How big is a big hazard ratio in clinical trials?

Yuanyuan Lu, Wen Wang, Yangxin Huang, Henian Chen
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引用次数: 3

Abstract

Background: The hazard ratio has been widely used as an index of effect size in clinical trials for time-to-event data. The use of the Cox proportional hazards models and other hazard centered models is ubiquitous in clinical trials for time-to-event data. The relativity of effect sizes (small, medium, large) has been widely discussed and accepted when comparing magnitude of association for continuous and categorical data, but not yet for time-to-event outcomes. Methods: We review published hazard ratios, investigate the relationships among HR, relative risk (RR), odds ratio (OR), and Cohen’s d, and calculate the corresponding HRs for given event rate in control group ( ) by adding standard normal deviation with 0.2 (small), 0.5 (medium) and 0.8 (large) to the event rate in the case group (  based on equation . Results: Our results indicate that HRs are from 1.68 to 1.16 when the event rate of control group moves from 1% to 90%, which are equivalent to Cohen’s d = 0.2 (small). HRs are ranged between 3.43 and 1.43 when the event rate of control group moves from 1% to 90%, which are equivalent to Cohen’s d = 0.5 (medium), HRs are valued between 6.52 and 1.73 when the event rate of control group moves from 1% to 90%, which are equivalent to Cohen’s d = 0.8 (large). Conclusions: This study provides general guidelines in interpreting the magnitudes of HRs for time-to-event data in clinical trials.
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临床试验中的大风险比有多大?
背景:在临床试验中,风险比被广泛用作衡量事件时间数据效应大小的指标。Cox比例风险模型和其他以风险为中心的模型在临床试验中普遍用于事件时间数据。在比较连续数据和分类数据的关联程度时,效应大小(小、中、大)的相关性已被广泛讨论和接受,但在时间到事件结果方面尚未得到广泛讨论和接受。方法:我们回顾已发表的风险比,探讨HR、相对风险(RR)、优势比(OR)和Cohen’s d之间的关系,并通过在病例组的事件发生率中加入0.2(小)、0.5(中)和0.8(大)的标准正态偏差,计算出对照组()给定事件发生率的相应HR()。我们的结果表明,当对照组的事件率从1%移动到90%时,hr从1.68到1.16,相当于Cohen的d = 0.2(小)。当对照组事件率为1% ~ 90%时,hr介于3.43 ~ 1.43之间,相当于Cohen’s d = 0.5(中);当对照组事件率为1% ~ 90%时,hr介于6.52 ~ 1.73之间,相当于Cohen’s d = 0.8(大)。结论:本研究提供了解释临床试验中事件时间数据hr大小的一般指南。
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