The log-rank test is a statistical method to compare two survival distributions—that is, to determine whether two samples may have arisen from two identical survivor functions. The log-rank test is easy to compute and has a simple heuristic justification and is therefore often advocated for use to nonstatisticians. The log-rank test can also be thought as a censored data rank test.

Suppose we obtain two samples from two populations and we are interested in the null hypothesis

H0: S1 = S2

that the survival distribution from Sample 1 is identical to the survival distribution in Sample 2.

The idea behind the log-rank test is to compare the observed number of deaths at each failure time with the expected number of deaths under the null hypothesis (i.e., assuming that the ...