  As other neurodegenerative diseases, Alzheimer's disease, the most frequent
dementia in the elderly, is characterized by multiple progressive impairments
in the brain structure and in clinical functions such as cognitive functioning
and functional disability. Until recently, these components were mostly studied
independently since no joint model for multivariate longitudinal data and time
to event was available in the statistical community. Yet, these components are
fundamentally inter-related in the degradation process towards dementia and
should be analyzed together. We thus propose a joint model to simultaneously
describe the dynamics of multiple correlated components. Each component,
defined as a latent process, is measured by one or several continuous markers
(not necessarily Gaussian). Rather than considering the associated time to
diagnosis as in standard joint models, we assume diagnosis corresponds to the
passing above a covariate-specific threshold (to be estimated) of a
pathological process which is modelled as a combination of the
component-specific latent processes. This definition captures the clinical
complexity of diagnoses such as dementia diagnosis but also benefits from
simplifications for the computation of Maximum Likelihood Estimates. We show
that the model and estimation procedure can also handle competing clinical
endpoints. The estimation procedure, implemented in a R package, is validated
by simulations and the method is illustrated on a large French population-based
cohort of cerebral aging in which we focused on the dynamics of three clinical
manifestations and the associated risk of dementia and death before dementia.
