Bayesian Survival, Longitudinal, and Joint Models with Inla
暫譯: 使用 INLA 的貝葉斯生存、縱向及聯合模型

這本書提供了一個全面且實用的指南，介紹如何使用整合嵌套拉普拉斯近似（Integrated Nested Laplace Approximations, INLA）方法來擬合複雜的貝葉斯生存、縱向和聯合模型，這是一種強大且計算效率高的替代傳統馬可夫鏈蒙地卡羅（MCMC）方法的選擇。本書針對研究生、研究人員以及生物統計學、流行病學和公共衛生領域的應用統計學家，解決了分析高維度和相關數據的關鍵挑戰。它展示了如何超越傳統方法的計算限制，使得分析先前無法達到的複雜模型成為可能。

通過一系列清晰且完全可重現的範例，讀者將學會：
- 實現各種生存模型，包括比例風險模型、競爭風險模型、多狀態模型、治癒模型和脆弱性模型。
- 擬合各種縱向模型，適用於連續、計數、二元、半連續和序數數據。
- 構建和解釋聯合模型，將多個縱向標記與單一或多個生存結果連結，並使用各種關聯結構。
- 融入空間隨機效應，以考慮區域和點參考數據中的空間自相關。

這本書是INLA方法的創建者和主要開發者之間獨特合作的結果。主要作者Denis Rustand是INLAjoint R套件的開發者，該套件是描述的方法的主要軟體。Håvard Rue是INLA方法和R-INLA套件的主要架構師。Janet van Niekerk是複雜生存分析中高效貝葉斯方法的專家，也是INLA的核心開發者。Elias Teixeira Krainski是空間統計理論和應用的知名專家，專注於INLA。

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.

Denis Rustand 是法國波爾多國立健康與醫學研究院（Inserm U1219）波爾多人口健康研究中心的生物統計研究科學家。他在波爾多大學獲得公共衛生與生物統計的博士學位，博士研究專注於發展半連續生物標記和腫瘤學生存結果的聯合模型。在獲得博士學位後，他在KAUST的BAYESCOMP小組擔任博士後研究員，指導教授為Håvard Rue。在此期間，他增強了在高效能貝葉斯計算方面的生物統計理論專業知識，並創建了INLAjoint R套件，這是本書中主要使用的軟體工具，與R-INLA一起使用。本書是該工作的直接延伸，提供了所實施模型的理論背景和實用指導。他的研究專注於開發快速且靈活的貝葉斯方法，用於複雜的多變量縱向和生存數據的聯合建模，並在臨床試驗和流行病學中有直接應用。

Janet van Niekerk 是南非比勒陀利亞大學的副教授，曾在KAUST的BAYESCOMP研究小組擔任研究科學家。她在南非比勒陀利亞大學獲得數學統計的博士學位。她的研究集中在高效貝葉斯方法的開發及其實際應用，特別關注於複雜的生存分析和醫學應用的統計。作為INLA開發團隊的關鍵成員，她對INLA方法論本身做出了重要貢獻，撰寫了關於增強算法速度、穩定性和可擴展性的基礎改進的開創性論文。她的工作確保了INLA框架不斷演進，以滿足現代數據豐富的統計建模需求。

Elias Teixeira Krainski 是KAUST的BAYESCOMP小組的研究科學家。他在挪威科技大學獲得數學科學的博士學位，指導教授為Håvard Rue。他的研究專注於結構化貝葉斯模型的應用和開發，專門研究空間和時空統計。他是書籍Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA（Krainski et al. (2018)）的主要作者，並開發了幾個R套件，以促進INLA在複雜模型中的使用。他的專業知識為本書中涵蓋的高級空間模型提供了基礎。

Håvard Rue 是KAUST的統計學教授，領導BAYESCOMP研究小組。他在挪威科技大學獲得博士學位。Rue教授是貝葉斯計算統計的國際知名權威，也是集成嵌套拉普拉斯近似法（Integrated Nested Laplace Approximations）方法論及相關R-INLA套件的主要開發者。他的工作通過為廣泛的潛在高斯模型提供快速、確定性的替代方案，徹底改變了應用貝葉斯統計的實踐。他是挪威科學與文學學院、挪威皇家科學與文學學會、挪威技術科學學院和國際統計學會的當選成員。2021年，他因對該領域的開創性貢獻而獲得英國皇家統計學會的銀獎（Guy Medal in Silver）。