Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, Wisconsin.
Biometrics. 2022 Sep;78(3):1257-1268. doi: 10.1111/biom.13501. Epub 2021 Jun 8.
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.
最初提出用于分析优先复合终点的赢率，现在已经扩展为基于一般成对比较的广泛的方法类别。然而，由于检验统计量的非独立同分布结构，赢率的样本量估计已经落后。在本文中，我们开发了通用且易于使用的公式，用于计算不同结果类型的赢率分析的样本量。在非参数设置中，使用 U 统计量理论根据称为标准秩偏差的离散参数推导出检验统计量的零方差，这是零结果分布的固有特征和用户定义的比较规则。可以根据原始人群赢率的比例或适合结果类型的“通常”效果大小的比例来假设效果大小。后一种方法允许通过例如完全/部分有序结果的优势/持续比和复合时间事件结果的风险比来测量效果大小。模拟研究表明，所推导的公式在不同的设置下为所需的样本量提供了准确的估计。作为说明，使用来自肝脏和心血管疾病的两项临床研究的真实数据作为试点数据来计算未来试验的样本量。
