Brain network analyses have exploded in recent years and hold great potential in helping us understand normal and abnormal brain function. Network science approaches have facilitated these analyses and our understanding of how the brain is structurally and functionally organized. However, the development of statistical methods that allow relating this organization to phenotypic traits has lagged behind. Our previous work developed a novel analytic framework to assess the relationship between brain network architecture and phenotypic differences while controlling for confounding variables. More specifically, this innovative regression framework related distances (or similarities) between brain network features from a single task to functions of absolute differences in continuous covariates and indicators of difference for categorical variables. Here we extend that work to the multitask and multisession context to allow for multiple brain networks per individual. 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 scan-level effects (SLE), and our proposed mixed model for multitask (and multisession) BrAin NeTwOrk Regression (3M_BANTOR). A novel strategy is implemented to simulate symmetric positive-definite (SPD) connection matrices, allowing for the testing of metrics on the Riemannian manifold. Via simulation studies, we assess all approaches for estimation and inference while comparing them with existing multivariate distance matrix regression (MDMR) methods. We then illustrate the utility of our framework by analyzing the relationship between fluid intelligence and brain network distances in Human Connectome Project (HCP) data.

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 (or similarities) 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 (or similarities) 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), feasible generalized least squares (FGLS), and permutation. Via simulation studies, we assess all approaches for estimation and inference while comparing them with existing multivariate distance matrix regression (MDMR) methods. We then illustrate the utility of our framework by analyzing the relationship between fluid intelligence and brain network distances in Human Connectome Project (HCP) data.