Sample Size and Power Calculations With Win Measures Based on Hierarchical Endpoints

Win measures, such as win ratio, win odds, net benefit, and desirability of outcome ranking (DOOR), have become popular approaches for the analysis of hierarchical endpoints in clinical studies. Sample size and power calculations with win measures based on hierarchical endpoints are often based on simulation studies that can be cumbersome. Existing sample size and power formulas require investigators to specify clinically significant and meaningful magnitudes of win measures and probability of ties that are difficult to elicit based on prior published literature or preliminary data. In this paper, we provide sample size and power calculation formulas for the four win measures. To facilitate the formula-based sample size or power calculations, we provide formulas to compute overall win measures and overall probability of ties needed by using the specification of marginal win measures and marginal probability of ties that are readily available from clinical investigators or literature. The latter formulas provide a novel way to specify a meaningful and justifiable magnitude of win measures and the magnitude of probability of ties. Therefore, they can be readily used to evaluate the powers based on the number of multiple endpoints, the ordering, and types of endpoints. Our extensive simulation studies show that the power estimations based on these formulas are often like the simulated powers for any type of correlated hierarchical endpoints except for scenarios with very high correlations between endpoints. We illustrate the usefulness of our formulas by using data from three trials with different types of hierarchical endpoints.