# Can I draw 1-CIF (Cumulative Incidence Function) as a survival curve?

I analyze survival data with competing risks. To me, the CIF is fine, but the researchers want to see how fast the survival falls, so they want the 1-CIF. They know it's NOT the Kaplan-Meier, it's a different analysis (cause specific, but with overall survival in it) than the cause-specific K-M, it's just a question for a different presentation.

Honestly, I couldn't find any examples of 1-CIF curves (all mention 1-KM = CIF when there's no competing risk). Will that be OK to draw a 1-CIF curve as a survival curve and mention in the plot title it's 1-CIF (so calculated differently, via Aalen-Johansen estimator; no covarites), just showing how fast people experience the event of interest?

EDIT: They want to see each cause-specific CIF. In the overall case it's not a problem, as CIF = sum of specific CIFs = 1-KM.

For the cause-specific CIF I cannot use the KM (would make it too high), but I can calculate CIF and THEN draw the 1-CIF to "mimic" the survival curve.

By competing risks I mean, death from many reasons, while the even of interest is some clinical event. The death(s) prevent the event to happen (while censoring does not).

• Please clarify what you mean by "the researchers want to see how fast the survival falls." Is that for each event type separately, or for any event? Also, just to check, when you say "competing risks" do you mean that occurrence of any type of event prevents the other types from occurring in that individual? Please provide that information by editing the question, as comments are often overlooked and can be lost.
– EdM
Sep 5, 2021 at 16:36
• Thank you for your suggestions, I updated the comment. Sep 5, 2021 at 16:58
• Thanks for the quick update. When the non-death "event" of interest happens to an individual, do you simply stop collecting data on that individual or do you further examine the "event"-to-death transition?
– EdM
Sep 5, 2021 at 17:04
• It stops collecting. There's no recurrent events in this case. For this I'd use joint frailty model. Here I just want to show the CIFs as if it was survival (just mirrored). Sep 5, 2021 at 17:45

This seems to be similar to the analysis in Section 2.3.2 of the R survival vignette, where individuals were evaluated until development of (a) plasma cell malignancy or (b) death, whichever came first, as competing risks. The standard plot for competing risks is, as you note, the cumulative probability of each type of event over time. The first figure in that section of the vignette is an example.

I know of no rule against plotting each of those cumulative probabilities as apparent survival curves as you propose, but that runs a risk of being misleading to those who don't already understand the issues thoroughly. It might be too tempting to interpret each of the individual "survival" curves as representing a "cure" model, as each curve will plateau at some finite apparent "survival." I would thus not recommend that for publication, only for internal use.

If you nevertheless do produce such a plot, I'd recommend including the survival curve representing occurrence of either event. That will help emphasize that those cause-specific "survival" curves represent alternate, mutually exclusive ways to be lost from the initial event/death-free state. The first plot in Section 2.3.2 of the survival vignette shows such a curve, along with the standard cumulative probabilities.

• Isn’t one of the fundamental problems of identification in competing risk analysis that you cannot, without making the untestable assumption that competing risks are independent, identify the cause-specific survival function? Apr 16, 2023 at 16:07
• @BrashEquilibrium in a classic "competing risks" model (at most one event, with the first event being an absorbing state) I suppose that the competing risks aren't independent, as in that model the occurrence of one event type means that the second event type will never occur. That's why it can be bad to evaluate one event type by censoring at times of other event types. A true competing-risks model, as described in the vignette, deals with the problem and provides reliable estimates of the probability of each type of event over time as a function of covariates.
– EdM
Apr 16, 2023 at 20:37
• It isn't the fact that one event precludes another's occurrence that makes marginal survival unidentified. It is that plus the statistical dependence of the competing risks (that is, the rates of the two events depend on one another statistically, say due to some common cause, or through some mediating factor, or even common effect). If the events are statistically independent (an untestable assumption) marginal survival is identified. Apr 25, 2023 at 21:56
• @BrashEquilibrium even if there is an underlying factor mediating both event types, you can still evaluate the probabilities of being in any of the 3 states (no event, event type 1, event type 2) over time, conditional on the covariate values.
– EdM
Apr 26, 2023 at 13:58