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We introduce a numerically tractable formulation of Bayesian joint models forlongitudinal and survival data. The longitudinal process is modelled usinggeneralised linear mixed models, while the survival process is modelled using aparametric general hazard structure. The two processes are linked by sharingfixed and random effects, separating the effects that play a role at the timescale from those that affect the hazard scale. This strategy allows for theinclusion of non-linear and time-dependent effects while avoiding the need fornumerical integration, which facilitates the implementation of the proposedjoint model. We explore the use of flexible parametric distributions formodelling the baseline hazard function which can capture the basic shapes ofinterest in practice. We discuss prior elicitation based on the interpretationof the parameters. We present an extensive simulation study, where we analysethe inferential properties of the proposed models, and illustrate the trade-offbetween flexibility, sample size, and censoring. We also apply our proposal totwo real data applications in order to demonstrate the adaptability of ourformulation both in univariate time-to-event data and in a competing risksframework. The methodology is implemented in rstan.

A tractable Bayesian joint model for longitudinal and survival data