  Joint models initially dedicated to a single longitudinal marker and a single
time-to-event need to be extended to account for the rich longitudinal data of
cohort studies. Multiple causes of clinical progression are indeed usually
observed, and multiple longitudinal markers are collected when the true latent
trait of interest is hard to capture (e.g. quality of life, functional
dependency, cognitive level). These multivariate and longitudinal data also
usually have nonstandard distributions (discrete, asymmetric, bounded,...). We
propose a joint model based on a latent process and latent classes to analyze
simultaneously such multiple longitudinal markers of different natures, and
multiple causes of progression. A latent process model describes the latent
trait of interest and links it to the observed longitudinal outcomes using
flexible measurement models adapted to different types of data, and a latent
class structure links the longitudinal and the cause-specific survival models.
The joint model is estimated in the maximum likelihood framework. A score test
is developed to evaluate the assumption of conditional independence of the
longitudinal markers and each cause of progression given the latent classes. In
addition, individual dynamic cumulative incidences of each cause of progression
based on the repeated marker data are derived. The methodology is validated in
a simulation study and applied on real data about cognitive aging coming from a
large population-based study. The aim is to predict the risk of dementia by
accounting for the competing death according to the profiles of semantic memory
measured by two asymmetric psychometric tests.
