Methods for longitudinal complex network analysis in neuroscience
Shappell, Heather M.
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The study of complex brain networks, where the brain can be viewed as a system with various interacting regions that produce complex behaviors, has grown tremendously over the past decade. With both an increase in longitudinal study designs, as well as an increased interest in the neurological network changes that occur during the progression of a disease, sophisticated methods for dynamic brain network analysis are needed. We first propose a paradigm for longitudinal brain network analysis over patient cohorts where we adapt the Stochastic Actor Oriented Model (SAOM) framework and model a subject's network over time as observations of a continuous time Markov chain. Network dynamics are represented as being driven by various factors, both endogenous (i.e., network effects) and exogenous, where the latter include mechanisms and relationships conjectured in the literature. We outline an application to the resting-state fMRI network setting, where we draw conclusions at the subject level and then perform a meta-analysis on the model output. As an extension of the models, we next propose an approach based on Hidden Markov Models to incorporate and estimate type I and type II error (i.e., of edge status) in our observed networks. Our model consists of two components: 1) the latent model, which assumes that the true networks evolve according to a Markov process as they did in the original SAOM framework; and 2) the measurement model, which describes the conditional distribution of the observed networks given the true networks. An expectation-maximization algorithm is developed for estimation. Lastly, we focus on the study of percolation - the sudden emergence of a giant connected component in a network. This has become an active area of research, with relevance in clinical neuroscience, and it is of interest to distinguish between different percolation regimes in practice. We propose a method for estimating a percolation model from a given sequence of observed networks with single edge transitions. We outline a Hidden Markov Model approach and EM algorithm for the estimation of the birth and death rates for the edges, as well as the type I and type II error rates.