Frailty Models in Survival Analysis  book cover
1st Edition

Frailty Models in Survival Analysis

ISBN 9781420073881
Published July 26, 2010 by Chapman and Hall/CRC
324 Pages 22 B/W Illustrations

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Book Description

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 models.

Table of Contents

Goals and outline

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
Lévy-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




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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 Trials.


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 2011h