  Background: The most widely used approach to joint modelling of repeated
measurement and time to event data is to combine a linear Gaussian random
effects model for the repeated measurements with a log-Gaussian frailty model
for the time-to-event outcome, linking the two through some form of correlation
structure between the random effects and the log-frailty. In this approach,
covariates are assumed to affect the mean response profile of the repeated
measurement data. Objectives: Some applications raise substantive questions
that cannot be captured by this structure. For example, an important question
in cystic fibrosis (CF) research is to understand the impact of a patient's
lung function trajectory on their risk of acquiring a variety of infections,
and how this varies at different quantiles of the lung function distribution.
Methods: Motivated by this question, we develop a joint quantile modelling
framework in this paper with an associated Markov Chain Monte Carlo algorithm
for Bayesian inference. Results: The translation from the common joint model
towards quantile regression succeeds and is applied to CF data from the United
Kingdom. The method helps detecting an overall difference in the relation
between lung function decline and onset of infection in the different
quantiles. Conclusions: Joint modelling without taking into account the special
heteroscedastic structure is not sufficient in certain research question and
the extensions towards models beyond the mean is necessary.
