Statistical Network Analysis of High-Dimensional Neuroimaging Data With Complex Topological Structures

Abstract

This dissertation contains three projects that collectively tackle statistical challenges in the field of high-dimensional brain connectome data analysis and enhance our understanding of the intricate workings of the human brain. Project 1 proposes a novel network method for detecting brain-disease-related alterations in voxel-pair-level brain functional connectivity with spatial constraints, thus improving spatial specificity and sensitivity. Its effectiveness is validated through extensive simulations and real data applications in nicotine addiction and schizophrenia studies. Project 2 introduces a multivariate multiple imputation method specifically designed for voxel-level neuroimaging data in high dimensions based on Bayesian models and Markov chain Monte Carlo processes. According to both synthetic data and real neurovascular water exchange data extracted from a neuroimaging dataset in a schizophrenia study, our method indicates high imputation accuracy and computational efficiency. Project 3 develops a multi-level network model based on graph combinatorics that captures vector-to-matrix associations between brain structural imaging measures and functional connectomic networks. The validity of the proposed model is justified through extensive simulations and a real structure-function imaging dataset from UK Biobank. These three projects contribute innovative methodologies and insights that advance neuroimaging data analysis, including improvements in spatial specificity, statistical power, imputation accuracy, and computational efficiency when revealing the brain’s complex neurological patterns.