A win ratio approach for comparing crossing survival curves in clinical trials

Many clinical trials include time-to-event or survival data as an outcome. To compare two survival distributions, the log-rank test is often used to produce a P-value for a statistical test of the null hypothesis that the two survival curves are identical. However, such a P-value does not provide the magnitude of the difference between the curves regarding the treatment effect. As a result, the P-value is often accompanied by an estimate of the hazard ratio from the proportional hazards model or Cox model as a measurement of treatment difference. However, one of the most important assumptions for Cox model is that the hazard functions for the two treatment groups are proportional. When the hazard curves cross, the Cox model could lead to misleading results and the log-rank test could also perform poorly. To address the problem of crossing curves in survival analysis, we propose the use of the win ratio method put forward by Pocock et al. as an estimand for analysing such data. The subjects in the test and control treatment groups are formed into all possible pairs. For each pair, the test treatment subject is labelled a winner or a loser if it is known who had the event of interest such as death. The win ratio is the total number of winners divided by the total number of losers and its standard error can be estimated using Bebu and Lachin method. Using real trial datasets and Monte Carlo simulations, this study investigates the power and type I error and compares the win ratio method with the log-rank test and Cox model under various scenarios of crossing survival curves with different censoring rates and distribution parameters. The results show that the win ratio method has similar power as the log-rank test and Cox model to detect the treatment difference when the assumption of proportional hazards holds true, and that the win ratio method outperforms log-rank test and Cox model in terms of power to detect the treatment difference when the survival curves cross.