Counting Processes and Survival Analysis
"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."
"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."
"This book gives a thorough introduction to martingale and counting process methods in survival analysis thereby filling a gap in the literature."
-Zentralblatt für 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.
0. The Applied Setting.
1. The Counting Process and Martingale Framework.
2. Local Square Integrable Martingales.
3. Finite Sample Moments and Large Sample Consistency of Tests and Estimators.
4. Censored Data Regression Models and Their Application.
5. Martingale Central Limit Theorem.
6. Large Sample results of the Kaplan-Meier Estimator.
7. Weighted Logrank Statistics.
8. Distribution Theory for Proportional Hazards Regression.
Appendix A: Some Results from stieltjes Integration and Probability Theory.
Appendix B: An Introduction to Weak convergence.
Appendix C: The Martingale Central Limit Theorem: Some Preliminaries.
Appendix D: Data.
Appendix E: Exercises.
DAVID P. HARRINGTON, PhD, is Professor of Biostatistics at the Harvard School of Public Health.