Thomas R. Fleming & David P. Harrington 
Counting Processes and Survival Analysis 

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’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 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.

Innehållsförteckning

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.

Om författaren

THOMAS R. FLEMING, Ph D, is Professor and Chairman of Biostatistics at the University of Washington.

DAVID P. HARRINGTON, Ph D, is Professor of Biostatistics at the Harvard School of Public Health.