Bayesian inference and dynamic prediction of multivariate joint model with functional data: An application to Alzheimer's disease

Alzheimer's disease (AD) is a severe neurodegenerative disorder impairing multiple domains, for example, cognition and behavior. Assessing the risk of AD progression and initiating timely interventions at early stages are critical to improve the quality of life for AD patients. Due to the heterogeneous nature and complex mechanisms of AD, one single longitudinal outcome is insufficient to assess AD severity and disease progression. Therefore, AD studies collect multiple longitudinal outcomes, including cognitive and behavioral measurements, as well as structural brain images such as magnetic resonance imaging (MRI). How to utilize the multivariate longitudinal outcomes and MRI data to make efficient statistical inference and prediction is an open question. In this article, we propose a multivariate joint model with functional data (MJM-FD) framework that relates multiple correlated longitudinal outcomes to a survival outcome, and use the scalar-on-function regression method to include voxel-based whole-brain MRI data as functional predictors in both longitudinal and survival models. We adopt a Bayesian paradigm to make statistical inference and develop a dynamic prediction framework to predict an individual's future longitudinal outcomes and risk of a survival event. We validate the MJM-FD framework through extensive simulation studies and apply it to the motivating Alzheimer's Disease Neuroimaging Initiative (ADNI) study.