Median survival time

The median survival is the time at which fractional survival equals 50%. Notes:

•If survival exceeds 50% at the longest time point, then median survival cannot be computed. Prism reports that the median survival is "undefined". The logrank comparison of curves really does compare entire curves, and does not compare median survival times. So the P value computed by the logrank test is still valid even if one or both median survival times are undefined.

•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 and reports that the median survival is the average of those two values, 13 months.

•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.

Ratio of median survival times

If you compare two survival curves, Prism reports the ratio of the median survival times along with its 95% confidence interval of the ratio.

This calculation of the confidence interval of the ratio of survival times is based on an assumption that is not part of the rest of the survival comparison:  that both survival curves follow an exponential decay. This means that the chance of dying in a small time interval is the same early in the study and late in the study. If your survival data follow a very different pattern, then the values that Prism reports for the 95% CI of the ratio of median survivals will not be meaningful.

Note that prior versions of Prism computed the confidence interval incorrectly (but computed the ratio just fine).

Why Prism doesn't compute the confidence interval of median survival time

While Prism computes the confidence interval for the ratio of median survivals (when you compare two groups), it does not compute the 95% confidence interval for the median survival time itself. The reason is that multiple methods for computing a confidence interval of median survival have been published and none seem to be standard, and the results don't match. To read more:

•One method is in Collett starting at page 35 .

•Brookmeer and Crowley, A confidence interval for the median survival time. Biometrics (1982) vol. 38 (1) pp. 29-41.

•Barker reviews several methods and points out how different their results can be. The Mean, Median, and Confidence Intervals of the Kaplan-Meier Survival Estimate—Computations and Applications. The American Statistician (2009) vol. 63 (1) pp. 78-80