Survival Analysis - A Self-Learning Text (Springer).pdf

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Statistics for Biology and Health Series Editors M. Gail, K. Krickeberg, J. Samet, A. Tsiatis, W. Wong

David G. Kleinbaum Mitchel Klein Survival Analysis A Self-Learning Text Second Edition

David G. Kleinbaum Department of Epidemiology Rollins School of Public Health at Emory University 1518 Clifton Road NE Atlanta GA 30306 Email: dkleinb@sph.emory.edu Mitchel Klein Department of Epidemiology Rollins School of Public Health at Emory University 1518 Clifton Road NE Atlanta GA 30306 Email: mklein@sph.emory.edu Series Editors M. Gail National Cancer Institute Rockville, MD 20892 USA K. Krickeberg Le Cha¨telet F-63270 Manglieu France A. Tsiatis Department of Statistics North Carolina State University Raleigh, NC 27695 USA Wing Wong Department of Statistics Stanford University Stanford, CA 94305 USA J. Samet Department of Epidemiology School of Public Health Johns Hopkins University 615 Wolfe Street Baltimore, MD 21205 USA SAS® and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. ® indicates USA registration. SPSS® is a registered trademark of SPSS Inc. STATA® and the STATA® logo are registered trademarks of StataCorp LP. Library of Congress Control Number: 2005925181 Printed on acid-free paper. ISBN-10: 0-387-23918-9 ISBN-13: 978-0387-23918-7 © 2005, 1996 Springer Science+Business Media, 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 Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connec- tion 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 not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. (TechBooks/HAM) 9 8 7 6 5 4 3 2 1 springeronline.com

Survival Analysis A Self-Learning Text Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo

David G. Kleinbaum Mitchel Klein Survival Analysis A Self-Learning Text Second Edition

To Rosa Parks Nelson Mandela Dean Smith Sandy Koufax And countless other persons, well-known or unknown, who have had the courage to stand up for their beliefs for the beneﬁt of humanity.

Preface This is the second edition of this text on survival analysis, originally published in 1996. As in the ﬁrst edition, each chap- ter contains a presentation of its topic in “lecture-book” for- mat together with objectives, an outline, key formulae, prac- tice exercises, and a test. The “lecture-book” format has a sequence of illustrations and formulae in the left column of each page and a script in the right column. This format allows you to read the script in conjunction with the illustrations and formulae that high-light the main points, formulae, or exam- ples being presented. This second edition has expanded the ﬁrst edition by adding three new chapters and a revised computer appendix. The three new chapters are: Chapter 7. Parametric Survival Models Chapter 8. Recurrent Event Survival Analysis Chapter 9. Competing Risks Survival Analysis Chapter 7 extends survival analysis methods to a class of sur- vival models, called parametric models, in which the distri- bution of the outcome (i.e., the time to event) is speciﬁed in terms of unknown parameters. Many such parametric models are acceleration failure time models, which provide an alter- native measure to the hazard ratio called the “acceleration factor”. The general form of the likelihood for a parametric model that allows for left, right, or interval censored data is also described. The chapter concludes with an introduction to frailty models. Chapter 8 considers survival events that may occur more than once over the follow-up time for a given subject. Such events are called “recurrent events”. Analysis of such data can be carried out using a Cox PH model with the data layout aug- mented so that each subject has a line of data for each re- current event. A variation of this approach uses a stratiﬁed Cox PH model, which stratiﬁes on the order in which recur- rent events occur. The use of “robust variance estimates” are recommended to adjust the variances of estimated model co- efﬁcients for correlation among recurrent events on the same subject.

viii Preface Suggestions for Use Chapter 9 considers survival data in which each subject can experience only one of several different types of events (“com- peting risks”) over follow-up. Modeling such data can be car- ried out using a Cox model, a parametric survival model or a model which uses cumulative incidence (rather than survival). The Computer Appendix in the ﬁrst edition of this text has now been revised and extended to provide step-by-step in- structions for using the computer packages STATA (version 7.0), SAS (version 8.2), and SPSS (version 11.5) to carry out the survival analyses presented in the main text. These com- puter packages are described in separate self-contained sec- tions of the Computer Appendix, with the analysis of the same datasets illustrated in each section. The SPIDA package used in the ﬁrst edition is no longer active and has therefore been omitted from the appendix and computer output in the main text. In addition to the above new material, the original six chap- ters have been modiﬁed slightly to correct for errata in the ﬁrst edition, to clarify certain issues, and to add theoretical back- ground, particularly regarding the formulation of the (partial) likelihood functions for the Cox PH (Chapter 3) and extended Cox (Chapter 6) models. The authors’ website for this textbook has the following web- link: http://www.sph.emory.edu/∼dkleinb/surv2.htm This website includes information on how to order this second edition from the publisher and a freely downloadable zip-ﬁle containing data-ﬁles for examples used in the text- book. This text was originally intended for self-study, but in the nine years since the ﬁrst edition was published, it has also been ef- fectively used as a text in a standard lecture-type classroom format. The text may also be use to supplement material cov- ered in a course or to review previously learned material in a self-instructional course or self-planned learning activity. A more individualized learning program may be particularly suitable to a working professional who does not have the time to participate in a regularly scheduled course.

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