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The difference between survival functions is usually described in terms of the results of statistical tests. This practice does not provide a uniform standard for quantifying the difference because the test results can be heavily influenced by the sample size.
Effect sizes provide a better measurement of differences between survival functions as they are independent of sample sizes. Existing effect sizes, such as the hazard ratio and restricted mean survival time, have limited applications due to their reliance on assumptions or subjective selection of parameters. We propose to use the effect sizes defined as weighted differences in hazards to measure the survival difference. Such effect sizes can be obtained by adjusting the test statistics from the weighted logrank tests or by exploiting the Mann-Whitney parameter. We also introduce a rule of the thumb for quantifying the difference between survival functions. Simulation and real-data experiments are conducted to illustrate and compare our proposed effect sizes. The results show that developed effect sizes can provide insights into understanding the difference in survival functions in clinical trials and medical research.
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