Two common methods for checking the null hypothesis that there is no difference between two survival curves include:
Log Rank Test
Gehan's Wilcoxon Test
Potentially useful online references include:
Graphpad (http://graphpad.com/faq/viewfaq.cfm?faq=1079)
Wikipedia - Gehan's Wilcoxon (http://en.wikipedia.org/wiki/List_of_important_publications_in_statistics#Survival_analysis)
Wikipedia - Log Rank (http://en.wikipedia.org/wiki/Log_rank_test)
Testing for differences between survival curves of multiple groups. (add later)
Post-hoc tests for differences between multiple survival curves that control for Experiment-wise Type 1 error. (add late)
The Log Rank test checks for differences between two survival curves.
H0: There is no difference between survival curves.
H1: There is a difference between survival curves.
The Log Rank test does not include weights for changes in the Risk Set over time.
One interpretation, when used in conjunction with Gehan's Wilcoxon Test, is that the Log Rank test is an indicator of differences in later survival times.
Gehan's Wilcoxon test is largely the same as the Log Rank test, except that it is weighted toward earlier survival times by including the number in the Risk Set in the calculation. It still checks for differences between two survival curves.
H0: There is no difference between survival curves for earlier survival times.
H1: There is a difference between survival curves for earlier survival times.
Gehan's Wilcoxon test does include weights for changes in the Risk Set over time.
One interpretation, when used in conjunction with the Log Rank Test, is that Gehan's Wilcoxon test is an indicator of differences in earlier survival times.