Originally proposed for the analysis of prioritized composite endpoints, the win ratio has now expanded into a broad class of methodology based on general pairwise comparisons. Complicated by the non-i.i.d. structure of the test statistic, however, sample size estimation for the win ratio has lagged behind. In this article, we develop general and easy-to-use formulas to calculate sample size for win ratio analysis of different outcome types. In a nonparametric setting, the null variance of the test statistic is derived using 𝑈-statistic theory in terms of a dispersion parameter called the standard rank deviation, an intrinsic characteristic of the null outcome distribution and the user-defined rule of comparison. The effect size can be hypothesized either on the original scale of the population win ratio, or on the scale of a "usual" effect size suited to the outcome type. The latter approach allows one to measure the effect size by, for example, odds/continuation ratio for totally/partially ordered outcomes and hazard ratios for composite time-to-event outcomes. Simulation studies show that the derived formulas provide accurate estimates for the required sample size across different settings. As illustration, real data from two clinical studies of hepatic and cardiovascular diseases are used as pilot data to calculate sample sizes for future trials.

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We report the final results of an NIH funded study of MRI-based quantification of liver iron. R2* MRI enables quantification of liver iron concentration (LIC), but the cross-vendor differences of R2*-based LIC estimation remain unknown. Therefore, we evaluated the performance of R2*-based LIC via a single-breath-hold, confounder-corrected R2*-MRI at both 1.5T and 3T, through a multi-center, multi-vendor study. We confirmed a linear relationship between R2* and LIC, with highly similar calibrations across centers and vendors. Calibrations for 1.5T and 3T were generated. The data generated in this study provide the necessary multi-center calibrations for broad dissemination of R2*-based LIC quantification.