1st Edition

Frailty Models in Survival Analysis

By Andreas Wienke Copyright 2011
    324 Pages 22 B/W Illustrations
    by Chapman & Hall

    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.

    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





    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