Survival and Event History Analysis: A Process Point of View (Statistics for Biology and Health)

Time-to-event data are ubiquitous in fields such as medicine, biology, demography, sociology, economics and reliability theory. Recently, a need to analyze more complex event histories has emerged. Examples are individuals that move among several states, frailty that makes some units fail before others, internal time-dependent covariates, and the estimation of causal effects from observational data. The aim of this book is to bridge the gap between standard textbook models and a range of models where the dynamic structure of the data manifests itself fully. The common denominator of such models is stochastic processes. The authors show how counting processes, martingales, and stochastic integrals fit very nicely with censored data. Beginning with standard analyses such as Kaplan-Meier plots and Cox regression, the presentation progresses to the additive hazard model and recurrent event data. Stochastic processes are also used as natural models for individual frailty; they allow sensible interpretations of a number of surprising artifacts seen in population data. The stochastic process framework is naturally connected to causality. The authors show how dynamic path analyses can incorporate many modern causality ideas in a framework that takes the time aspect seriously. To make the material accessible to the reader, a large number of practical examples, mainly from medicine, are developed in detail. Stochastic processes are introduced in an intuitive and non-technical manner. The book is aimed at investigators who use event history methods and want a better understanding of the statistical concepts. It is suitable as a textbook for graduate courses in statistics and biostatistics. Odd O. Aalen is professor of medical statistics at the University of Oslo, Norway. His Ph.D. from the University of California, Berkeley in 1975 introduced counting processes and martingales in event history analysis. He has also contributed to numerous other areas of event history analysis, such as additive hazards regression, frailty, and causality through dynamic modeling. Ørnulf Borgan is professor of statistics at the University of Oslo, Norway. Since his Ph.D. in 1984 he has contributed extensively to event history analysis. He is co-author of the monograph Statistical Models Based on Counting Processes, and is editor of Scandinavian Journal of Statistics. Håkon K. Gjessing is professor of medical statistics at the Norwegian Institute of Public Health and the University of Bergen, Norway. Since his Ph.D. in probability in 1995, he has worked on a broad range of theoretical and applied problems in biostatistics. Time-to-event data are ubiquitous in fields such as medicine, biology, demography, sociology, economics and reliability theory. Recently, a need to analyze more complex event histories has emerged. Examples are individuals that move among several states, frailty that makes some units fail before others, internal time-dependent covariates, and the estimation of causal effects from observational data. The aim of this book is to bridge the gap between standard textbook models and a range of models where the dynamic structure of the data manifests itself fully. The common denominator of such models is stochastic processes. The authors show how counting processes, martingales, and stochastic integrals fit very nicely with censored data. Beginning with standard analyses such as Kaplan-Meier plots and Cox regression, the presentation progresses to the additive hazard model and recurrent event data. Stochastic processes are also used as natural models for individual frailty; they allow sensible interpretations of a number of surprising artifacts seen in population data. The stochastic process framework is naturally connected to causality. The authors show how dynamic path analyses can incorporate many modern causality ideas in a framework that takes the time aspect seriously. To make the material accessible to the reader, a large number of practical examples, mainly from medicine, are developed in detail. Stochastic processes are introduced in an intuitive and non-technical manner. The book is aimed at investigators who use event history methods and want a better understanding of the statistical concepts. It is suitable as a textbook for graduate courses in statistics and biostatistics. Odd O. Aalen is professor of medical statistics at the University of Oslo, Norway. His Ph. D. from the University of California, Berkeley in 1975 introduced counting processes and martingales in event history analysis. He has also contributed to numerous other areas of event history analysis, such as additive hazards regression, frailty, and causality through dynamic modeling. Ørnulf Borgan is professor of statistics at the University of Oslo, Norway. Since his Ph. D. in 1984 he has contributed extensively to event history analysis. He is co-author of the monograph Statistical Models Based on Counting Processes, and is editor of Scandinavian Journal of Statistics. Håkon K. Gjessing is professor of medical statistics at the Norwegian Institute of Public Health and the University of Bergen, Norway. Since his Ph. D. in probability in 1995, he has worked on a broad range of theoretical and applied problems in biostatistics

time-to-event Data Are Ubiquitous In Fields Such As Medicine, Biology, Demography, Sociology, Economics And Reliability Theory. Recently, A Need To Analyze More Complex Event Histories Has Emerged. Examples Are Individuals That Move Among Several States, Frailty That Makes Some Units Fail Before Others, Internal Time-dependent Covariates, And The Estimation Of Causal Effects From Observational Data.

the Aim Of This Book Is To Bridge The Gap Between Standard Textbook Models And A Range Of Models Where The Dynamic Structure Of The Data Manifests Itself Fully. The Common Denominator Of Such Models Is Stochastic Processes. The Authors Show How Counting Processes, Martingales, And Stochastic Integrals Fit Very Nicely With Censored Data. Beginning With Standard Analyses Such As Kaplan-meier Plots And Cox Regression, The Presentation Progresses To The Additive Hazard Model And Recurrent Event Data. Stochastic Processes Are Also Used As Natural Models For Individual Frailty; They Allow Sensible Interpretations Of A Number Of Surprising Artifacts Seen In Population Data.

the Stochastic Process Framework Is Naturally Connected To Causality. The Authors Show How Dynamic Path Analyses Can Incorporate Many Modern Causality Ideas In A Framework That Takes The Time Aspect Seriously.

to Make The Material Accessible To The Reader, A Large Number Of Practical Examples, Mainly From Medicine, Are Developed In Detail. Stochastic Processes Are Introduced In An Intuitive And Non-technical Manner. The Book Is Aimed At Investigators Who Use Event History Methods And Want A Better Understanding Of The Statistical Concepts. It Is Suitable As A Textbook For Graduate Courses In Statistics And Biostatistics.

Front Matter....Pages 1-16 An introduction to survival and event history analysis....Pages 1-39 Stochastic processes in event history analysis....Pages 41-67 Nonparametric analysis of survival and event history data....Pages 69-130 Regression models....Pages 131-205 Parametric counting process models....Pages 207-229 Unobserved heterogeneity: The odd effects of frailty....Pages 231-270 Multivariate frailty models....Pages 271-300 Marginal and dynamic models for recurrent events and clustered survival data....Pages 301-346 Causality....Pages 347-385 First passage time models: Understanding the shape of the hazard rate....Pages 387-424 Diffusion and Lévy process models for dynamic frailty....Pages 425-455 Back Matter....Pages 457-541 Demonstrates how counting processes, martingales, and stochastic integrals fit nicely with censored data. This book shows how dynamic path analyses can incorporate many modern causality ideas in a framework that takes the time aspect seriously. It includes examples from medicine. It is intended for investigators who use event history methods.