Statistics for Biology and Health
Series Editors
K. Dietz, M. Gail, K. Krickeberg, J. Samet, A. Tsiatis
Springer
New York
Berlin
Heidelberg
Hong Kong
London
Milan
Paris
Tokyo
SURVIVAL
ANALYSIS
Techniques for
Censored and
Truncated Data
Second Edition
John P. Klein
Medical College of Wisconsin
Melvin L. Moeschberger
The Ohio State University Medical Center
With 97 Illustrations
1
Springer
John P. Klein Melvin L. Moeschberger
Division of Biostatistics School of Public Health
Medical College of Wisconsin Division of Epidemiology and Biometrics
Milwaukee, WI 53226 The Ohio State University Medical Center
USA Columbus, OH 43210
USA
Series Editors
K. Dietz M. Gail
Institut f
¨
ur Medizinische Biometrie National Cancer Institute
Universit
¨
at T
¨
ubingen Rockville, MD 20892
Westbahnhofstrasse 55 USA
D-72070 T
¨
ubingen
Germany
K. Krickeberg J. Samet
Le Chatelet School of Public Health
F-63270 Manglieu Department of Epidemiology
France Johns Hopkins University
615 Wolfe St.
Baltimore, MD 21205-2103
USA
A. Tsiatis
Department of Statistics
North Carolina State University
Raleigh, NC 27695
USA
Library of Congress Cataloging-in-Publication Data
Klein, John P., 1950–
Survival analysis : techniques for censored and truncated data / John P. Klein, Melvin
L. Moeschberger. — 2nd ed.
p. cm. — (Statistics for biology and health)
Includes bibliographical references and index.
ISBN 0-387-95399-X (alk. paper)
1. Survival analysis (Biometry) I. Moeschberger, Melvin L.
II. Title. III. Series.
R853.S7 K535 2003
610
.7
27–dc21 2002026667
ISBN 0-387-95399-X Printed on acid-free paper.
© 2003, 1997 Springer-Verlag New York, Inc.
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010,
USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with
any form of information storage and retrieval, electronic adaptation, computer software, or by similar or
dissimilar methodology now known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are
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are subject to proprietary rights.
Printed in the United States of America.
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Springer-Verlag New York Berlin Heidelberg
A member of BertelsmannSpringer Science ⫹Business Media GmbH
Preface
The second edition contains some new material as well as solutions to
the odd-numbered revised exercises. New material consists of a discus-
sion of summary statistics for competing risks probabilities in Chapter 2
and the estimation process for these probabilities in Chapter 4. A new
section on tests of the equality of survival curves at a fixed point in
time is added in Chapter 7. In Chapter 8 an expanded discussion is pre-
sented on how to code covariates and a new section on discretizing a
continuous covariate is added. A new section on Lin and Ying’s additive
hazards regression model is presented in Chapter 10. We now proceed
to a general discussion of the usefulness of this book incorporating the
new material with that of the first edition.
A problem frequently faced by applied statisticians is the analysis of
time to event data. Examples of such data arise in diverse fields such
as medicine, biology, public health, epidemiology, engineering, eco-
nomics and demography. While the statistical tools we shall present
are applicable to all these disciplines our focus is on applications of
the techniques to biology and medicine. Here interest is, for example,
on analyzing data on the time to death from a certain cause, dura-
tion of response to treatment, time to recurrence of a disease, time to
development of a disease, or simply time to death.
The analysis of survival experiments is complicated by issues of cen-
soring, where an individual’s life length is known to occur only in a
certain period of time, and by truncation, where individuals enter the
study only if they survive a sufficient length of time or individuals are
v
vi Preface
included in the study only if the event has occurred by a given date. The
use of counting process methodology has, in recent years, allowed for
substantial advances in the statistical theory to account for censoring
and truncation in survival experiments. The book by Andersen et al.
(1993) provides an excellent survey of the mathematics of this theory.
In this book we shall attempt to make these complex methods more
accessible to applied researchers without an advanced mathematical
background by presenting the essence of the statistical methods and
illustrating these results in an applied framework. Our emphasis is on
applying these techniques, as well as classical techniques not based
on the counting process theory, to data rather than on the theoreti-
cal development of these tools. Practical suggestions for implementing
the various methods are set off in a series of practical notes at the
end of each section. Technical details of the derivation of these tech-
niques (which are helpful to the understanding of concepts, though not
essential to using the methods of this book) are sketched in a series of
theoretical notes at the end of each section or are separated into their
own sections. Some more advanced topics, for which some additional
mathematical sophistication is needed for their understanding or for
which standard software is not available, are given in separate chapters
or sections. These notes and advanced topics can be skipped without
a loss of continuity.
We envision two complementary uses for this book. The first is as
a reference book for investigators who find the need to analyze cen-
sored or truncated life time data. The second use is as a textbook for
a graduate level course in survival analysis. The minimum prerequisite
for such course is a traditional course in statistical methodology. The
material included in this book comes from our experience in teaching
such a course for master’s level biostatistics students at The Ohio State
University and at the Medical College of Wisconsin, as well as from our
experience in consulting with investigators from The Ohio State Univer-
sity, The University of Missouri, The Medical College of Wisconsin, The
Oak Ridge National Laboratory, The National Center for Toxicological
Research, and The International Bone Marrow Transplant Registry.
The book is divided into thirteen chapters that can be grouped into
five major themes. The first theme introduces the reader to basic con-
cepts and terminology. It consists of the first three chapters which deal
with examples of typical data sets one may encounter in biomedical
applications of this methodology, a discussion of the basic parameters
to which inference is to be made, and a detailed discussion of censoring
and truncation. New to the second edition is Section 2.7 that presents a
discussion of summary statistics for competing risks probabilities. Sec-
tion 3.6 gives a brief introduction to counting processes, and is included
for those individuals with a minimal background in this area who wish
to have a conceptual understanding of this methodology. This section
can be omitted without jeopardizing the reader’s understanding of later
sections of the book.
