I have a survival problem that's bugging me.
My client has an ongoing single-sample survival study in advanced cancer with 75 patients initially.
There have been 50 deaths. The death times and the censoring times for the remaining 25 patients are available.
The client wants to know when there will be 75 deaths (calendar time). I know that I can't actually know the death times for the patients who are currently censored, but I should be able to provide a probabilistic statement such as a probability of 75 deaths by calendar time T*.
The survival distribution for time to death from Day 0 can be estimated using a non-parametric approach such as KM or a parametric approach, but I don't see how to use that.
I can estimate the distribution of time to T* from censoring date for currently censored patients, but that doesn't seem to helpful for answering the question either.
I am considering simulation; that seems unnecessarily complicated, but can't think of a less complicated solution.
Any thoughts?
Thanks,
David