A tractable Bayesian joint model for longitudinal and survival data

TL;DR

This paper presents a computationally efficient Bayesian joint modeling approach for longitudinal and survival data, integrating flexible hazard functions and mixed models, with practical applications demonstrated through simulations and real data.

Contribution

It introduces a numerically tractable Bayesian joint model that combines generalized linear mixed models with flexible hazard structures, avoiding complex numerical integration.

Findings

Model effectively captures complex hazard shapes.

Simulation shows reliable inference with varying sample sizes.

Real data applications demonstrate model adaptability.

Abstract

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.