Ambiguities in computing the median survival time.

Median survival is the time it takes to reach 50% survival. But note three ambiguities:

• If the percent survival at the end of the study exceeds 50%, then the median survival time is simply not defined. It is longer than the last time plotted, but there is no way to know how much longer.The P value comes from the log-rank test, which compares the entire curve, and works fine even if the percent survival is always greater than 50%. Two curves can be very different, even if they never dip down below 50%. 
• If the survival curve is horizontal at 50% survival, then the median survival time is not really defined. In the survival curve below, the curve is horizontal at Y=50% between 9 and 17 months. It would be accurate to say that half the patients had died by 9 months, or that half were still alive at 17 months. Prism follows the suggestion of Machin (reference below) and reports that the median survival is the average of those two values, 13 months. Note this bug in Prism 5.

• Prism, like most programs, defines median survival as the time at which the staircase survival curve crosses 50% survival. Thus is is an accurate statement of median survival in the subjects or animals actually included in the data set. The graph on the left below, shows how Prism computes median survival (211 days for this example). If you connected the survival times with point-to-point lines rather than a staircase, you'd find that the line may intersect Y=50% at an earlier time, and thus you'd come up with a different value for median survival (193 days in the example on the right below) This would make sense if you were trying to predict median survival for future patients. Prism does not do this, as it is not standard.

Prism file for these examples. 

Prism does not compute the confidence interval for median survival. Why not.