  We propose a joint model for a time-to-event outcome and a quantile of a
continuous response repeatedly measured over time. The quantile and survival
processes are associated via shared latent and manifest variables. Our joint
model provides a flexible approach to handle informative drop-out in quantile
regression. A general Monte Carlo Expectation Maximization strategy based on
importance sampling is proposed, which is directly applicable under any
distributional assumption for the longitudinal outcome and random effects, and
parametric and non-parametric assumptions for the baseline hazard. Model
properties are illustrated through a simulation study and an application to an
original data set about dilated cardiomyopathies.
