Description

Book Synopsis
This 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 Contents
Preface.

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.

Counting Processes and Survival Analysis

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    A Paperback / softback by Thomas R. Fleming, David P. Harrington

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      Book details

      Publisher John Wiley & Sons Inc
      Published 18 October 2005
      ISBN-13 9780471769880
      978-0471769880
      ISBN-10 0471769886
      Also in:
      Mathematics Stochastics

      Description

      Book Synopsis
      This 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 Contents
      Preface.

      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.

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