01-06-2017 09:03 AM
On page 3130 of the SAS 9.2 Proc Lifetest user's guide, the median survival time is defined as the minimum time in which the survival probability is less than but does not include 50%.
What I learned from graduate school and online sources is that median survival time is the minimum time in which the survival probability is less than or equal to 50%.
Why does SAS define median survival time as when survival probability is less than 50% while other sources define median survival time as less than or equal to 50%?
01-06-2017 10:11 AM
I've seen it both ways. For instance, "It means that the chance of surviving beyond that time is 50 percent." (https://www.verywell.com/median-survival-ms-2252158) would use the <50% than approach.
The problem is that the definition is based on a continuous distribution and the data are discrete, so the people who implement the definition have to make a choice. The choice doesn't matter very much unless you have so few failures that the distribution is unstable to begin with.
01-06-2017 01:29 PM
Basically few failures means few subjects. Anytime you have a small sample size you risk an unstable estimator or, more precisely, one with a wide confidence or credible interval.