New Test for the Comparison of Survival Curves to Detect Late Differences

Background. Survival analysis attracted the attention of different scientists from various domains such as engineering, health, and social sciences. It has been widely exploited in clinical trials when comparing different treatments looking at their survival probabilities. Kaplan–Meier curves plotted from the Kaplan–Meier estimates of survival probabilities are used to depict the general image for such situations. Methods. The weighted log-rank test has been dealt with by suggesting different weight functions which give specific strength in specific situations. In this work, we proposed a new weight function comprising all numbers at risk, i.e., the overall number at risk and the separate numbers at risk in the groups under study, to detect late differences between survival curves. Results. The new test has been found to be a good alternative after the FH (0, 1) test in detecting late differences, and it outperformed all tests in case of small samples and heavy censoring rates according to the simulation studies. The new test kept the same strength when applied to real data where it showed itself to be among the powerful ones or even outperforms all other tests under consideration. Conclusion. As the new test stays stronger in the case of small samples and heavy censoring rates, it may be a better choice whenever targeting the detection of late differences between the survival curves.