Kernel machine tests of association using extrinsic and intrinsic cluster evaluation metrics

Modeling the network topology of the human brain within the mesoscale has become an increasing focus within the neuroscientific community due to its variation across diverse cognitive processes, in the presence of neuropsychiatric disease or injury, and over the lifespan. Much research has been done on the creation of algorithms to detect these mesoscopic structures, called communities or modules, but less has been done to conduct inference on these structures. The literature on analysis of these community detection algorithms has focused on comparing them within the same subject. These approaches, however, either do not accomodate a more general association between community structure and an outcome or cannot accommodate additional covariates that may confound the association of interest. We propose a semiparametric kernel machine regression model for either a continuous or binary outcome, where covariate effects are modeled parametrically and brain connectivity measures are measured nonparametrically. By incorporating notions of similarity between network community structures into a kernel distance function, the high-dimensional feature space of brain networks, defined on input pairs, can be generalized to non-linear spaces, allowing for a wider class of distance-based algorithms. We evaluate our proposed methodology on both simulated and real datasets.Author summary: Parcellating the brain into clusters, which can be characterized as a way to describe the balance between dense relationships among areas highly engaged in the same processing tasks as well as sparser relationships between regions with different processing assignments, has been an area of recent focus within the neuroscientific community. While many algorithms exist to discover and characterize these clusters, there is a paucity of literature seeking to conduct inference on these parcellations between subjects. We have proposed a semiparametric kernel machine regression framework that can accommodate either a binary or continuous outcome, where brain connectivity measures are modeled nonparametrically and any additional covariates of interest (e.g., age, sex, etc.) are modeled parametrically. Evaluating our proposed methodology on both simulated and real datasets, we provide evidence of the robustness of this method within a single layer of clusters, thus showing the potential utility in the rapidly-changing field of network neuroscience.