Graph combinatorics based group-level network inference for brain connectome analysis

Abstract We consider group-level statistical inference for networks, where outcomes are multivariate edge variables constrained in an adjacency matrix. The graph notation is used to represent the network outcome variables, where nodes are identical biological units (e.g. brain regions) shared across subjects and edge-variables indicate the strengths of the interactive relationships between nodes. The edge-variables vary across subjects and may be associated with covariates of interest. The statistical inference for multivariate edge-variables is challenging because both localized inference on individual edges and the joint inference of a combinatorial of edges (network-level) are desired. We develop a group-level network inference model to integrate graph theory and combinatorics into group-level network statistical inference. We first propose an objective function with ?0 norm regularization to capture latent subgraphs/subnetworks accurately by suppressing false positive edges. We next statistically test each detected subnetwork using graph combinatorics based statistical inferential procedure. We apply the proposed approach to a brain connectome study to identify latent brain functional subnetworks that are associated with brain disorders and verify the findings using an independent replicate data set. The results demonstrate the proposed method outperform existing multivariate statistical methods by simultaneously reducing false positive and false negative discovery rates and increasing replicability.