This book provides a comprehensive and practical guide to fitting complex Bayesian survival, longitudinal and joint models using the Integrated Nested Laplace Approximations (INLA) methodology, a powerful and computationally efficient alternative to traditional MCMC methods. Aimed at graduate students, researchers, and applied statisticians in biostatistics, epidemiology, and public health, this book addresses the critical challenge of analyzing high-dimensional and correlated data. It demonstrates how to move beyond the computational limitations of conventional methods, enabling the analysis of sophisticated models that were previously out of reach.
Through a series of clear, fully reproducible examples, readers will learn to:
- Implement a wide range of survival models, including proportional hazards, competing risks, multi-state, cure, and frailty models.
- Fit various longitudinal models for continuous, count, binary, semicontinuous, and ordinal data.
- Construct and interpret joint models that link multiple longitudinal markers to single or multiple survival outcomes using various association structures.
- Incorporate spatial random effects to account for spatial autocorrelation in areal and point-referenced data.
This book is the result of a unique collaboration between the creators and key developers of the INLA methodology. The lead author, Denis Rustand, is the developer of the INLAjoint R package which serves as the primary software for the methods described. Håvard Rue is the principal architect of the INLA methodology and the R-INLA package. Janet van Niekerk is an expert in efficient Bayesian methods for complex survival analysis and a core INLA developer. Elias Teixeira Krainski is a renowned specialist in the theory and application of spatial statistics with INLA.
Table of Contents:
Preface About the authors Introduction 1 The Integrated Nested Laplace Approximations methodology 2 Survival analysis 3 Longitudinal data analysis 4 Joint modeling of longitudinal and survival data 5 Spatial models Summary References
About the Author :
Denis Rustand is a research scientist in biostatistics at the Bordeaux Population Health Research Center, National Institute of Health and Medical Research (Inserm U1219), Bordeaux, France. He earned his Ph.D. in Public Health and Biostatistics from the University of Bordeaux, where his doctoral research focused on the development of joint models for semicontinuous biomarkers and survival outcomes in oncology. Following his Ph.D., he was a postdoctoral research fellow in the BAYESCOMP group at KAUST under the supervision of Professor Håvard Rue. It was during this time that he enhanced his expertise in biostatistical theory with high-performance Bayesian computation, leading to the creation of the INLAjoint R package, the primary software tool used in this book along with R-INLA. This book is a direct extension of that work, providing the theoretical background and practical guidance for the models implemented. His research focuses on developing fast and flexible Bayesian methods for the joint modeling of complex, multivariate longitudinal and survival data, with direct applications in clinical trials and epidemiology.
Janet van Niekerk is an Associate Professor at the University of Pretoria in South Africa and was a research scientist in the BAYESCOMP research group at KAUST. She received her Ph.D. in Mathematical Statistics from the University of Pretoria, South Africa. Her research is centered on the development of efficient Bayesian methods and their practical implementation, with a particular focus on complex survival analysis and statistics for medical applications. As a key member of the INLA development team, she has made significant contributions to the INLA methodology itself, authoring seminal papers on fundamental improvements that enhance the algorithm’s speed, stability, and scalability. Her work ensures that the INLA framework continues to evolve to meet the demands of modern, data-rich statistical modeling.
Elias Teixeira Krainski is a research scientist in the BAYESCOMP group at KAUST. He earned his Ph.D. in Mathematical Sciences from the Norwegian University of Science and Technology under the supervision of Professor Håvard Rue. His research focuses on the application and development of structured Bayesian models, with a specialization in spatial and spatio-temporal statistics. He is the main author of the book Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA (Krainski et al. (2018)) and a developer of several R packages that facilitate the use of INLA for complex models. His expertise provides the foundation for the advanced spatial models covered in this book.
Håvard Rue is Professor of Statistics at KAUST, where he leads the BAYESCOMP research group. He received his Ph.D. from the Norwegian University of Science and Technology. Professor Rue is an internationally renowned authority in Bayesian computational statistics and is the main developer of the Integrated Nested Laplace Approximations methodology and the associated R-INLA package. His work has revolutionized the practice of applied Bayesian statistics by providing a fast, deterministic alternative to MCMC for the vast class of latent Gaussian models. He is an elected member of the Norwegian Academy of Science and Letters, the Royal Norwegian Society of Science and Letters, the Norwegian Academy of Technological Sciences and the International Statistical Institute. In 2021, he was awarded the Guy Medal in Silver by the Royal Statistical Society in recognition of his groundbreaking contributions to the field.
