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

A topic that has received attention in both the statistical and medical lit erature 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 interpret ed as the probability of failure. If one desires an estimate that can be in terpreted in this way, however, the cumulative incidence estimate is the ap propriate 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 th is 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 mote intuitive understanding of each estimate and therefore an app reciation of why the Kaplan-Meier method is inappropriate for estimation pu rposes in the presence of competing risks, while the cumulative incidence e stimate is appropriate. Copyright (C) 1999 John Wiley & Sons, Ltd.