the stability criteria. In the recent work , bootstrap of the time series was used to obtain the variation of the graphical summary indices. Stability criteria have been shown to outperform other methods such as cross‐validation, AIC, and BIC .…”