  Studies of Alzheimer's disease (AD) often collect multiple longitudinal
clinical outcomes, which are correlated and predictive of AD progression. It is
of great scientific interest to investigate the association between the
outcomes and time to AD onset. We model the multiple longitudinal outcomes as
multivariate sparse functional data and propose a functional joint model
linking multivariate functional data to event time data. In particular, we
propose a multivariate functional mixed model (MFMM) to identify the shared
progression pattern and outcome-specific progression patterns of the outcomes,
which enables more interpretable modeling of associations between outcomes and
AD onset. The proposed method is applied to the Alzheimer's Disease
Neuroimaging Initiative study (ADNI) and the functional joint model sheds new
light on inference of five longitudinal outcomes and their associations with AD
onset. Simulation studies also confirm the validity of the proposed model.
