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Bayesian Survival Analysis : Springer Series in Statistics - Joseph G. Ibrahim

Bayesian Survival Analysis

Springer Series in Statistics

Hardcover

Published: 24th January 2005
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Survival analysis arises in many fields of study including medicine, biology, engineering, public health, epidemiology, and economics. This book provides a comprehensive treatment of Bayesian survival analysis. It presents a balance between theory and applications, and for each class of models discussed, detailed examples and analyses from case studies are presented whenever possible. The applications are all from the health sciences, including cancer, AIDS, and the environment.

From the reviews:

"The analysis of time-event data arises naturally in many fields of study. This book focuses exclusively on medicine and public health but the methods presented can be applied in a number of other areas, including biology, economics and engineering. Although several previously published texts address survival analysis from a frequentist perspective, this book examines solely Bayesian approaches to survival analysis. Recent advances in computing and practical methods for prior elicitation have now made Bayesian survival analysis of complex models feasible. This book provides a comprehensive and modern treatment of the subject. In addition, the authors demonstrate the use of the statistical package BUGS for several of the models and methodologies discussed in the book. The authors provide a collection of theoretical and applied problems in the exercises at the end of each chapter."
ISI Short Book Reviews, April 2002

"This is definitely a worthwhile read for any statistician specializing in survival analysis. It is pitched so that part of it is readily usable by the medical statisitciann, but it will also provide stimulation for statisticians involved in methodological development or the writing of new software for survival analysis." International Journal of Epidemiology

"Many books have been published concerning survival analysis or Bayesian methods; Bayesian Survival Analysis is the first comprehensive treatment that combines these two important areas of statistics. Ibrahim, Chen, and Sinha have made an admirable accomplishment on the subject in a well-organized and easily accessible fashion." Journal of the American Statistical Association

"This is one of the best combinations of advanced methodology and practical applications that I have ever encountered." Technometrics, May 2002

"This is a book by three authors who are well-known for their contribution to Bayesian survival analysis. ... It is a good book with many areas of strength. ... There are several new methods, ideas, results, some of which are due to the authors. There is a good discussion of historical priors ... . Other things that strike me as new are a good technical discussion of frailty and cure models ... . I have learnt a lot and enjoyed reading the book." (Jayanta K. Ghosh, Sankhya: The Indian Journal of Statistics, Vol. 65 (3), 2003)

"This book illustrates several Bayesian techniques to analyze survival data in biology, medicine, public health, epidemiology, clinical trials, and economics. ... It could be used as a textbook in a graduate level course. ... In particular, I enjoyed the presentations of cure models and cancer vaccine trials. Biostatisticians will like reading this book from the Bayesian points of view." (Ramalingam Shanmugam, Journal of Statistical Computation and Simulation, Vol. 74 (10), 2004)

"This book offers an excellent and thorough summary of an exciting methodological development since the seventies of the last century. ... The authors offer a gentle journey through the archipelago of Bayesian Survival analysis. They combine in a pleasant way theory, examples, and exercises. ... I hope that this stimulating book may tempt many readers to enter the field of Bayesian survival analysis ... ." (Ulrich Mansmann, Metrika, September, 2004)

"It offers a presentation of Bayesian methods in Survival Analysis that is, at a time, comprehensive and suitably balanced between theory and applications; many relevant models and methods are illustrated and most of them are provided with detailed examples and case studies drawn from the medical research. ... The book offers a quite up-to-date view of Bayesian Statistics and accounts extensively for Monte Carlo-based sampling methods and for the various methods of prior elicitation, suitable to cope with non-parametric as well as with semi-parametric models." (Fabio Spizzichino, Statistics in Medicine, Vol. 23, 2004)

"This is not an elementary book. ... The book develops methodology and does this at a high level, because the reader is presumed to have a mathematical statistics background in both classical and Bayesian methods. Happily, the book is replete with examples. This is one of the best combinations of advanced methodology and practical applications that I have encountered. ... Computing support for the book comes from the package called BUGS ... ." (Technometrics, Vol. 44 (2), 2002)

