Differences between observed and expected <i>p</i>-values from different forms of the log-rank test on a randomized cancer dataset consisting of somatic mutations in 6184 genes.
<p>The <i>p</i>-values for the genes should be distributed uniformly (green line), since there is no association between mutations and survival in this random data. Asymptotic approximations of the log-rank statistic (purple and blue) yield <i>p</i>-values that deviate significantly from the uniform distribution, incorrectly reporting many genes whose mutations are significantly associated with survival. In particular, the asymptotic log-rank test in R reports 110 genes with significant association, using a Bonferroni corrected <i>p</i>-value < 0.05 (black line), or 291 genes with significant association using a less conservative FDR = 0.05. In contrast, the exact test makes no false discoveries.</p
