A regression framework for brain network distance metrics

Analyzing brain networks has long been a prominent research topic in neuroimaging. However, statistical methods to detect differences between these networks and relate them to phenotypic traits are still sorely needed. Our previous work developed a novel permutation testing framework to detect differences between two groups. Here we advance that work to allow both assessing differences by continuous phenotypes and controlling for confounding variables. To achieve this, we propose an innovative regression framework to relate distances between brain network features to functions of absolute differences in continuous covariates and indicators of difference for categorical variables. We explore several similarity metrics for comparing distances between connection matrices, and adapt several standard methods for estimation and inference within our framework: Standard F-test, F-test with individual level effects (ILE), Generalized Least Squares (GLS), Mixed Model, and Permutation. We also propose a novel modification of the standard GLS approach for estimation and inference. We assess all approaches for estimation and inference via simulation studies, and illustrate the utility of our framework by analyzing the relationship between fluid intelligence and brain network distances in Human Connectome Project (HCP) data.