Tests for the equality of survival functions

The most popular test. Equivalent to the Mantel-Haenszel test of the hypothesis that the stratum specific odds-ratio is equal to one.

Test if the survival functions are equal with more weight on differences between the survival functions at smaller values of time (higher weights on early death). This test is appropriate when hazard functions vary in ways other than proportionally and when censoring patterns are similar across groups.

Test if the survival functions are equal using weights equal to the sqrt(number at risk) rather than the number at risk used in Wilcoxon. Like the Wilcoxon test, it gives larger weights (although not as large) to earlier failure times. Although less susceptible to the censoring pattern in the data than Wilcoxon’s test, this could remain a problem if large differences in these patterns exist between groups.

Test if the survival functions are equal using weights km^p multiplied by (1-km)^q. When p > q, the test weights earlier failures more than later ones. When p < q, the opposite is true, and more weight is given to later failures than to earlier ones. The Fleming–Harrington test reduces to the log-rank test when p = 1 and q = 0.