# Is the cumulative incidence function just an inverted Kaplan-Meier survival curve?

Is CIF just an inverted Kaplan-Meier survival curve, and nothing more?

If you're talking about the cumulative incidence function that arises from a Kaplan-Meier estimator, then it's just $1 - S(t)$ where $t$ is time. In R:

library(survival)
fit <- survfit(Surv(time, status) ~ x, data = aml)
plot(fit) # the standard survival curve
plot(fit, fun="event") # the cumulative incidence curve


But, CIF is more commonly used in other contexts, for example in competing risk analysis using cause-specific Cox regression. There, the CIF is not necessarily equal to $1-S(t)$ because it takes into account the competing risk, estimating the risk of an event happening given survival up to time $t$ and also that a competing risk hasn't occurred up to time $t$.

• GREAT THANKS! COULD I CALL (IN THE ARTICLE, IN WHICH I ANALYZE GROUP OF PATIENTS) CIF AS A "CUMULATIVE FREQUENCY OF RISK" (ASSOCIATED WITH SOME FACTOR) OR SIMPLER: "CUMULATIVE RISK"? – Beginner Mar 27 '15 at 14:32
• If you're referring to the no-competing risk scenario, then I'd just call it cumulative risk. – purple51 Mar 28 '15 at 0:53