A Cautionary Note on the Nonparametric Test for Equality of Survival Medians

• Activity Number: 85
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Zhongxue Chen*+
• Companies: Indiana University Bloomington
• Keywords: survival median ; non-parametric test ; Cochran test ; chi-square distribution ; bootstrap

Abstract

In a paper,"A nonparametric test for equality of survival medians" (Stat Med. 2012; 31(9):844-54), the authors proposed a nonparametric method for testing the equality of survival medians. This test statistic was based on the weighted squared differences between individual survival median and the weighted overall survival median. This test statistic has been shown to have an asymptotic chi-square distribution with K-1 degrees of freedom, where K is the number of groups to be compared. Recently, we found that the Cochran test for homogeneity in one-way ANOVA is invariant of the choice of the weights (Stat Papers, 2012; DOI 10.1007/s00362-012-0475-9). The aforementioned test statistic is identical, not just asymptotically equivalent, to the Cochran test. This means two things. First, the proposed test statistic can be simplified. Second, and more importantly, it is well known that the Cochran test has a serious problem of anti-conservativeness: the actual type I error rate from this test is much larger than the nominal significance level when sample sizes are small. We propose a bootstrap based method. Our simulation results show that the new approach outperforms current methods.