Supervised Functional Principal Component Analysis Under the Mixture Cure Rate Model: An Application to Alzheimer'S Disease

Brain imaging data is one of the primary predictors for assessing the risk of Alzheimer's disease (AD). This study aims to extract image-based features associated with the possibly right-censored time-to-event outcomes and to improve predictive performance. While the functional proportional hazards model is well-studied in the literature, these studies often do not consider the existence of patients who have a very low risk and are approximately insusceptible to AD. We introduce a functional mixture cure rate model that extends the proportional hazards model by allowing a proportion of event-free patients. We propose a novel supervised functional principal component analysis (sFPCA) method to extract image features associated with AD risk while accounting for the complexity arising from right censoring. The proposed method accommodates the irregular boundary issue inherent in brain images with bivariate splines over triangulations. We demonstrate the advantages of the proposed method through extensive simulation studies and provide an application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study.