Significance testing in the comparison of survival curves from clinical trials of cancer treatment

Abstract

The log-rank test (Peto and Peto 1972) is now widely used for comparing survival data from randomised clinical trials of cancer treatment that require prolonged follow-up. The test is optimal when the death rate in one group consistently exceeds that in the other group by a given proportion, the so-called proportional hazards situation. Alternative tests that are sometimes used are Gehan’s generalisation of the Wilcoxon rank sum test (Gehan 1965) and its subsequent modifications by Peto and Peto (1972) and by Prentice (1978). Of these, the latter is to be preferred with censored data (Prentice and Marek 1979), and, as shown by Lee et al. (1975) in a simulation experiment comparing survival curves modelled on Wei- bull distributions, it may perform better in a nonproportional hazards situation. Similarly, Fleming et al. (1980) have demonstrated the loss of power of the log- rank compared with that of the Wilcoxon test in comparing survival curves where the greatest differences occur at early follow-up times, and Harrington and Fleming (1982) have shown a similar loss when the hazard ratio is a maximum at time zero and decreases smoothly towards unity as follow-up increases. The reason for the difference between the performance of the two tests is that the calculation of the Wilcoxon statistic weights the differences between observed and expected events according to the estimated survival at the time of the event, whereas the log-rank calculation gives equal weights at all event times (Tarone and Ware 1977). Thus, the Wilcoxon test gives more weight to differences which appear early in follow-up.