Approximating win-loss probabilities based on the overall and event-free survival functions

Despite its growing popularity for hierarchical composite endpoints, the win ratio poses a challenge for meta-analysis, as earlier studies typically do not report such measures. In the absence of subject-level data, we show how to approximate it using component-specific Kaplan-Meier curves that are almost universally reported. Given these marginal distributions, we infer the between-component association, as measured by the cross ratio, using summary data on event counts and rates. This leads to approximations of the win-loss probabilities that align closely with raw data-based estimates, as demonstrated in simulations and two case studies. The methodology is implemented in the winkm R package, publicly available on GitHub at https://lmaowisc.github.io/winkm.