Joint models as latent Gaussian models - not reinventing the wheel
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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. Many of these resulted in new R packages and new formulations of the joint model. However, a joint model with a linear bivariate Gaussian association structure is still a latent Gaussian model (LGM) and thus can be implemented using most existing packages for LGM's. In this paper, we will show that these joint models can be implemented from a LGM viewpoint using the R-INLA package. As a particular example, we will focus on the joint model with a non-linear longitudinal trajectory, recently developed and termed the partially linear joint model. Instead of the usual spline approach, we argue for using a Bayesian smoothing spline framework for the joint model that is stable with respect to knot selection and hence less cumbersome for practitioners.
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