Degree-based statistic

Abstract

Large-scale analyses of brain networks are informative. Previous studies have shown small-worldness, hierarchical and modular organization of the brain. In addition to large-scale approaches, localized connectivity analyses are widely performed. One of the major issues in connectivity analysis is a mass-univariate hypothesis testing problem from a huge number of edge elements in a connectivity matrix. To solve this, several cluster-wise correction methods have been suggested. Cluster-wise inference was previously provided for the analysis of brain MR imaging data. It has been shown to work successfully with higher sensitivity and now been applied to the brain connectivity analysis. However cluster-wise inferences have basically two shortcomings in common

a lack of localization power and arbitrariness of an initial cluster-forming threshold. First, a result from cluster-wise inference cannot be used to infer a significance of each element (i.e. voxel in MRI or edge in connectivity matrix) in a cluster. A cluster of a result is allowed to report as it is. Second, cluster-wise inference requires an initial cluster-forming threshold. The selection of an initial threshold depends on researcher’s arbitrary decision. In this study, I propose a novel method, degree-based statistic (DBS), to control for the family-wise error in multiple testing using the graph theoretical concept of the degree. From a network perspective, a small number of regions are of critical importance and considered as hubs playing pivotal roles in network integration and thus in brain function. Regarding this notion, DBS defines a cluster as a set of edges connected to a single node. This definition enables the efficient detection of clusters and their centric nodes that have significant associations with an effect of interest. In other words, this definition helps to increase spatial specificity (localization power) of the result. In addition, DBS is developed to resolve, at least partially, the arbitrariness of an initial cluster-forming threshold. For this purpose, I define a new measure of a cluster, centre persistency (CP). This CP score is computed for every cluster and the significance of each score is estimated. I tested DBS in variable situations. DBS was applied to 4 different datasets and demonstrated that DBS successfully detects the persistent clusters centres. In conclusion, I proposed a novel method, degree-based statistic (DBS). By adopting a graph theoretical concept of degrees and borrowing the concept of persistence from algebraic topology, DBS could sensitively identify clusters having centric nodes that would play pivotal roles in an effect of interest. I demonstrated that DBS is widely applicable to cognitive or clinical studies and yields statistically robust and easily interpretable results.