On approximate equality of Z-values of the statistical tests for win statistics (win ratio, win odds, and net benefit)

Dong et al. (2023) showed that the win statistics (win ratio, win odds, and net benefit) can complement each another to demonstrate the strength of treatment effects in randomized trials with prioritized multiple outcomes. This result was built on the connections among the point and variance estimates of the three statistics, and the approximate equality of Z-values in their statistical tests. However, the impact of this approximation was not clear. This Discussion refines this approach and shows that the approximate equality of Z-values for the win statistics holds more generally. Thus, the three win statistics consistently yield closely similar p-values. In addition, our simulations show an example that the naive approach without adjustment for censoring bias may produce a completely opposite conclusion from the true results, whereas the IPCW (inverse-probability-of-censoring weighting) approach can effectively adjust the win statistics to the corresponding true values (i.e. IPCW-adjusted win statistics are unbiased estimators of treatment effect).