Frailty Models in Survival Analysis, by Andreas Wienke, Boca Raton, Chapman & Hall/CRC, 2010, xxi + 301 pp., £63.99 or US$ 99.95 (hardback), ISBN 978-1-4200-7388-1
Frailty models are extensions of the well-known Cox proportional hazards model and provide a convenient way of introducing random effects, association, and unobserved heterogeneity into the modelling process. There are very few books that focus on frailty models with the most recent one authored by Duchateau and Janssen Citation1. 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 first chapter of the book provides a series of examples which are analysed in subsequent chapters. Three of the examples deal with Danish and Swedish twin data which have been used by the author in a series of research articles. Chapters 2 and 3, which comprise half of the book, are devoted to standard topics of survival analysis and frailty models including the typical survival analysis theory and the basic concepts of frailty modelling. The material is more or less known from other sources except that the author is much less technical than others and provides a few more explanations and several more examples. Among the topics covered in these two chapters are the Cox proportional hazards model, the accelerated failure time model, the standard frailty models (gamma, log-normal, inverse Gaussian, etc.), the quadratic (conditional) hazard frailty model, and the univariate frailty cure model which is an extension of the cure model that allows for heterogeneity among the fraction under risk.
Chapter 4 deals with the shared frailty model where the frailty is used to model associations between event times. The author covers briefly this type of model which is typical in multivariate survival analysis and has been fully covered elsewhere Citation2. The shared frailty model is a special case of the more general correlated frailty model which is the main focus of Chapter 5. The correlated frailty model is an important conditional independence model where the frailties of individuals in each cluster are correlated but not necessarily shared. The most popular gamma and log-normal models are presented. For the latter, the application of MCMC for parameter estimation is discussed. Other models covered in this chapter include the quadratic hazards and bivariate frailty cure models.
The book ends with two very short chapters and an appendix with some technical results. A brief introduction to copula models is given in Chapter 6. Such models can be used for modelling clustered data with equal cluster sizes. Various aspects of frailty models are briefly presented in Chapter 7. Such aspects include the dependence between the frailty and the observed covariates, nested frailty models when the individuals are grouped in subclusters within clusters (multilevel clustering), and the use of frailty models in the analysis of recurrent event time data. The author also discusses heterogeneity tests and the log-rank test. Finally, a brief discussion about the so-called time-dependent frailty is provided where the frailty of an individual may not necessarily remain constant over time. The chapter ends with a collection of applications of frailty models from the literature.
The book has few repetitions, especially at the beginning of chapters and sections, and a number of typographical/grammatical errors, though these are minor. Although the author makes constant references to statistical packages, no code is provided. As a result, the interested reader will experience difficulties in reproducing the numerical results of the book. Short code scripts in R and SAS would have been very welcome and extremely useful. The author would have served much better the practitioners in the biostatistical community, if he had chosen to collect in an appendix or on a website the various codes, macros, etc., prepared by the author or being available elsewhere. Also, it should be noted that the book makes no significant reference to the Bayesian approach. Finally, an author index would have been useful.
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 of the presentation of the material 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.
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References
- Duchateau , L. and Janssen , P. 2008 . The Frailty Model , New York : Springer .
- Hougaard , P. 2000 . Analysis of Multivariate Survival Data , New York : Springer .