Pocock et al. (2012) following Finkelstein and Schoenfeld (1999), has popularized the win ratio for analysis of controlled clinical trials with multiple types of outcome event. The approach uses pairwise comparisons between patients in the treatment and control groups, using a primary outcome, say time to death, with ties broken using a secondary outcome, say time to hospitalization. Oakes (2016) pointed out that except in very special cases the population value of the resulting estimand depends on the distribution of the potential follow-up time. Finkelstein and Schoenfeld (2018) illustrated this phenomenon graphically using data from clinical trials in cancer, heart disease and ALS. In the present talk I study estimation of what will be called the c-win ratio, the win ratio curtailed (or censored) at time c. This is the population value of the win ratio that would be observed if there were complete follow-up all individuals up to time c, but none beyond. We show that this quantity, and its asymptotic variance, can be estimated non-parametrically using methodology for univariate survival analysis.