Sample size formula for a win ratio endpoint

The win ratio composite endpoint, which organizes the components of the composite hierarchically, is becoming popular in late-stage clinical trials. The method involves comparing data in a pair-wise manner starting with the endpoint highest in priority (eg, cardiovascular death). If the comparison is a tie, the endpoint next highest in priority (eg, hospitalizations for heart failure) is compared, and so on. Its sample size is usually calculated through complex simulations because there does not exist in the literature a simple sample size formula. This article provides a formula that depends on the probability that a randomly selected patient from one group does better than a randomly selected patient from another group, and on the probability of a tie. We compare the published 95% confidence intervals, which require patient-level data, with that calculated from the formula, requiring only summary-level data, for 17 composite or single win ratio endpoints. The two sets of results are similar. Simulations show the sample size formula performs well. The formula provides important insights. It shows when adding an endpoint to the hierarchy can increase power even if the added endpoint has low power by itself. It provides relevant information to modify an on-going blinded trial if necessary. The formula allows a non-specialist to quickly determine the size of the trial with a win ratio endpoint whose use is expected to increase over time.