Research Article

Estimation of failure probabilities in the presence of competing risks: new representations of old estimators

  1. Ted A. Gooley1,2,3,*,
  2. Wendy Leisenring1,2,3,
  3. John Crowley2,3,
  4. Barry E. Storer1,2,3

Article first published online: 12 MAR 1999

DOI: 10.1002/(SICI)1097-0258(19990330)18:6<695::AID-SIM60>3.0.CO;2-O

Issue

Statistics in Medicine

Statistics in Medicine

Volume 18, Issue 6, pages 695–706, 30 March 1999

Additional Information

How to Cite

Gooley, T. A., Leisenring, W., Crowley, J. and Storer, B. E. (1999), Estimation of failure probabilities in the presence of competing risks: new representations of old estimators. Statistics in Medicine, 18: 695–706. doi: 10.1002/(SICI)1097-0258(19990330)18:6<695::AID-SIM60>3.0.CO;2-O

Author Information

  1. 1

    Fred Hutchinson Cancer Research Center, Clinical Research Division, Seattle, WA 98109-1024, U.S.A.

  2. 2

    Fred Hutchinson Cancer Research Center, Public Health Sciences Division, Seattle, WA 98109-1024, U.S.A.

  3. 3

    Department of Biostatistics, University of Washington, U.S.A.

*Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue N., D5-290, P.O. Box 19024, Seattle, WA 98109-1024, U.S.A.

Publication History

  1. Issue published online: 12 MAR 1999
  2. Article first published online: 12 MAR 1999
  3. Manuscript Accepted:
  4. Manuscript Received:

Funded by

  • National Institutes of Health. Grant Numbers: CA 18029, CA 38296, HL 36444

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Abstract

A topic that has received attention in both the statistical and medical literature is the estimation of the probability of failure for endpoints that are subject to competing risks. Despite this, it is not uncommon to see the complement of the Kaplan–Meier estimate used in this setting and interpreted as the probability of failure. If one desires an estimate that can be interpreted in this way, however, the cumulative incidence estimate is the appropriate tool to use in such situations. We believe the more commonly seen representations of the Kaplan–Meier estimate and the cumulative incidence estimate do not lend themselves to easy explanation and understanding of this interpretation. We present, therefore, a representation of each estimate in a manner not ordinarily seen, each representation utilizing the concept of censored observations being ‘redistributed to the right.’ We feel these allow a more intuitive understanding of each estimate and therefore an appreciation of why the Kaplan–Meier method is inappropriate for estimation purposes in the presence of competing risks, while the cumulative incidence estimate is appropriate. Copyright © 1999 John Wiley & Sons, Ltd.

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