The Integrated Nested Laplace Approximations methodology

We first introduce and briefly outline Bayesian inference and the specifics of the Integrated Nested Laplace Approximations (INLA) methodology. While algorithms like Markov Chain Monte Carlo (MCMC) are more general and capable of handling a broader spectrum of models, INLA can only be applied to models that can be formulated as latent Gaussian models (LGMs). However, the flexibility of LGMs comes to the forefront, as many diverse models, including mixed effects, temporal, spatial, and survival models, can be effectively formulated within the LGM framework. This characteristic makes INLA a powerful tool for a wide range of practical applications, showcasing its versatility in accommodating various models that fall under the umbrella of LGMs. We give an overview of the INLA method to compute the posterior density functions of interest and its recent enhancements, with relevant references for more details. We then present the user interface INLAjoint to define different regression models for both longitudinal and survival data as LGMs. This formulation establishes a cohesive framework, aligning these models with the INLA methodology. Consequently, it enables the creation of flexible joint models that include both longitudinal and survival components.