How SAS calculates median survival time

[minhai30]

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%?

[Reeza]

Can you point to the reference in the online docs? Not many people will have the 9.2 PDF or paper version. 

[minhai30]

The link to the online document is listed below:

https://support.sas.com/documentation/cdl/en/statuglifetest/61800/PDF/default/statuglifetest.pdf

[Doc_Duke]

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.

[minhai30]

Thanks. How would having very few failures specifically affect what is the median survival time?

[Doc_Duke]

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.

[minhai30]

Does this mean that the median survival time could be inaccurate when the sample size is small?

[Reeza]

It's not a matter of accurate vs inaccurate they're all estimates. But look at the confidence intervals when you have a large N vs small N.