A Qualitative Discrepancy between Censored Data Rank Tests

Two popular censored data rank tests were used to compare cancer incidence rates between dogs receiving bone marrow transplantation and control dogs. The logrank test gave a significance level of 0.01. In contrast, Gehan's generalized Wilcoxon test gave a significance level of 0.76. The statistics are displayed in a manner that shows how such contrasting significance levels can arise. The Gehan statistic is shown to be subject to a serious criticism that does not apply to other Wilcoxon generalizations. Further insight into the data is obtained using a time-dependent logrank test and the proportional hazards regression model.