Using Weighted Differences in Hazards as Effect Sizes for Survival Data

Sensitive to the change in sample sizes, traditional measures such as values of test statistics or p values can fail to quantify the difference in survival between populations for time-to-event data. We thereby propose to use effect sizes defined as the weighted differences in hazards to evaluate the survival difference between two groups. On the basis of the logrank test statistic, Gehan–Wilcoxon test statistic and Prentice–Wilcoxon test statistic, we developed three effect sizes that compare the survival experiences over the time period of investigation. Estimates of these three effect sizes were provided and their large sample behaviors were studied. In light of the Mann–Whitney parameter, we presented an effect size that compares the survival experiences over the entire possible/hypothetical time period. Two estimates of this effect size were constructed. We compared the proposed effect sizes and illuminated their use by theoretical studies, simulations and real cancer data. The effect sizes proposed in this article can help understand the survival difference in populations and are expected to have promising applications in the field of survival analysis.