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Bayesian Survival Analysis |  | Authors: Joseph G. Ibrahim, Ming-Hui Chen, Debajyoti Sinha
Publisher: Springer
List Price: $109.00
Buy New: $89.36
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New (19) Used (9) from $89.36
Rating:  8 reviews
Sales Rank: 676106
Media: Hardcover
Edition: Corrected
Pages: 481
Number Of Items: 1
Shipping Weight (lbs): 1.8
Dimensions (in): 9.3 x 6.2 x 1
ISBN: 0387952772
Dewey Decimal Number: 519.542
EAN: 9780387952772
ASIN: 0387952772
Publication Date: December 7, 2004
Availability: Usually ships in 1-2 business days
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Product Description
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. 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, joint models for longitudinal and survival data, models with time varying covariates, missing covariate data, design and monitoring of clinical trials, accelerated failure time models, models for multivariate survival data, and special types of hierarchical survival models. Also various censoring schemes are examined including right and interval censored data. Several additional topics are discussed, including noninformative and informative prior specificiations, computing posterior qualities of interest, Bayesian hypothesis testing, variable selection, model selection with nonnested models, model checking techniques using Bayesian diagnostic methods, and Markov chain Monte Carlo (MCMC) algorithms for sampling from the posteiror and predictive distributions. 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. The applications are all essentially from the health sciences, including cancer, AIDS, and the environment. The book is intended as a graduate textbook or a reference book for a one semester course at the advanced masters or Ph.D. level. This book would be most suitable for second or third year graduate students in statistics or biostatistics. It would also serve as a useful reference book for applied or theoretical researchers as well as practitioners. Joseph G. Ibrahim is Associate Professor of Biostatistics at the Harvard School of Public Health and Dana-Farber Cancer Institute; Ming-Hui Chen is Associate Professor of Mathematical Science at Worcester Polytechnic Institute; Debajyoti Sinha is Associate Professor of Biostatistics at the Medical University of South Carolina.
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| Customer Reviews:
Showing reviews 1-5 of 8
 important for biostatisticians to know January 24, 2008
Michael R. Chernick (Holland PA)
23 out of 24 found this review helpful
The first reviewer of this book seems to be knowledgeable about the subject but in my view overly harsh. The book is not intended for researchers without background in statistics. In fact, the authors state that the text is an advanced text for graduate students requiring as a prerequisite a course in mathematical statistics and one in Bayesian statistics at the level of Box and Tiao. The authors do claim to place a balance between theory and applications. Although I do feel this is an advanced text that is heavy on theory, there claim is somewhat justified in the sense that they provide several motivating examples particularly from the area of cancer research right upfront in chapter 1 even before discussing the basics of survival analysis and Bayesian methods.
An attractive feature of the text is that many topics are covered in book form for the first time. I found the coverage of cure rate models particularly interesting. Another reviewer criticized the use of piecewise models for hazard rate modelling as esoteric. However I find the exploration of these new and somewhat complicated techniques rather fascinating. The Cox proportional hazard rate model has been a mainstay in survival analysis since introduced by Cox in the 1970s. But experience has shown many applications where the proportionality assumption is not valid. Generalizations such as those in Therneau's book and the ones that Ibrahim et al. introduce here should be welcomed. The authors illustrate their applications of these techniques throughout the book. Future use will determine the degree of applicability of these techniques and issues of overparameterization needs to be addressed, but the authors should be praised for making the attempt.
The text is not just an advanced book on the authors' research. It also includes a wealth of discussion and references to the growing literature on MCMC, survival analysis and specialized topics such as cure models, frailty models and methods for comparing models.
The reference list is authoritative, scholarly and extensive, providing reference to the very early articles from the 1950s (e.g. Berkson and Gage) as well as the most recent from the 1990s and 2000-2001.
In the first chapter the authors make a strong case for the advantages of the Bayesian approach through the use of MCMC. I would only caution that the real issue between the Bayesian and frequentist inference schools lies in the appropriateness of prior distribution in inference and whether or not subjective probability is more appropriate than objective probability. These are deeper philosophical issues and seemed to be glossed over a little by the authors. However, MCMC has allowed the use of richer classes of prior distributions and the ability to look at the sensitivity of the prior modeling assumptions. For this reason many statisticians are accepting the Bayesian approach and are doing data analysis using both paradigms.
Bayesian methods are seeing growth in clinical trials particularly regarding the choice of sequential rules for stopping a trial. This has been particularly true in the medical device area where FDA statisticians have even encouraged its use in the design of trials.
With the publication of this book we can only hope to see greater use of it in survival analysis.
My one disappointment is that I would have liked to have seen a more systematic account of the various MCMC algorithms explaining their differences, limitations and advantages. The current literature on MCMC is suitably referenced including the fine tutorials on Gibbs Sampling and the Metropolis-Hastings algorithm. I just wish this book had been a little more self-contained from the MCMC point of view. Perhaps that will come in a second edition a few years hence.
The authors do jump into advanced topics and this can be frustrating for the novice. However its intended aim is for research statisticians and graduate students in statistics and with the prerequisites in hand, the book is very valuable. It does achieve its intended goal.
The theory is well covered but to make it an easier reference source, mathematical proofs are left to appendices. Other advanced topics not commonly found in text books and worthy of note are Dirichlet priors and multivariate survival models. Other recent texts that include such advanced topics as extensions to proportional hazards and multivariate surival models are respectively the text by Therneau and Grambsch and the text by Hougaard.
