A difference degree test for comparing brain networks.

Recently, there has been a proliferation of methods investigating functional connectivity as a biomarker for mental disorders. Typical approaches include massive univariate testing at each edge or comparisons of network metrics to identify differing topological features. Limitations of these methods include low statistical power due to the large number of comparisons and difficulty attributing overall differences in networks to local variation. We propose a method to capture the difference degree, which is the number of edges incident to each region in the difference network. Our difference degree test (DDT) is a two-step procedure for identifying brain regions incident to a significant number of differentially weighted edges (DWEs). First, we select a data-adaptive threshold which identifies the DWEs followed by a statistical test for the number of DWEs incident to each brain region. 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 algorithm. This formulation permits separation of the network's true topology from the nuisance topology induced by the correlation measure that alters interregional connectivity in ways unrelated to brain function. In simulations, the proposed approach outperforms competing methods in detecting differentially connected regions of interest. Application of DDT to a major depressive disorder dataset leads to the identification of brain regions in the default mode network commonly implicated in this ruminative disorder.