I would like to perform a time to event analysis on some biological example with animals. The event of interest is a terminal event X. But the animal may die from other reason before it happens. So I would like to compare three curves:
Death and the terminal event X are equated. I can assign "1" to an animal regardless of the cause. I can use Kaplan-Meier.
Death is censored. I am interested only in the event X. I can assign "0" to death. I can use Kaplan-Meier.
Death is a competing risk. So I model the time to event X "corrected" for deaths. I am asked to use the Fine-Gray subdistribution hazard (I know it's under criticism, but I have to).
First question - do these models have any special name? I heard about crude, cause specific, and net survival, but still confuse them.
Each of the models can "generate" a survival curve to me. In R it's "survfit" I believe. Now, having three curves, telling me the probability of the event, I would like to compare them with a test, say, LogRank.
How to do that, knowing these are 3 separate models?
Or maybe it would be easier to compare median survival times? But it may happen the curve won't reach 50%. And I don't know any test that compares survival medians.