The Annals of Applied Statistics
- Ann. Appl. Stat.
- Volume 10, Number 4 (2016), 1930-1957.
Investigating differences in brain functional networks using hierarchical covariate-adjusted independent component analysis
Human brains perform tasks via complex functional networks consisting of separated brain regions. A popular approach to characterize brain functional networks in fMRI studies is independent component analysis (ICA), which is a powerful method to reconstruct latent source signals from their linear mixtures. In many fMRI studies, an important goal is to investigate how brain functional networks change according to specific clinical and demographic variabilities. Existing ICA methods, however, cannot directly incorporate covariate effects in ICA decomposition. Heuristic post-ICA analysis to address this need can be inaccurate and inefficient. In this paper, we propose a hierarchical covariate-adjusted ICA (hc-ICA) model that provides a formal statistical framework for estimating covariate effects and testing differences between brain functional networks. Our method provides a more reliable and powerful statistical tool for evaluating group differences in brain functional networks while appropriately controlling for potential confounding factors. We present an analytically tractable EM algorithm to obtain maximum likelihood estimates of our model. We also develop a subspace-based approximate EM that runs significantly faster while retaining high accuracy. To test the differences in functional networks, we introduce a voxel-wise approximate inference procedure which eliminates the need of computationally expensive covariance matrix estimation and inversion. We demonstrate the advantages of our methods over the existing method via simulation studies. We apply our method to an fMRI study to investigate differences in brain functional networks associated with post-traumatic stress disorder (PTSD).
Ann. Appl. Stat., Volume 10, Number 4 (2016), 1930-1957.
Received: November 2014
Revised: April 2016
First available in Project Euclid: 5 January 2017
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Shi, Ran; Guo, Ying. Investigating differences in brain functional networks using hierarchical covariate-adjusted independent component analysis. Ann. Appl. Stat. 10 (2016), no. 4, 1930--1957. doi:10.1214/16-AOAS946. https://projecteuclid.org/euclid.aoas/1483606846
- Supplement to the paper “Investigating differences in brain functional networks using hierarchical covariate-adjusted independent component analysis”. This document presents the following contents: details about our EM algorithm and the approximate EM algorithm; the proof of Theorem 1; the criteria of selecting activating voxels within each brain network; the specification of initial guesses to our algorithm; additional simulation results with $q=10$; additional simulation results and theoretical results on the robustness of the approximate EM; additional results on the robustness of our method in real data analysis.