A Differential Degree Test for Comparing Brain Networks

Abstract

Recently, graph theory has become a popular method for characterizing brain functional organization. One important goal in graph theoretical analysis of brain networks is to identify network differences across disease types or conditions. Typical approaches include massive univariate testing of each edge or comparisons of local and/or global network metrics to identify deviations in topological organization. Some limitations of these methods include low statistical power due to the large number of comparisons and difficulty attributing overall differences in networks to local variations in brain function. We propose a novel differential degree test (DDT) to identify brain regions incident to a large number of differentially weighted edges across two populations. The proposed test could help detect key brain locations involved in diseases by demonstrating significantly altered neural connections. We achieve this by generating an appropriate set of null networks which are matched on the first and second moments of the observed difference network using the Hirschberger-Qi-Steuer (HQS) algorithm. This formulation permits separation of the network's true topology from the nuisance topology which is induced by the correlation measure and may drive inter-regional connectivity in ways unrelated to the brain function. Simulations indicate that the proposed approach routinely outperforms competing methods in detecting differentially connected regions of interest. Furthermore, we propose a data-adaptive threshold selection procedure which is able to detect differentially weighted edges and is shown to outperform competing methods that perform edge-wise comparisons controlling for the error rate. An application of our method to a major depressive disorder dataset leads to the identification of brain regions in the default mode network commonly implicated in this ruminative disorder.