Frailty Models in Survival Analysis: 1st Edition (Hardback) book cover

Frailty Models in Survival Analysis

1st Edition

By Andreas Wienke

Chapman and Hall/CRC

324 pages | 22 B/W Illus.

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Hardback: 9781420073881
pub: 2010-07-26
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pub: 2010-07-26
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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 models.


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

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




About the Author/Editors

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.

About the Series

Chapman & Hall/CRC Biostatistics Series

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General
MEDICAL / Pharmacology
MEDICAL / Biostatistics