Why you cannot censor a competing event
Censoring assumes the patient could still have had your event. When they died of something else, they could not — and one minus the Kaplan–Meier stops meaning what you want it to mean.
Censoring a patient means something specific: their follow-up stopped, but they remain the kind of patient who could still have the event, and the ones who continue being followed stand in for them. That is what makes the Kaplan–Meier estimator work.
A competing event breaks that assumption outright. If a patient dies of cardiovascular disease, they cannot subsequently relapse. Treating that death as censoring asks the remaining patients to represent someone whose relapse risk is not merely unobserved but zero. The result is that one minus the Kaplan–Meier overestimates the risk of your event, and it does so more the more common the competing event is — which is precisely when you were most likely to reach for it.
The quantity you almost always want instead is the cumulative incidence function: the probability of having your event by a given time, in a world where the other events also happen. It is estimated from the cause-specific hazards of all the events together, not from your event alone, and the cumulative incidences of all causes sum to the probability of having had any event.
This has a consequence that surprises people the first time they meet it. A covariate can raise the cause-specific hazard of your event and lower its cumulative incidence, because it raised the hazard of a competing event more. Both statements are true and they answer different questions: the cause-specific hazard is about the biology of your event, the cumulative incidence is about what happens to a population. Decide which you are asking before you choose the model, and say which you reported.
MethodCompeting risks