Frailty Models in Survival Analysis

Frailty Models in Survival Analysis

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The concept of frailty offers a convenient way to introduce unobserved heterogeneity and associations into models for survival data. In its simplest form, frailty is an unobserved random proportionality factor that modifies the hazard function of an individual or a group of related individuals. Frailty Models in Survival Analysis presents a comprehensive overview of the fundamental approaches in the area of frailty models. The book extensively explores how univariate frailty models can represent unobserved heterogeneity. It also emphasizes correlated frailty models as extensions of univariate and shared frailty models. The author analyzes similarities and differences between frailty and copula models; discusses problems related to frailty models, such as tests for homogeneity; and describes parametric and semiparametric models using both frequentist and Bayesian approaches. He also shows how to apply the models to real data using the statistical packages of R, SAS, and Stata. The appendix provides the technical mathematical results used throughout. Written in nontechnical terms accessible to nonspecialists, this book explains the basic ideas in frailty modeling and statistical techniques, with a focus on real-world data application and interpretation of the results. By applying several models to the same data, it allows for the comparison of their advantages and limitations under varying model assumptions. The book also employs simulations to analyze the finite sample size performance of the more

Product details

  • Hardback | 324 pages
  • 162.56 x 238.76 x 22.86mm | 612.35g
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • New
  • 22 black & white illustrations, 58 black & white tables
  • 1420073885
  • 9781420073881
  • 1,398,297

Review quote

Unlike previous books on this topic, this book has a special focus on correlated frailty models for bivariate survival data. ... A strength of the book is the wide variety of real datasets used to illustrate models and methods. ...This book will be a very useful reference for researchers in the area. The concise summaries of relevant literature that appear at intervals throughout the text are particularly valuable in this regard. ... I would recommend this book to specialists for the breadth of its coverage of the literature and to other readers seeking to sample the flavor of ongoing methodological research in frailty models. -David Oakes, Biometrics, June 2012 There are very few books that focus on frailty models, with the most recent one authored by Duchateau and Janssen. The present book goes beyond its predecessors by focusing not only on univariate models but also on extensions to multivariate modelling where event times are clustered. ... The main contribution of the book is that it brings together the available methodology of frailty modelling in a single monograph. The presentation is quite clear and easily understood by both specialists and non-specialists. The non-technical approach makes the reader comprehend the material and at the same time understand the capabilities of the methods and models discussed. The inclusion of several examples makes the book much more attractive than its competitors. In conclusion, the book provides a comprehensive overview of frailty models and it is well written and easy to read and understand. It serves nicely the purpose for which it was written, namely to introduce and attract attention to various issues associated with the frailty models. The book is well suited primarily for bioscience practitioners but also for students, professionals, and researchers. -Alex Karagrigoriou, Journal of Applied Statistics, 2011 In my opinion, this book is a comprehensive, authoritative reference on the use of frailty models in survival analysis. The author has identified the key issues from theoretical and practical points of view and has provided numerous references and applications. The use of the data sets was effective in illustrating the concepts. I recommend this book for anyone who would like to become familiar with the key principles and issues with the use of frailty models in survival analysis -William Mietlowski, Journal of Biopharmaceutical Statistics, Vol. 21, 2011 This book gives a detailed introduction to frailty models and their applications primarily in biomedical and epidemiological fields. The models are developed with real life data. ... This book may serve as a textbook for a Master's level (or early Ph.D.) course on frailty models. It also may serve as a good reference book for a specialist in survival analysis. -Olga A. Korosteleva, Mathematical Reviews, Issue 2011hshow more

Table of contents

Introduction Goals and outline Examples Survival Analysis Basic concepts in survival analysis Censoring and truncation Parametric models Estimation of survival and hazard functions Regression models Identifiability problems Univariate Frailty Models The concept of univariate frailty Discrete frailty model Gamma frailty model Log-normal frailty model Inverse Gaussian frailty model Positive stable frailty model PVF frailty model Compound Poisson frailty model Quadratic hazard frailty model Levy-type frailty models Log-t frailty model Univariate frailty cure models Missing covariates in proportional hazard models Shared Frailty Models Marginal versus frailty model The concept of shared frailty Shared gamma frailty model Shared log-normal frailty model Shared positive stable frailty model Shared compound Poisson/PVF frailty model Shared frailty models more general Dependence measures Limitations of the shared frailty model Correlated Frailty Models The concept of correlated frailty Correlated gamma frailty model Correlated log-normal frailty model MCMC methods for the correlated log-normal frailty model Correlated compound Poisson frailty model Correlated quadratic hazard frailty model Other correlated frailty models Bivariate frailty cure models Comparison of different estimation strategies Dependent competing risks in frailty models Copula Models Shared gamma frailty copula Correlated gamma frailty copula General correlated frailty copula Cross-ratio function Different Aspects of Frailty Modeling Dependence and interaction between frailty and observed covariates Cox model with general Gaussian random effects Nested frailty models Recurrent event time data Tests for heterogeneity Log-rank test in frailty models Time-dependent frailty models Identifiability of frailty models Applications of frailty models Software for frailty models Appendix References Indexshow more

About Andreas Wienke

Andreas Wienke is a docent in the Institute of Medical Epidemiology, Biostatistics, and Informatics at Martin-Luther-University Halle-Wittenberg in Germany. In addition to statistical consulting and teaching courses on biostatistics and epidemiology, Dr. Wienke plans, designs, and supervises clinical trials in the University's Coordination Centre of Clinical more