The INLA package provides a tool for computationally efficient Bayesian modeling and inference for various widely used models, more formally the class of latent Gaussian models. It is a non-sampling based framework which provides approximate results for Bayesian inference, using sparse matrices. The swift uptake of this framework for Bayesian modeling is rooted in the computational efficiency of the approach and catalyzed by the demand presented by the big data era. In this paper, we present new developments within the INLA package with the aim to provide a computationally efficient mechanism for the Bayesian inference of relevant challenging situations.

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The INLA package provides a tool for computationally efficient Bayesian modeling and inference for various widely used models, more formally the class of latent Gaussian models. It is a non-sampling based framework which provides approximate results for Bayesian inference, using sparse matrices. The swift uptake of this framework for Bayesian modeling is rooted in the computational efficiency of the approach and catalyzed by the demand presented by the big data era. In this paper, we present new developments within the INLA package with the aim to provide a computationally efficient mechanism for the Bayesian inference of relevant challenging situations.

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.

The methodological advancements made in the field of joint models are numerous. None the less, the case of competing risks joint models has largely been neglected, especially from a practitioner's point of view. In the relevant works on competing risks joint models, the assumptions of a Gaussian linear longitudinal series and proportional cause-specific hazard functions, amongst others, have remained unchallenged. In this article, we provide a framework based on R-INLA to apply competing risks joint models in a unifying way such that non-Gaussian longitudinal data, spatial structures, times-dependent splines and various latent association structures, to mention a few, are all embraced in our approach. Our motivation stems from the SANAD trial which exhibits non-linear longitudinal trajectories and competing risks for failure of treatment. We also present a discrete competing risks joint model for longitudinal count data as well as a spatial competing risks joint model as specific examples.