High-Dimensional Smoothing Splines and Application in Alzheimer’s Disease Prediction Using Magnetic Resonance Imaging

Recent evidence has shown that structural magnetic resonance imaging (MRI) is an effective tool for Alzheimer’s disease (AD) prediction. While traditional MRI-based prediction uses images acquired at a single time point, a longitudinal study is more sensitive and accurate in detecting early pathological changes of the AD. Two main statistical difficulties arise in the longitudinal MRI-based analysis: (i) the inconsistent longitudinal scans among subjects (i.e., the different scanning time and the different total number of scans); (ii) the heterogeneous progressions of high-dimensional regions of interest (ROIs) in MRI. In this work, we propose a new feature selection and estimation method which can be applied to extract AD-related features from the heterogeneous longitudinal MRI. A key ingredient of our approach is a hybrid of the smoothing splines and the l1-penalty. Smoothing splines can integrate information from heterogeneous progressions of ROIs and adapt to inconsistent scans of MRIs. The selection property of the l1-penalty helps to select important ROIs related to AD. We introduce an efficient algorithm to perform the proposed method. Real data experiments on the Alzheimer’s Disease Neuroimaging Initiative database are provided to corroborate some advantages of the proposed method for AD prediction in longitudinal studies.