"This book provides a comprehensive treatment of Bayesian survival analysis. Several topics are addressed, including parametric models, semiparametric models based on prior processes, proportional and non-proportional hazards models, frailty models, cure rate models, model selection and comparison ... . The book presents a balance between theory and applications, and for each class of models discussed, detailed examples and analyses from case studies are presented whenever possible." (L'Enseignement Mathematique, Vol. 48 (1-2), 2002)

"The book is about Bayesian survival analysis which is illustrated with examples that mostly use the BUGS software package. ... this is definitively a worthwhile read for any statistician specializing in survival analysis. It is pitched so that part of it is readily usable by the medical statistician, but it will also provide stimulation for statisticians involved in methodological development or the writing of new software for survival analysis." (Margaret May, International Journal of Epidemiology, Vol. 31 (2), 2002)

"This book focuses exclusively on medicine and public health but the methods presented can be applied in a number of other areas, including biology, economics and engineering. ... This book provides a comprehensive and modern treatment of the subject. In addition, the authors demonstrate the use of the statistical package BUGS for several of the models and methodologies discussed in the book. The authors provide a collection of theoretical and applied problems in the exercises at the end of each chapter." (C. M. O'Brien, Short Book Reviews, Vol. 22 (1), 2002)

"Ibrahim, Chen and Sinha command over a rich experience in both Bayesian and survival analysis. Drawing from this experience they have put together a comprehensive description of Bayesian methodology in survival analysis. The book is written for researchers and graduate students. ... The book is a useful tool for practitioners who analyze survival data using Bayesian methods." (Mathias Schaller, Statistical Papers, Vol. 47, 2005)

