Models for Multi-State Survival Data

Henrik Ravn is senior statistical director at Novo Nordisk A/S, Denmark. He graduated with an MSc in theoretical statistics in 1992 from University of Aarhus, Denmark and completed a PhD in biostatistics in 2002 from the University of Copenhagen, Denmark. He joined Novo Nordisk in late 2015 after more than 22 years of experience from biostatistical and epidemiological research, at Statens Serum Institut, Denmark and in Guinea-Bissau, West Africa. He has co-authored more than 160 papers, mainly within epidemiology and application of survival analysis and has taught several courses as external lecturer at Section of Biostatistics, University of Copenhagen.Per Kragh Andersen is professor of biostatistics at the Department of Public Health, University of Copenhagen, Denmark since 1998. He graduated in mathematical statistics from University of Copenhagen in 1978, got his PhD in 1982 and a DMSc degree in 1997. From 1993 to 2002 he worked half time as chief statistician at Danish Epidemiology Science. He is an author or co-author of more than 125 papers on statistical methodology and more than 250 papers in the medical literature. His research has concentrated on survival analysis and he is a co-author of the 1993 book ‘Statistical Models Based on Counting Processes’. He has taught several courses both nationally and internationally both for students with a mathematical background and for students in medicine or public health.

"We highly recommend this book for researchers, statisticians, and data analysts interested in longitudinal and multistate survival data analysis. It is also highly relevant for clinical professionals seeking to understand statistical approaches to risk analysis and marginal parameter estimation. Combining rigorous theory with practical applications, this book is ideal for academics, graduate students, and practitioners in epidemiology, demography, and clinical studies who need advanced analytical tools for complex data. With comprehensive coverage of theoretical frameworks, case studies, and programming examples, readers will gain the knowledge and confidence to implement statistical methods effectively in real-world scenarios."-Siti Mutiah and Indra Rivaldi Siregar in Technometrics, February 2025"This nicely written book clearly succeeds in its goal of summarizing key models andestimation procedures for multi-state survival data, and does so in a friendly and primarilynon-technical manner. [...] In summary, I would like to congratulate the “Crow and the Raven” (see book preface forexplanation) for this accurate and highly readable account of models and methods for multi-state survival processes. I am pleased to recommend it without reservation to interestedstudents and researchers, even those with limited background in survival analysis methods."-Ross L. Prentice in Journal of the American Statistical Association, August 2024"The book provides a thorough overview of recent developments in the field of time-to-event analyses. It covers models for competing risks, multi-state models and recurrent events. The main distinction in the book is between intensity-based models and marginal models. Intensity-based models are based on the rate or hazard, which is a quantity conditional on previous development of the event process (e.g. conditional on being event-free). Examples are the Cox model, Poisson models and Aalen's additive hazard model. Marginal models are based on the (cumulative) risk or probability, and include models for state occupation probabilities and restricted mean time lost. Marginal models do not involve conditioning on the past. These models make use of newer techniques like inverse probability weighting and pseudo-values for estimation. One of the authors is a leading expert in the field of pseudo-values and a separate chapter is devoted to the intuition behind and the use of pseudo-values. Given the recent discussion on the lack of interpretability of intensity based effect measures, the use and importance of marginal models is likely to increase. This is the first book to give an in-depth coverage of marginal models. The book devotes one chapter to intuition for each of intensity-based models and marginal models, and the models are illustrated by several examples. The book can be used by applied researchers as well as by those with a more theoretical interest. The more theoretical sections are clearly separated from the applied ones via asterisks. Software code to run the example is provided on a companion github page."-Ronald Geskus, Associate Professor in Biostatistics, University of Oxford"This book, authored by Per Kragh Andersen and Henrik Ravn, two esteemed researchers in the field, is an outstanding book that offers an in-depth exploration of the analysis of multi-state survival data. I am delighted to provide a positive review, highlighting the book's notable strengths and contributions. The authors have strived for offering a text that appeals to both applied and theoretical readers, by first providing the intuition behind concepts and methods, illustrating with well chosen examples, and then giving more technical details in sections that can be skipped by applied readers. I think this set-up works really well; along with the clarity of writing, it makes for an accessible book that is a delight to read.The authors make a clear distinction between rates or intensities on the one hand, and marginal parameters like risks or expected life years on the other. A chapter focusing on pseudo-values directly targeting marginal parameters is an important added bonus. The distinction between rates and marginal parameters, and the authors' detailed discussion on statistical approaches based on rates and marginal parameters, proves quite valuable as it enhances researchers' ability to understand the underlying dynamics and make informed decisions in their analyses. The book gives many practical examples, illustrating the methods discussed. A companion website is available giving data and software code in R and SAS for the calculations in the examples. This should give the applied reader the means to use the methods in their own work.In conclusion, this is an exceptionally well-written book that offers a comprehensive and insightful exploration of multi-state survival analysis. With its clear explanations, practical examples, and emphasis on both foundational and advanced concepts, this book is a must-have resource for researchers at all stages of their career."- Hein Putter, Professor in Longtudinal Data Anlysis, Leiden University."Combining rigorous theory with practical applications, this book is ideal for academics, graduate students, and practitioners in epidemiology, demography, and clinical studies who need advanced analytical tools for complex data. With comprehensive coverage of theoretical frameworks, case studies, and programming examples, readers will gain the knowledge and confidence to implement statistical methods effectively in real-world scenarios." - Siti Mutiah and Indra Rivaldi Siregar, Techonometrics, February 2025

• 1. Introduction 2. Intuition for intensity models 3. Intensity models 4. Intuition for marginal models 5. Marginal models 6. Pseudo-values 7. Further topics