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I recently got involved in a study on survival of teeth where the time until extraction was measured. The reason for extraction could be either an infection or some other cause. These other causes seemed to me as a competing risk in relation to infection since an exatracted tooth cannot get an infection.

However, it turned out that the cumulative incidence for the infected teeth was about the same regardless of whether extractions with other causes were censored in an "ordinary" Kaplan-Meier analysis or entered as a competing risk (using the cmprsk package i R). Both causes have a fairly low incidence, the 10 year survival is about 0.07 for infected teeth and 0.15 for other causes. Or expressed as numbers: out of 270 teeth, a total of 22 teeth were extracted due to infections and 40 due to other causes over a 10 year period.

How could this be explained? Isn't it somewhat strange that the competing causes do not make any significant difference?

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The explanation is probably your observation that

out of 270 teeth, a total of 22 teeth were extracted due to infections and 40 due to other causes over a 10 year period.

During the 10-year period there were thus at least 248 teeth at risk for extraction from causes other than infection. Take an extreme example in which all 22 extractions due to infections occurred at the beginning of the study. The 40 extractions due to other causes would be 16% of the remaining 248, versus 15% of the full set of 270. That's an effectively imperceptible difference, particularly when you realize that the sampling error in finding 40 rare events (Poisson distribution) is about $\pm 6$, or 2% of your 270 total teeth.

If both competing events are rare enough, you won't be able to see much competition.

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