Prediction of Cognitive Function via Brain Region Volumes with Applications to Alzheimer’s Disease Based on Space-Factor-Guided Functional Principal Component Analysis

Alzheimer’s disease (AD) is a prevalent and irreversible brain disorder and early prediction of cognitive function is vital for detecting the onset. The volumes of brain regions can serve as features for predicting cognitive decline, facilitating early detection and intervention. In order to offer a comprehensive representation of brain tissue changes in AD, we employ volume density curves to investigate the relationship between brain regions and cognitive function. However, analyzing these volume curves is complex due to their highly spatial and intrinsic dependence and piecewise structure. To address these challenges, we propose Space-Factor-Guided Functional Principal Component Analysis (SF-FPCA). This method uses factor processes to extract low-dimensional features for intrinsic correlations among regions of interest (ROIs) and applies Functional Principal Component Analysis (FPCA) to these processes to address temporal dependence. Furthermore, by decomposing the loadings into smooth functions of spatial coordinates and a piecewise constant matrix, we identify regions exhibiting smoothness within each region while discontinuities between these regions. We apply SF-FPCA to analyze data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI). Our results demonstrate that SF-FPCA provides the best fit compared to other methods. In addition, features extracted from volume curves using SF-FPCA enable more accurate prediction of cognitive function compared to scalar volumes alone. Leveraging these extracted features, we identify 36 important ROIs influencing cognitive decline. Our investigation into brain atrophy also reveals distinct mechanisms between the left and right hemispheres, shedding light on the nuanced effects of brain region changes on cognitive decline in AD. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.