Comparison of procedures for testing the equality of survival distributions

Sequential procedures based on the Mantel-Haenszel statistic (Muenz, Green and Byar, 1977, Biometrics 33, 617-626), the Wilcoxon statistic (Davis, 1978, Communications in Statistics, Series A 7, 389-398) and the Savage statistic (Koziol and Petkau, 1978, Biometrika 65, 615-623) have been proposed for testing the equality of two survival distributions when observations are singly censored. These procedures, and their fixed sample-size counterparts, are numerically compared with respect to power against Lehmann alternatives and expected proportions sampled. Of the sequential procedures, those based on the Wilcoxon and the Savage statistics seem preferable to that based on the Mantel-Haenszel statistic. Early decision rules are introduced and shown to be of value if used in conjunction with either the sequential or the fixed-sample procedures. Small-sample corrections to the asymptotic critical values of the sequential Savage procedure are presented.