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Frailty Models in Survival Analysis [Kietas viršelis]

(Martin-Luther-University Halle-Wittenberg, Germany)
  • Formatas: Hardback, 324 pages, aukštis x plotis: 234x156 mm, weight: 760 g, 58 Tables, black and white; 22 Illustrations, black and white
  • Serija: Chapman & Hall/CRC Biostatistics Series
  • Išleidimo metai: 26-Jul-2010
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1420073885
  • ISBN-13: 9781420073881
Kitos knygos pagal šią temą:
Frailty Models in Survival AnalysisDidesnis paveikslėlis
  • Formatas: Hardback, 324 pages, aukštis x plotis: 234x156 mm, weight: 760 g, 58 Tables, black and white; 22 Illustrations, black and white
  • Serija: Chapman & Hall/CRC Biostatistics Series
  • Išleidimo metai: 26-Jul-2010
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1420073885
  • ISBN-13: 9781420073881
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781420073881.html
Raktažodžiai:
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.

Recenzijos

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 Masters 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

List of Tables
xii
List of Figures
xv
Preface xix
1 Introduction
1(14)
1.1 Goals and Outline
1(2)
1.2 Examples
3(12)
2 Survival Analysis
15(40)
2.1 Basic Concepts in Survival Analysis
15(4)
2.2 Censoring and Truncation
19(8)
2.3 Parametric Models
27(11)
2.3.1 Exponential distribution
28(2)
2.3.2 Weibull distribution
30(2)
2.3.3 Log-logistic distribution
32(1)
2.3.4 Gompertz distribution
33(1)
2.3.5 Log-normal distribution
34(2)
2.3.6 Gamma distribution
36(1)
2.3.7 Pareto distribution
37(1)
2.4 Estimation of Survival and Hazard Functions
38(5)
2.4.1 Kaplan-Meier estimator
38(3)
2.4.2 Nelson-Aalen estimator
41(2)
2.5 Regression Models
43(9)
2.5.1 Proportional hazards model
43(7)
2.5.2 Accelerated failure time model
50(2)
2.6 Identifiability Problems
52(3)
3 Univariate Frailty Models
55(76)
3.1 The Concept of Univariate Frailty
57(8)
3.2 Discrete Frailty Model
65(7)
3.3 Gamma Frailty Model
72(24)
3.3.1 Parametric gamma frailty model
79(5)
3.3.2 Semiparametric gamma frailty model
84(6)
3.3.3 Gamma frailty model for current status data
90(2)
3.3.4 Extensions of the gamma frailty model
92(4)
3.4 Log-normal Frailty Model
96(5)
3.4.1 Parametric log-normal frailty model
98(1)
3.4.2 Semiparametric log-normal frailty model
99(2)
3.5 Inverse Gaussian Frailty Model
101(4)
3.6 Positive Stable Frailty Model
105(3)
3.7 PVF Frailty Model
108(3)
3.8 Compound Poisson Frailty Model
111(5)
3.9 Quadratic Hazard Frailty Model
116(4)
3.10 Levy Frailty Models
120(1)
3.11 Log-t Frailty Model
121(1)
3.12 Univariate Frailty Cure Models
122(5)
3.13 Missing Covariates in Proportional Hazards Models
127(4)
4 Shared Frailty Models
131(30)
4.1 Marginal versus Frailty Model
132(3)
4.2 The Concept of Shared Frailty
135(4)
4.3 Shared Gamma Frailty Model
139(9)
4.3.1 Parametric shared gamma frailty model
140(2)
4.3.2 Semiparametric shared gamma frailty model
142(3)
4.3.3 Shared gamma frailty model for current status data
145(3)
4.4 Shared Log-normal Frailty Model
148(2)
4.5 Shared Positive Stable Frailty Model
150(1)
4.6 Shared Compound Poisson/PVF Frailty Model
151(1)
4.7 Shared Frailty Models More General
152(1)
4.8 Dependence measures
153(5)
4.9 Limitations of the Shared Frailty Model
158(3)
5 Correlated Frailty Models
161(48)
5.1 The Concept of Correlated Frailty
163(2)
5.2 Correlated Gamma Frailty Model
165(12)
5.3 Correlated Log-normal Frailty Model
177(4)
5.4 MCMC Methods for the Correlated Log-normal Frailty Model
181(4)
5.5 Correlated Compound Poisson Frailty Model
185(4)
5.6 Correlated Quadratic Hazard Frailty Model
189(4)
5.7 Other Correlated Frailty Models
193(2)
5.8 Bivariate Frailty Cure Models
195(3)
5.9 Comparison of Different Estimation Strategies
198(6)
5.10 Dependent Competing Risks in Frailty Models
204(5)
6 Copula Models
209(14)
6.1 Shared Gamma Frailty Copula
210(2)
6.2 Correlated Gamma Frailty Copula
212(3)
6.3 General Correlated Frailty Copulas
215(5)
6.4 Cross-Ratio Function
220(3)
7 Different Aspects of Frailty Modeling
223(20)
7.1 Dependence and Interaction between Frailty and Observed Covariates
223(3)
7.2 Cox Model with General Gaussian Random Effects
226(1)
7.3 Nested Frailty Models
227(1)
7.4 Recurrent Event Time Data
228(2)
7.5 Tests for Heterogeneity
230(1)
7.6 Log-Rank Test in Frailty Models
231(1)
7.7 Time-Dependent Frailty Models
232(3)
7.8 Identifiability of Frailty Models
235(3)
7.8.1 Univariate frailty models
235(2)
7.8.2 Multivariate frailty models
237(1)
7.9 Applications of Frailty Models
238(2)
7.10 Software for Frailty Models
240(3)
7.10.1 R packages
241(1)
7.10.2 SAS packages
242(1)
7.10.3 STATA package
242(1)
A Appendix
243(22)
A.1 Bivariate Lifetime Models
243(2)
A.2 Correlated Gamma Frailty Model
245(2)
A.3 Correlated Compound Poisson Frailty Model
247(2)
A.4 Correlated Quadratic Hazard Frailty Model
249(4)
A.5 Dependent Competing Risks Model
253(8)
A.6 Quantitative Genetics
261(4)
References 265(34)
Index 299
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 Universitys Coordination Centre of Clinical Trials.