I would like to look at survival in time to event data. So individuals either have an event, or are censored. My problem is the sensitivity for detecting an event differs between arms. I.e. in the intervention, 10% of the events are mislabeled as a censor. In the control, 15%. I do not know the true sensitivity and specificity for detecting the event, just rough estimates and that they are almost certainly different between arms.
Is there a method for dealing with this?
My main problem is that I do not know when an outcome is missing - I just see it as a censored event mislabeled. If the outcome was missing outright (i.e. the outcome was a missing lab value), I could try something like a PMM model imputing data with different levels of bias.
Any help would be gratefully appreciated!