Functional magnetic resonance imaging (fMRI) is a powerful tool for the in vivo study of the pathophysiology of brain disorders and disease. In this manuscript, we propose an analysis stream for fMRI functional connectivity data and apply it to a novel study of Alzheimer's disease. In the first stage, spatial independent component analysis is applied to group fMRI data to obtain common brain networks (spatial maps) and subject-specific mixing matrices (time courses). In the second stage, functional principal component analysis is utilized to decompose the mixing matrices into population-level eigenvectors and subject-specific loadings. Inference is performed using permutation-based exact logistic regression for matched pairs data. The method is applied to a novel fMRI study of Alzheimer's disease risk under a verbal paired associates task. We found empirical evidence of alternative ICA-based metrics of connectivity when comparing subjects evidencing mild cognitive impairment relative to carefully matched controls.