If you compare two survival curves, Prism reports the ratio of the median survival times for these curves along with the 95% confidence interval and reciprocal of this ratio. The 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 experiencing the event of interest 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 survival times will not be meaningful.
Note that earlier versions of Prism computed the confidence interval incorrectly (but computed the ratio correctly).
While Prism computes the confidence interval for the ratio of median survival times (when comparing two groups), it does not compute the 95% confidence interval for the median survival time of each group independently. The reason is that multiple methods for computing confidence intervals of median survival times have been published, while none seem to be standard and the results do not match. To read more:
•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