Office of Biostatistics Research, National Heart, Lung, and Blood Institute, Bethesda, Maryland, USA.
Division of Data Science, Yonsei University, Wonju, South Korea.
Stat Med. 2022 Mar 30;41(7):1225-1241. doi: 10.1002/sim.9266. Epub 2021 Nov 23.
For semi-competing risks data involving a non-terminal event and a terminal event we derive the asymptotic distributions of the event-specific win ratios under proportional hazards (PH) assumptions for the relevant cause-specific hazard functions of the non-terminal and terminal event, respectively. The win ratios converge to the respective hazard ratios under the PH assumptions and therefore are censoring-free, whether or not the censoring distributions in the two treatment arms are the same. With the asymptotic bivariate normal distributions of the win ratios, confidence intervals and testing procedures are obtained. Through extensive simulation studies and data analysis, we identified proper transformations of the win ratios that yield good control of the type one error rate for various testing procedures while maintaining competitive power. The confidence intervals also have good coverage probabilities. Furthermore, a test for the PH assumptions and a test of equal hazard ratios are developed. The new procedures are illustrated in the clinical trial Aldosterone Antagonist Therapy for Adults With Heart Failure and Preserved Systolic Function, which evaluated the effects of spironolactone in patients with heart failure and a preserved left ventricular ejection fraction.
对于涉及非终末事件和终末事件的半竞争风险数据，我们推导出在非终末和终末事件的相关原因特异性风险函数下分别满足比例风险（PH）假设时，事件特异性优势比的渐近分布。在 PH 假设下，优势比收敛于各自的风险比，因此无论两个治疗臂中的删失分布是否相同，都是无偏的。通过渐近二元正态分布的优势比，我们获得了置信区间和检验程序。通过广泛的模拟研究和数据分析，我们确定了适当的优势比转换，可以在保持竞争力的同时，针对各种检验程序很好地控制第一类错误率。置信区间也具有良好的覆盖概率。此外，还开发了用于检验 PH 假设和相等风险比的检验。新程序在临床试验醛固酮拮抗剂治疗心力衰竭和左心室射血分数保留的成年人中得到了说明，该试验评估了螺内酯对心力衰竭和左心室射血分数保留的患者的影响。
