Functional joint model for longitudinal and time-to-event data: an application to Alzheimer's disease.

Functional data are increasingly collected in public health and medical studies to better understand many complex diseases. Besides the functional data, other clinical measures are often collected repeatedly. Investigating the association between these longitudinal data and time to a survival event is of great interest to these studies. In this article, we develop a functional joint model (FJM) to account for functional predictors in both longitudinal and survival submodels in the joint modeling framework. The parameters of FJM are estimated in a maximum likelihood framework via expectation maximization algorithm. The proposed FJM provides a flexible framework to incorporate many features both in joint modeling of longitudinal and survival data and in functional data analysis. The FJM is evaluated by a simulation study and is applied to the Alzheimer's Disease Neuroimaging Initiative study, a motivating clinical study testing whether serial brain imaging, clinical, and neuropsychological assessments can be combined to measure the progression of Alzheimer's disease.