If I have disease free survival data (defined as whether or not a particular disease has been diagnosed or not along with the time to that event or loss to follow up) and also overall survival data, how do I deal with deaths that occur without the disease event? Are these censored or should I exclude such patients from the disease-free survival (dfs) analysis? I plan to run dfs analyses for several particular types of disease separately.
My interpretation of disease free survival is that the only event is diagnose of return of the disease. Any other event be it patient withdrawal from the study, lost to follow-up for any other reason or death is a censored event because at that time the defined "event" had not occurred and there is no way for it to either occur or for the investigator to ever find out if it occurred.
You should not remove patients that died. That creates potential bias. With survival the whole idea of censoring is to use the incomplete observations and not create bias that could occur if you threw out the incomplete observation.
In comparing treatments I find in agreement with Peter's remarks I have seen it done (and have done myself) analyses of time to recurrence (where death by other causes are censored) and all cause mortality. Death by disease specific cause is another way such data can be analyzed.