Functional linear regression model with randomly censored data: Predicting conversion time to Alzheimer ’s disease

Predicting the onset time of Alzheimer's disease is of great importance in preventive medicine. Structural changes in brain regions have been actively investigated in the association study of Alzheimer's disease diagnosis and prognosis. In this study, we propose a functional linear regression model to predict the conversion time to Alzheimer's disease among mild cognitive impairment patients. Midsagittal thickness change in corpus callosum is measured from magnetic resonance imaging scan and put into the model as a functional covariate. A synthetic response approach is taken to deal with the censored data. The simulation studies demonstrate that the proposed model successfully predicts the unobserved true survival time but indicate that high censoring rate may cause poor prediction in time. Through ADNI data application, we find that the atrophy in the rear area of corpus callosum is a possible neuroimaging marker on Alzheimer's disease prognosis.