Win-loss parameters for right-censored event data, with application to recurrent events

The win ratio has become a popular method for comparing multiple event data between two groups in clinical cohort studies. The win ratio compares the event data in prioritized order, where the first prioritized event is death and a typical example for the second prioritized event is hospitalization. Literature is sparse on inference for win and loss parameters, including the win ratio, for censored event data. Inference for two prioritized censored event times has been developed for independent right-censoring. Many clinical studies include recurrent event data such as hospitalizations. In this article, we suggest inference for win-loss parameters for death and a recurrent event outcome under independent right-censoring. The small sample properties of the proposed method are studied in a simulation study showing that the variance formula is accurate even for small samples. The method is applied on a data set from a randomized clinical trial.