Description
Book SynopsisThis book 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.
Trade Review"…a unique source for combining the theory and the application of the survival analysis with censored data." (
Technometrics, August 2007)
Table of ContentsPreface.
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.
Bibliography.
Notation.
Author Index.
Subject Index.
