Counting Processes and Survival Analysis [Hardcover]

Thomas R. Fleming (Author), David P. Harrington (Author)

Book Description

ISBN-10: 047152218X | ISBN-13: 978-0471522188 | Publication Date: March 13, 1991 | Edition: 1

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.

"The book is a valuable completion of the literature in this field. It is written in an ambitious mathematical style and can be recommended to statisticians as well as biostatisticians."
-Biometrische Zeitschrift

"Not many books manage to combine convincingly topics from probability theory over mathematical statistics to applied statistics. This is one of them. The book has other strong points to recommend it: it is written with meticulous care, in a lucid style, general results being illustrated by examples from statistical theory and practice, and a bunch of exercises serve to further elucidate and elaborate on the text."
-Mathematical Reviews

"This book gives a thorough introduction to martingale and counting process methods in survival analysis thereby filling a gap in the literature."
-Zentralblatt f?r Mathematik und ihre Grenzgebiete/Mathematics Abstracts

"The authors have performed a valuable service to researchers in providing this material in [a] self-contained and accessible form. . . This text [is] essential reading for the probabilist or mathematical statistician working in the area of survival analysis."
-Short Book Reviews, International Statistical Institute

Counting Processes and Survival Analysis explores the martingale approach to the statistical analysis of counting processes, with an emphasis on the application of those methods to censored failure time data. This approach has proven remarkably successful in yielding results about statistical methods for many problems arising in censored data. A thorough treatment of the calculus of martingales as well as the most important applications of these methods to censored data is offered. Additionally, the book examines classical problems in asymptotic distribution theory for counting process methods and newer methods for graphical analysis and diagnostics of censored data. Exercises are included to provide practice in applying martingale methods and insight into the calculus itself.

Editorial Reviews

Review

"…a unique source for combining the theory and the application of the survival analysis with censored data." (Technometrics, August 2007) --This text refers to the Paperback edition.

From the Publisher

Explores the martingale approach to the statistical analysis of counting processes, with an emphasis on application of those methods to censored failure time data. Introduced in the 1970s, this approach has proven to be remarkably successful in yielding results about statistical methods for many problems arising in censored data. Offers a thorough treatment of both the calculus of martingales needed for the study of counting processes and of the most important applications of these methods to censored data. In addition, it examines classical problems in asymptotic distribution theory for counting process methods as well as some newer methods for graphical analysis and diagnostics of censored data. Exercises are included to provide students with practice in applying martingale methods and insight into the calculus itself.

See all Editorial Reviews

Product Details

• Hardcover: 448 pages
• Publisher: Wiley; 1 edition (March 13, 1991)
• Language: English
• ISBN-10: 047152218X
• ISBN-13: 978-0471522188
• Product Dimensions: 9.6 x 6.5 x 1.4 inches
• Shipping Weight: 1.8 pounds
• Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,718,041 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

17 of 17 people found the following review helpful:

4.0 out of 5 stars Well-written and Informative, June 6, 2005

By 

Paul Thurston (New York, NY USA) - See all my reviews
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This review is from: Counting Processes and Survival Analysis (Hardcover)

This is one of the best treatments I have read on the martingale theory of the analysis of survival data. This material really gets you under-the-hood of proportional hazards modeling and details when the theory is applicable and where things can break down in the models. This is positively a "must-own" for advanced researchers working with survival data and a "good-to-have" desk reference for anyone dealing with survival data.

Chapter 0 provides a meaningful introduction, and the authors use real-world survival data sets to set the stage for the basic concepts. They like the PBC liver study data set a lot and use it frequently through the text. There is some great material in this short chapter, including a formal definition of the hazard function, a nice overview of the Kaplan-Meier estimator, and an introduction of the Cox model with a very nice, intuitive treatment of the derivation of Cox's partial likelihood function. The authors also set the stage for the martingale theoretic treatment and give three motivating (and compelling) reasons for the theory.

Chapter 1 covers the basics from stochastic analysis that are required for the remainder of the book. Basic definitions and concepts like filtration, conditional expectation, the definition of a martingale and the Doob-Meyer decomposition are covered. No prior knowledge of stochastic analysis is assumed. However, a good understanding of measure theory is very helpful (something along the lines of the first four chapters for Rudin's Real and Complex Analysis). The chapter wraps up with the martingale transformation theorem.

The main aim of Chapter 2 is to establish quadratic variation properties for continuous compensators of counting processes. This material is heavily used in the asymptotic Brownian motion material in Chapter 5 (where a large part of the story rests on the limiting behavior of quadratic variation). To get there, a number of localization results are established. The Optional Sampling Theorem is stated and used (the proof is referenced out to the literature). The main workhorse, the Optional Stopping Theorem is established as a nice application of optional sampling.

Chapter 3 is a wonderful, rigorous treatment of the survival estimators and test statistics that we know and love and always wondered why these are vaguely true. The main result is the consistency of the Kaplan-Meier estimator, which foreshadows the consistency results for the Cox regression estimator established in Chapter 8.

The proportional hazards model and multiplicative intensity models are the main focus of Chapter 4. The modeling framework is introduced, basic concepts such as uninformative censoring are introduced and the method of partial likelihoods is explored in depth. The chapter just has great little pearls sprinkled throughout, including martingale properties for Breslow's estimator for baseline hazard and a number of modeling building diagnostic techniques. There is also a very nice set of graphs on the martingale residual technique of assessing functional form of continuous covariates.

Chapter 5 is the core of the book and develops the asymptotic limit results, including the martingale central limit theorem for counting processes. The chapter is nearly self-contained, with the occasional reference to one of the classical probability texts like Chung or Billingsley. Proofs that could prove a distraction to the main thread are placed in the appendix.

Chapters 6, 7 and 8 provide very nice applications of the martingale central limit theorem. These include: building confidence bands, establishing large sample properties of test statistics and putting Cox's technique of partial likelihoods on solid footing by establishing by establishing consistency and asymptotic normality. As an important final topic for consideration, asymptotic efficiency of the Cox estimator is explored. It is somewhat disappointing that no formal theorem establishing conditions for asymptotic efficiency is presented.

As a wish list item for the next edition, it would be nice to see a chapter or two introducing multivariate survival analysis (competing risks), and the role of Markov processes. For the definitive work on the topic of multivariate survival analysis, I recommend Andersen, Borgan, Gill and Kieding's Statistical Models Based on Counting Processes (Springer Series in Statistics).

0 of 2 people found the following review helpful:

4.0 out of 5 stars Fast and almost new, October 19, 2010

By 

Nuli - See all my reviews

Amazon Verified Purchase

This review is from: Counting Processes and Survival Analysis (Wiley Series in Probability and Statistics) (Paperback)

It's very fast delivered and it looks almost new. Since I've borrowed this book from library, I already know this book is quite helpful to understand how to apply countinng process to survival analysis.

1 of 4 people found the following review helpful:

5.0 out of 5 stars a must read in survival analysis, January 6, 2009

By 

Mr. Feng Chen (Sydney, NSW, Australia) - See all my reviews
(REAL NAME)   

This review is from: Counting Processes and Survival Analysis (Wiley Series in Probability and Statistics) (Paperback)

A beautifully written self-contained book on the theory of counting processes and its applications in survival analysis. It is definitely one of the must-reads to researchers working in the field of medical statistics. It also makes an excellent textbook for a graduate or senior undergraduate level course on the subject.