Statistical methods for high-dimensional data with complex correlation structure applied to the brain dynamic functional connectivity studyDY

Abstract

A popular non-invasive brain activity measurement method is based on the functional magnetic resonance imaging (fMRI). Such data are frequently used to study functional connectivity (FC) defined as statistical association among two or more anatomically distinct fMRI signals (Friston, 1994). FC has emerged in recent years as a valuable tool for providing a deeper understanding of neurodegenerative diseases and neuropsychiatric disorders, such as Alzheimer's disease and autism. Information about complex association structure in high-dimensional fMRI data is often discarded by a calculating an average across complex spatiotemporal processes without providing an uncertainty measure around it. First, we propose a non-parametric approach to estimate the uncertainty of dynamic FC (dFC) estimates. Our method is based on three components: an extension of a boot strapping method for multivariate time series, recently introduced by Jentsch and Politis (2015); sliding window correlation estimation; and kernel smoothing. Second, we propose a two-step approach to analyze and summarize dFC estimates from a task-based fMRI study of social-to-heavy alcohol drinkers during stimulation with avors. In the first step, we apply our method from the first paper to estimate dFC for each region subject combination. In the second step, we use semiparametric additive mixed models to account for complex correlation structure and model dFC on a population level following the study's experimental design. Third, we propose to utilize the estimated dFC to study the system's modularity defined as the mutually exclusive division of brain regions into blocks with intra-connectivity greater than the one obtained by chance. As a result, we obtain brain partition suggesting the existence of common functionally-based brain organization. The main contribution of our work stems from the combination of the methods from the fields of statistics, machine learning and network theory to provide statistical tools for studying brain connectivity from a holistic, multi-disciplinary perspective.