  We introduce a numerically tractable formulation of Bayesian joint models for
longitudinal and survival data. The longitudinal process is modelled using
generalised linear mixed models, while the survival process is modelled using a
parametric general hazard structure. The two processes are linked by sharing
fixed and random effects, separating the effects that play a role at the time
scale from those that affect the hazard scale. This strategy allows for the
inclusion of non-linear and time-dependent effects while avoiding the need for
numerical integration, which facilitates the implementation of the proposed
joint model. We explore the use of flexible parametric distributions for
modelling the baseline hazard function which can capture the basic shapes of
interest in practice. We discuss prior elicitation based on the interpretation
of the parameters. We present an extensive simulation study, where we analyse
the inferential properties of the proposed models, and illustrate the trade-off
between flexibility, sample size, and censoring. We also apply our proposal to
two real data applications in order to demonstrate the adaptability of our
formulation both in univariate time-to-event data and in a competing risks
framework. The methodology is implemented in rstan.
