# Survival analysis: How to handle data where I know the event occurred, but I don't know when it occurred?

I am trying to do a survival analysis on some cancer data. I plan on doing Kaplan-Meier and Cox proportional hazards regression. I am interested in looking at the impact of various variables on overall survival. I have three potentially relevant pieces of data for each sample:

• Status (binary variable; whether the patient died or is alive)
• Days to death (elapsed time between when the study began and when the patient died)
• Days to final follow up (elapsed time between when the study began and the last time the patient was followed up with; from what I can tell, this is <= to days to death)

For the patients who are marked as "alive" in the data, I plan to use the 'days to final follow up' as the right censored survival value. The event (death) did not occur for these patients, so event = 0.

For the patients who are marked as "dead" in the data, I plan to use 'days to death', when available, as the survival value. The event occurred for these patients, so event = 1.

I am confused what to do when patients are marked as "dead" in the data, but I do not have a 'days to death' value for them. I only have a 'days to final follow up' value for these patients. The event occurred for these patients, but it may have occurred anytime on or after 'days to final follow up' (since they had to have been alive at the follow up). I am assuming that what happened in these cases was that the patient died sometime after their final follow up or maybe after the conclusion of the study, so they were marked as 'dead' but their 'days to death' value may have been not recorded.

For these "dead" patients, should I assume that they were alive at the 'days to final follow up' date, and mark them as "alive" (event = 0) and use the 'days to final follow up' as right-censored survival time? Or should I keep them as 'dead' (event = 1) and use 'days to final follow up' as right-censored survival time? Does it make sense to have censoring for patients for whom the event occurred?

I would like to avoid dropping data, if possible - around half of the events are patients marked as 'dead' but for whom 'days to death' is not available.

Thank you so much!

Such cases are called interval censored: unlike right censoring, where you have only a lower bound for the time-to-event, you have both a lower and an upper limit. That is best analyzed by specifying both the left and right limits in time from study start between which the event happened (those can be the same values, to specify uncensored event times) and using a program (unlike the standard coxph() function in R) that is designed to perform the calculations needed to handle this sort of data.
The R icenReg package has a vignette that explains the issues with interval-censored survival times and ways to analyze such data. A web search on interval censoring will suggest many more sources of information.
• @user318967 for that set “P” of patients, it might be simplest to right-censor as of last follow-up date. Alternatively, you could interval-censor between the last follow-up date and the date that you received information that they had died. With icenReg and the (leftLimit, rightLimit] coding of event times I think there is no need for a separate alive/dead variable; you use $\infty$ or NA for the rightLimit for right-censored event times.