Differential network knockoff filter with application to brain connectivity analysis

The brain functional connectivity can typically be represented as a brain functional network, where nodes represent regions of interest (ROIs) and edges symbolize their connections. Studying group differences in brain functional connectivity can help identify brain regions and recover the brain functional network linked to neurodegenerative diseases. This process, known as differential network analysis focuses on the differences between estimated precision matrices for two groups. Current methods struggle with individual heterogeneity in measuring the brain connectivity, false discovery rate (FDR) control, and accounting for confounding factors, resulting in biased estimates and diminished power. To address these issues, we present a two-stage FDR-controlled feature selection method for differential network analysis using functional magnetic resonance imaging (fMRI) data. First, we create individual brain connectivity measures using a high-dimensional precision matrix estimation technique. Next, we devise a penalized logistic regression model that employs individual brain connectivity data and integrates a new knockoff filter for FDR control when detecting significant differential edges. Through extensive simulations, we showcase the superiority of our approach compared to other methods. Additionally, we apply our technique to fMRI data to identify differential edges between Alzheimer's disease and control groups. Our results are consistent with prior experimental studies, emphasizing the practical applicability of our method.