 Nice survey of Bayesian model selection May 14, 2005
Paul Thurston (New York, NY USA)
5 out of 5 found this review helpful
The authors have prepared a very nice survey-style treatment of Bayesian model building and specification with applications to the Cox theory of hazard models. The text is quite accessible; however, there isn't a lot of theory here. You'll need a little background material before jumping into this book. Reasonable prerequisites are Hosmer & Lemeshow's Applied Survival Analysis: Regression Modeling of Time to Event Data and Bayesian Data Analysis by Gelman, et al.
In Chapter 1, the authors provide a quick review of survival analysis before setting up the Bayesian modeling paradigm. For the Bayesians, the problem of inference of an unknown parameter is broken down into two components (thanks to Bayes' Theorem). The first component represents the contribution from the observed data set (the likelihood function). The second, and often troublesome, component comes from an assumption about the distribution of the unknown parameter, called the prior distribution. The two components combine in a natural way to give the inference. This it the so-called posterior distribution and is the goal of a Bayesian analyst.
We can therefore think of the Bayesian modeling problem as the need to acquire observed data, make a model selection and choose a prior distribution. Given these three elements, it is a straightforward application of Markov Chain Monte Carlo techniques (e.g. Gibbs Sampler) to fit the model and obtain parameter estimates.
Chapter 2 begins the survey of available Bayesian models for survival data by considering parametric survival models. This chapter gives a nice illustration of Bayesian model fitting techniques for some basic survival model techniques. Readers of the Cox theory may find themselves thinking that the parametric models presented have not one parametric item (the form of the hazard function) but two, the prior distribution of the beta coefficients.
The focus of Chapter 3 is a survey of semi-parametric models. These models are semi-parametric in the sense that the over-all form of the model is selected (usually some variation of the Cox Model), but the baseline hazard is unspecified by the standard theory. The Bayesian theory approaches the problem of the unspecified baseline by assuming its prior distribution changes with time as some identified stochastic process. The authors focus on the Gamma distribution and the Gamma process (a type of Levy process) for the first part of the chapter. Beta process models and their generalization, Dirichlet process models are presented next, but notably the treatment here isn't flexible enough to allow the model to include subject-specific covariates.
It is often the case in fitting survival data to a Cox model that one finds the proportional hazard assumptions fail to hold. Chapter 4 discusses this heterogeneity, called subject specific frailty, and surveys the Bayesian approach to fitting frailty models. Models using the Gamma distribution to encode frailty are examined from the finite variance perspective. The failure of these models to recapture the proportional hazards assumptions is discussed and the infinite variance positive stable distribution is discussed as technique to recapture proportionality into the model. The chapter ends with section discussing frailty from the point-of-view of competing risks models (multivariate survival models).
Chapter 5 is a short, but nicely prepared chapter on cure rate models. These are a family of models which incorporate recovery rates in the classical fatality time models. The authors discuss parametric and semi-parametric models from the cure rate perspective.
A collection of Bayesian model comparison techniques are offered in Chapter 6, including Bayes Factors, calculating posterior model probabilities, the Bayesian Information Criterion, the Conditional Predictive Ordinate along with the L measure tests. These tests can be used as part of a covariate selection scheme for a particular model or in a hypothesis test comparing two different models.
Chapter 7 discusses handling time-varying covariates and motivates this with longitudinal data modeling. Joint models are discussed and the EM algorithm is mentioned as the estimation technique of choice for fitting this models. A detailed exposition on this technique can be found in MacLachlan & Krishnan's The EM Algorithm and Extensions.
In the last three chapters, the authors turn to the problem of actually using Bayesian models in a real-world environment. Practical considerations such as missing data, model diagnostics, goodness-of-fit and questions of sample size are addressed. The Polya Tree process (a generalization of the Dirichlet process) is discussed as a way to address the shortcomings that the Dirichlet process prior models have with regards to subject-specific covariates.
The book contains HTTP links to download the data sets analyzed in this text. The authors also provide links to freeware code sources for the BUGS implementation of the Gibbs sampler the authors used throughout to fit their models.
Bayesian survival analysis January 16, 2002
2 out of 6 found this review helpful
This is a very well written book and the first of its kind on Bayesian survival analysis. The authors have a very keen sense of the important issues and models in this area, and they do a wonderful job of presenting the various topics. The book discusses state-of-the-art methods for fitting Bayesian survival models. The content on the power prior and its uses in survival analysis was very exciting. The motivating examples in Chapter 1 were novel and very appealing. The authors have a great deal of experience in this area and in the applications they present. I definitely recommend buying this book. It serves as an exceptional reference or textbook.
A Great Book January 14, 2002
4 out of 7 found this review helpful
This is truly a marvelous book on Bayesian survival analysis.
The authors, who are true experts in the field, have written
a gem that covers modern Bayesian methods in survival analysis.
They have a nice blend between modeling, theory, and applications
that truly makes this book the first of its kind. It has some
very nicely written chapters on semiparametric models based on
prior processes and frailty models. The book is very extensive
in its coverage and has a very long bibliography. This book is
going to be a best seller for a long time.
a great book January 11, 2002
2 out of 7 found this review helpful
This is a fabulous book covering an extensive number of topics
in Bayesian Survival Analysis. This book will be hot for
biostatisticians as well as statisticians interested in
survival analysis. A great buy.
Showing reviews 1-5 of 8
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