  In health cohort studies, repeated measures of markers are often used to
describe the natural history of a disease. Joint models allow to study their
evolution by taking into account the possible informative dropout usually due
to clinical events. However, joint modeling developments mostly focused on
continuous Gaussian markers while, in an increasing number of studies, the
actual quantity of interest is non-directly measurable; it constitutes a latent
variable evaluated by a set of observed indicators from questionnaires or
measurement scales. Classical examples include anxiety, fatigue, cognition. In
this work,we explain how joint models can be extended to the framework of a
latent quantity measured over time by indicators of different nature (e.g.
continuous, binary, ordinal). The longitudinal submodel describes the evolution
over time of the quantity of interest defined as a latent process in a
structural mixed model, and links the latent process to each observation of the
indicators through appropriate measurement models. Simultaneously, the risk of
multi-cause event is modelled via a proportional cause-specific hazard model
that includes a function of the mixed model elements as linear predictor to
take into account the association between the latent process and the risk of
event. Estimation, carried out in the maximum likelihood framework and
implemented in the R-package JLPM, has been validated by simulations. The
methodology is illustrated in the French cohort on Multiple-System Atrophy
(MSA), a rare and fatal neurodegenerative disease, with the study of dysphagia
progression over time stopped by the occurrence of death.
