A joint model for survival time and the quantiles of a related longitudinal process Seminar

We propose a joint model for a time-to-event outcome and any quantile of a continuous response repeatedly measured over time. The quantile and survival processes are associated via shared latent and manifest variables. The model can be seen as a generalization to quantile regression of shared-parameter models for longitudinal regression with informative drop-out. It can also be used as a tool for dealing with skewed error terms in the measurement error of time-dependent covariates in survival models. We relax the commonly used assumptions of low dimensionality and joint normality of random effects and response error terms, by proposing an original Monte Carlo Expectation Maximization strategy based on importance sampling. This approach is directly applicable under any distributional assumption for the longitudinal outcome and random effects, and parametric and non-parametric assumptions for the baseline hazard. We illustrate through a simulation study and an application to an original data set about the left ventricular ejection fraction of patients with dilated cardiomyopathies.