The inverse-probability-of-censoring weighting (IPCW) adjusted win ratio statistic: an unbiased estimator in the presence of independent censoring

The win ratio method has received much attention in methodological research, ad hoc analyses, and designs of prospective studies. As the primary analysis, it supported the approval of tafamidis for the treatment of cardiomyopathy to reduce cardiovascular mortality and cardiovascular-related hospitalization. However, its dependence on censoring is a potential shortcoming. In this article, we propose the inverse-probability-of-censoring weighting (IPCW) adjusted win ratio statistic (i.e., the IPCW-adjusted win ratio statistic) to overcome censoring issues. We consider independent censoring, common censoring across endpoints, and right censoring. We develop an asymptotic variance estimator for the logarithm of the IPCW-adjusted win ratio statistic and evaluate it via simulation. Our simulation studies show that, as the amount of censoring increases, the unadjusted win proportions may decrease greatly. Consequently, the bias of the unadjusted win ratio estimate may increase greatly, producing either an overestimate or an underestimate. We demonstrate theoretically and through simulation that the IPCW-adjusted win ratio statistic gives an unbiased estimate of treatment effect.

在方法学研究、特设分析及前瞻性研究设计中，获胜比（win ratio）法已受到广泛关注。作为首要分析方法，该方法曾支持他法米地（tafamidis）获批用于治疗心肌病，以降低心血管死亡率及心血管相关住院风险。然而，其对删失（censoring）的依赖是一项潜在缺陷。本文提出逆概率删失加权（inverse-probability-of-censoring weighting, IPCW）调整后的获胜比统计量，即IPCW调整获胜比统计量，以解决删失问题。我们考虑了独立删失、终点间共用删失以及右删失三种情形，推导了该统计量对数的渐近方差估计量，并通过模拟对其进行评估。我们的模拟研究显示，随着删失比例升高，未调整的获胜比例可能大幅下降，由此导致未调整获胜比估计量的偏差显著增大，进而出现高估或低估的情况。我们通过理论推导与模拟实验证实，IPCW调整获胜比统计量可得到无偏的治疗效应估计值。