Stable Non-Linear Generalized Bayesian Joint Models for Survival-Longitudinal Data

Abstract

Joint models have received increasing attention during recent years with extensions into various directions; numerous hazard functions, different association structures, linear and non-linear longitudinal trajectories amongst others. Here, we present a partially linear joint model with a Bayesian smoothing spline component to capture non-linear longitudinal trajectories where the longitudinal data can assume non-Gaussian distributions. Our approach is stable with regards to the knot set as opposed to most well-known spline models. We implement this method using the R-INLA package and show that most joint models with shared Gaussian random effects are part of the class of latent Gaussian models (LGMs). We present an illustrative example to show the use of the stable partially linear joint model and an application to real data using a skew-normal partially linear joint model. This paves the way for efficient implementation of joint models with various complex model components using the same methodology and computational platform.