Prefacep. vii
Introductionp. 1
Aimsp. 1
Outlinep. 2
Motivating Examplesp. 3
Survival Analysisp. 13
Proportional Hazards Modelsp. 15
Censoringp. 15
Partial Likelihoodp. 16
The Bayesian Paradigmp. 17
Sampling from the Posterior Distributionp. 18
Informative Prior Elicitationp. 22
Why Bayes?p. 26
Exercisesp. 27
Parametric Modelsp. 30
Exponential Modelp. 30
Weibull Modelp. 35
Extreme Value Modelp. 37
Log-Normal Modelp. 39
Gamma Modelp. 40
Exercisesp. 42
Semiparametric Modelsp. 47
Piecewise Constant Hazard Modelp. 47
Models Using a Gamma Processp. 50
Gamma Process on Cumulative Hazardp. 50
Gamma Process with Grouped-Data Likelihoodp. 51
Relationship to Partial Likelihoodp. 53
Gamma Process on Baseline Hazardp. 55
Prior Elicitationp. 56
Approximation of the Priorp. 57
Choices of Hyperparametersp. 59
Sampling from the Joint Posterior Distribution of ([beta], [delta], a[subscript 0])p. 60
A Generalization of the Cox Modelp. 63
Beta Process Modelsp. 66
Beta Process Priorsp. 66
Interval Censored Datap. 71
Correlated Gamma Processesp. 72
Dirichlet Process Modelsp. 78
Dirichlet Process Priorp. 78
Dirichlet Process in Survival Analysisp. 81
Dirichlet Process with Doubly Censored Datap. 84
Mixtures of Dirichlet Process Modelsp. 87
Conjugate MDP Modelsp. 89
Nonconjugate MDP Modelsp. 90
MDP Priors with Censored Datap. 91
Inclusion of Covariatesp. 94
Exercisesp. 94
Frailty Modelsp. 100
Proportional Hazards Model with Frailtyp. 101
Weibull Model with Gamma Frailtiesp. 102
Gamma Process Prior for H[subscript 0](t)p. 104
Piecewise Exponential Model for h[subscript 0](t)p. 106
Positive Stable Frailtiesp. 112
A Bayesian Model for Institutional Effectsp. 118
Posterior Likelihood Methodsp. 126
Methods Based on Partial Likelihoodp. 131
Multiple Event and Panel Count Datap. 134
Multilevel Multivariate Survival Datap. 136
Bivariate Measures of Dependencep. 147
Exercisesp. 148
Cure Rate Modelsp. 155
Introductionp. 155
Parametric Cure Rate Modelp. 156
Modelsp. 156
Prior and Posterior Distributionsp. 160
Posterior Computationp. 163
Semiparametric Cure Rate Modelp. 171
An Alternative Semiparametric Cure Rate Modelp. 179
Prior Distributionsp. 180
Multivariate Cure Rate Modelsp. 185
Modelsp. 185
The Likelihood Functionp. 188
The Prior and Posterior Distributionsp. 190
Computational Implementationp. 191
Appendixp. 199
Exercisesp. 205
Model Comparisonp. 208
Posterior Model Probabilitiesp. 209
Variable Selection in the Cox Modelp. 210
Prior Distribution on the Model Spacep. 211
Computing Prior and Posterior Model Probabilitiesp. 212
Criterion-Based Methodsp. 219
The L Measurep. 220
The Calibration Distributionp. 223
Conditional Predictive Ordinatep. 227
Bayesian Model Averagingp. 234
BMA for Variable Selection in the Cox Modelp. 236
Identifying the Models in A'p. 237
Assessment of Predictive Performancep. 239
Bayesian Information Criterionp. 246
Model Selection Using BICp. 249
Exponential Survival Modelp. 249
The Cox Proportional Hazards Modelp. 250
Exercisesp. 254
Joint Models for Longitudinal and Survival Datap. 262
Introductionp. 262
Joint Modeling in AIDS Studiesp. 263
Joint Modeling in Cancer Vaccine Trialsp. 263
Joint Modeling in Health-Related Quality of Life Studiesp. 264
Methods for Joint Modeling of Longitudinal and Survival Datap. 265
Partial Likelihood Modelsp. 265
Joint Likelihood Modelsp. 267
Mixture Modelsp. 273
Bayesian Methods for Joint Modeling of Longitudinal and Survival Datap. 275
Exercisesp. 287
Missing Covariate Datap. 290
Introductionp. 290
The Cure Rate Model with Missing Covariate Datap. 292
A General Class of Covariate Modelsp. 293
The Prior and Posterior Distributionsp. 297
Model Checkingp. 301
Appendixp. 311
Exercisesp. 317
Design and Monitoring of Randomized Clinical Trialsp. 320
Group Sequential Log-Rank Tests for Survival Datap. 320
Bayesian Approachesp. 322
Range of Equivalencep. 326
Prior Elicitationp. 328
Predictionsp. 332
Checking Prior-Data Compatibilityp. 334
Bayesian Sample Size Determinationp. 336
Alternative Approaches to Sample Size Determinationp. 340
Exercisesp. 349
Other Topicsp. 352
Proportional Hazards Models Built from Monotone Functionsp. 352
Likelihood Specificationp. 354
Prior Specificationp. 356
Time-Dependent Covariatesp. 357
Accelerated Failure Time modelsp. 359
MDP Prior for [theta subscript i]p. 360
Polya Tree Prior for [theta subscript i]p. 364
Bayesian Survival Analysis Using MARSp. 373
The Bayesian Modelp. 374
Survival Analysis with Frailtiesp. 379
Change Point Modelsp. 381
Basic Assumptions and Modelp. 382
Extra Poisson Variationp. 385
Lag Functionsp. 386
Recurrent Tumorsp. 388
Bayesian Inferencep. 389
The Poly-Weibull Modelp. 395
Likelihood and Priorsp. 396
Sampling the Posterior Distributionp. 397
Flexible Hierarchical Survival Modelsp. 398
Three Stages of the Hierarchical Modelp. 400
Implementationp. 403
Bayesian Model Diagnosticsp. 413
Bayesian Latent Residualsp. 413
Prequential Methodsp. 417
Future Research Topicsp. 429
Appendixp. 431
Exercisesp. 433
List of Distributionsp. 436
Referencesp. 438
Author Indexp. 467
Subject Indexp. 475
Table of Contents provided by Rittenhouse. All Rights Reserved.

ISBN: 9780387952772
ISBN-10: 0387952772
Series: Springer Series in Statistics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 480
Published: 24th January 2005
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 2.54
Weight (kg): 0.84