The P value tests the null hypothesis that the survival curves are identical in the overall populations. In other words, the null hypothesis is that the treatment did not change survival.
The P value answers this question:
Note that the P value is based on comparing entire survival curves, not on comparing only the median survival.
Prism always reports a two-tail P value when comparing survival curves. If you wish to report a one-tail P value, you must have predicted which group would have the longer median survival before collecting any data. Computing the one-tail P value depends on whether your prediction was correct or not.
•If your prediction was correct, the one-tail P value is half the two-tail P value.
•If your prediction was wrong, the one-tail P value equals 1.0 minus half the two-tail P value. This value will be greater than 0.50, and you must conclude that the survival difference is not statistically significant.