Synopses & Reviews
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.
Synopsis
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.
Description
Includes bibliographical references (p. 401-412) and indexes.
Table of Contents
The Applied Setting.
The Counting Process and Martingale Framework.
Local Square Integrable Martingales.
Finite Sample Moments and Large Sample Consistency of Tests and Estimators.
Censored Data Regression Models and Their Application.
Martingale Central Limit Theorem.
Large Sample Results of the Kaplan-Meier Estimator.
Weighted Log Rank Statistics.
Distribution Theory for Proportional Hazards Regression.
Appendices.
Bibliography.
Notation.
Author Index.
Subject Index.