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. 2011 Feb;35(2):151-5.
doi: 10.1007/s00264-010-1097-2. Epub 2010 Jul 23.

Estimating implant survival in the presence of competing risks

David J Biau  1 , Moussa Hamadouche
Affiliations

Estimating implant survival in the presence of competing risks

David J Biau et al. Int Orthop. 2011 Feb.

Abstract

In medical research, commonly, one is interested in the time to the occurrence of a particular event, such as the revision of an implant, and the analysis of these data is referred to as survival analysis. However, for some patients, the event is not observed and their observations are censored. These censored observations are particular to survival data and require specific methods for estimation. The Kaplan and Meier method is a popular method to estimate the probability of being free of the event over time and it is now widely applied in orthopaedics such as to report implant survival. However, one of the assumptions underlying the Kaplan-Meier estimator implies that patients whose observations are censored have the same risk of occurrence of the event than patients remaining in the study. However, because the revision of an implant cannot occur after a patient dies, and that dead patients have their observations censored in the Kaplan-Meier method, another setting must be considered. In the sequel we will demonstrate the inadequacy of the Kaplan-Meier method to estimate implant survival and detail the cumulative incidence estimator.

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Figures

Fig. 1
Fig. 1
States and transfers considered in a one transition model, such as the Kaplan-Meier method, for patient (a) and implant (b) survival
Fig. 2
Fig. 2
Estimation of the survival probability of an event such as death or implant revision with the Kaplan-Meier method
Fig. 3
Fig. 3
Estimation of the survival for implant revision with the Kaplan-Meier estimate (data from Hamadouche et al. [13])
Fig. 4
Fig. 4
States and transfers considered in a competing event setting with revision of the implant as the event of interest and death as competing
Fig. 5
Fig. 5
Estimation of the cumulative probability of implant revision with the cumulative incidence function
Fig. 6
Fig. 6
Comparison of the estimation of the cumulative probability of implant revision with the cumulative incidence function and 1-Kaplan-Meier (data from Hamadouche et al. [13])
See this image and copyright information in PMC

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