Survival Analysis I

Abstract

In many medical studies, the main outcome variable is the time to the occurrence of a particular event. In a randomized controlled trial of cancer, for example, surgery, radiation and chemotherapy might be compared with respect to time from randomization and the start of therapy until death. In this case, the event of interest is the death of a patient, but in other situations, it might be remission from a disease, relief from symptoms, or the recurrence of a particular condition. Such observations are generally referred to by the generic term survival data even when the endpoint or event being considered is not death but something else. Such data generally require special techniques for analysis for two main reasons:

• 1. Survival data are generally not symmetrically distributed—they will often appear positively skewed, with a few people surviving a very long time compared with the majority; so assuming a normal distribution will not be reasonable.

• 2. At the completion of the study, some patients may not have reached the endpoint of interest (death, relapse, etc.). Consequently, the exact survival times are not known. All that is known is that the survival times are greater than the amount of time the individual has been in the study. The survival times of these individuals are said to be censored (precisely, they are right-censored).