Longitudinal quantile regression in the presence of informative dropout through longitudinal-survival joint modeling.

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 dropout in quantile regression. A 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. We consider both parametric and nonparametric assumptions for the baseline hazard. We illustrate through a simulation study and an application to an original data set about dilated cardiomyopathies.