Competing risks: cumulative incidence and Fine-Gray
Estimates the cumulative incidence of an event when another event can prevent it, instead of treating the competing event as censoring.
Clinical example
Time to relapse, where patients who die before relapsing can no longer relapse.
When to use it
- The outcome is the time until an event, and another event can prevent it.
- The competing event is common, such as death before relapse.
- You want the proportion expected to have the event over time, not only a rate.
Assumptions to check
Competing event is defined
Decide in advance which events compete with the one you study, and code each patient as censored, event or competing event.
Non-informative censoring
Patients who are censored, for example lost to follow-up, should have the same future risk as patients who remain under observation.
What to report
- Cumulative incidence curves for the event of interest and for the competing event
- Cumulative incidence at a clinically relevant time with 95% CI
- Subdistribution hazard ratio with 95% CI, if you model it
Common mistakes
Don't censor competing events
Treating death as censoring when studying relapse overstates the relapse risk. Use cumulative incidence instead of 1 minus Kaplan-Meier.
Alternatives
| If your situation is… | Use |
|---|---|
| The competing event is rare | Cox proportional hazards regression |
In your software
# R
library(tidycmprsk)
# status: factor with levels censored, relapse, death (in that order)
cuminc(Surv(time_months, status) ~ arm, data = cohort)
crr(Surv(time_months, status) ~ arm + age, data = cohort)