A Note on the Sample Size Formula for a Win Ratio Endpoint

The sample size formula for a win ratio endpoint proposed by Yu and Ganju is re-evaluated from an implementation perspective. This formula relies on an approximated null variance, rather than the exact permutation variance originally introduced by Finkelstein and Schoenfeld. As a result, the formula is analytically straightforward, does not require patient-level data to determine sample size, and is advantageous for practitioners, as it avoids the need for simulations in power analysis. In this paper, we empirically demonstrate that the power based on this sample size formula is generally lower than the power derived using the exact permutation variance across various scenarios. This discrepancy arises primarily due to the overestimation of the true variance when the approximated null variance is used in place of the exact permutation variance. We hope this will encourage further discussion regarding the appropriate application of this formula.