Bayesian Survival, Longitudinal, and Joint Models with INLA
- Published
- May 5, 2026
- Publisher
- Chapman & Hall/CRC, Taylor & Francis Group
- ISBN
- 9781041087694
This free HTML version is maintained by agreement with the publisher. The official published version is available from Routledge and Taylor & Francis.
Preface
Modern biomedical research, particularly in fields such as epidemiology and clinical trials, is increasingly relying on complex, high-dimensional data. Longitudinal studies, which monitor subjects over time, now routinely collect repeated measurements of multiple biomarkers, quality-of-life metrics, and other health outcomes. On the other hand, time-to-event data, such as disease progression or mortality, remains a central focus for clinical evaluation. The combination of these data types in a statistical analysis represents a significant challenge. Longitudinal data are characterized by hierarchical correlation structures, as repeated measurements within the same individual are inherently related. Survival data involves specific mechanisms such as censoring, where the event of interest is not observed for all subjects, requiring specialized statistical techniques to handle this incomplete information correctly.
Bayesian hierarchical models naturally handle key features of both survival and longitudinal data, including the censoring mechanisms inherent in survival data and the clustered nature of longitudinal data, which is accommodated through the inclusion of random effects. This concept of random effects extends to survival analysis through the use of “frailty” terms to model correlated risks and forms the basis of joint modeling, where the association between the longitudinal and survival processes is captured by linking them through these shared random effects.
Conventional approaches to fit complex regression models often rely on iterative, sampling-based methods. While often asymptotically exact, such methods are computationally expensive for the highly parameterized hierarchical models required for longitudinal and survival data. The computational limitations of traditional methods have limited the scientific questions of interest that could be asked. The inability to fit complex multivariate joint models for survival and longitudinal data in a reasonable computation time has often forced researchers to rely on simpler models. While statisticians like George Box argued that models should be judged on their utility as useful approximations rather than their absolute correctness (i.e. “all models are wrong, but some are useful”), computational barriers can force a choice based on feasibility rather than scientific appropriateness. As noted by the statistician sir David Cox, models are by nature simplifications of reality, but the crucial question is whether they capture the important aspects of a system. When computational limits dictate model choice, the resulting simpler models risk being not only wrong but also fundamentally less useful, potentially leading to biased or misleading conclusions. In this context, there is a need for a new computational method to bridge the gap between advanced statistical theory and real-world clinical applications.
It is precisely this gap that the Integrated Nested Laplace Approximations (INLA) methodology fills. The methodology offers a solution to the computational challenges that have limited the use of complex regression models for survival and longitudinal data. Developed as a deterministic alternative to simulation-based methods like Markov chain Monte Carlo, INLA provides fast and accurate approximate Bayesian inference. Its efficiency is tailored to the flexible class of models known as latent Gaussian models, which includes the full range of survival, longitudinal and joint models discussed in this book. Instead of generating samples from the posterior distribution, INLA directly calculates highly accurate approximations of the posterior marginals for each model parameter, making it computationally feasible to fit complex models that were previously out of reach.
This book is the result of a four-year, intensive research collaboration among the authors within the Bayesian Computational Statistics & Modeling (BAYESCOMP) group at King Abdullah University of Science and Technology (KAUST), Saudi Arabia. Our main goal was to expand the INLA methodology to handle the tough challenge of fitting some of the most complex regression models for survival and longitudinal data. This book is the final result of all that work. The main author, Dr. Denis Rustand, is the creator and maintainer of the INLAjoint R package that serves as the primary software for the methods described. However, this project was truly a team effort, a collective achievement of the INLA development group that includes Dr. Janet van Niekerk, Dr. Elias Teixeira Krainski and Professor Håvard Rue, the principal architect of the INLA methodology. It was their combined expertise in biostatistics, computing, and statistics that made possible the creation of the INLAjoint R package and subsequently, to the comprehensive theoretical and practical guide presented in this book.
This book is intended for anyone willing to analyze repeated measurement data, event time data, and their joint combination. It is particularly aimed at graduate students, researchers, and applied statisticians in fields such as biostatistics, epidemiology, and public health. All examples and analyses in this book are conducted using the R programming language (R Core Team (2025)). To ensure the complete reproducibility of the fitted models and figures presented in this book, all the R scripts and data simulation are made publicly available on GitHub and can be accessed at the following URL: