Targeted therapies tend to have biomarker defined subgroups that derive differential efficacy from treatments. This article corrects three prevailing oversights in stratified analyses comparing treatments in randomized controlled trials (RCTs) with binary and time-to-event outcomes:

• 1. Using efficacy measures such as odds ratio (OR) and hazard ratio (HR) can make a prognostic biomarker appear predictive, targeting wrong patients, because the inference is affected by a confounding/covert factor even with ignorable treatment assignment in an RCT. As shown analytically and with real immunotherapy patient level data, OR and HR cannot meet the causal Estimand requirement of ICH E9R1.
• 2. Mixing efficacy in subgroups by prevalence, the prevailing practice, can give misleading results also, for any efficacy measured as a ratio. However, mixing relative response (RR) and ratio of median (RoM) survival times by the prognostic effect, the confounding/covert factor hiding in plain sight, will give causal inference in an RCT.
• 3. Effects in subgroups should not be mixed on the logarithmic scale, because it creates an artificial Estimand for the whole population which changes depending on how the population is divided into subgroups.

Current computer package implementations contain all these oversights. Probabilities, including survival curve probabilities, naturally average within each treatment arm by prevalence. The subgroup mixable estimation (SME) principle fixes the oversights by first averaging probabilities (not their logarithms) within each treatment arm, then computing simultaneous confidence intervals for ratio efficacy in subgroups and their mixtures based on rigorous mathematical derivation, to finally provide causal inference in the form of apps.

中文翻译：

---

随机对照试验中二元和事件发生时间结果的正确和合乎逻辑的因果推断

靶向治疗往往具有生物标志物定义的亚组，这些亚组从治疗中获得不同的疗效。本文纠正了在比较随机对照试验 (RCT) 中的治疗与二元和事件发生时间结果的分层分析中普遍存在的三个疏忽：

• 1.使用优势比 (OR) 和风险比 (HR) 等疗效指标可以使预后生物标志物看起来具有预测性，针对错误的患者，因为即使在 RCT 中可忽略治疗分配，推断也会受到混杂/隐蔽因素的影响。如分析和真实免疫治疗患者水平数据所示，OR 和 HR 不能满足 ICH E9R1 的因果估计要求。
• 2.按流行率混合亚组中的功效，流行的做法，对于任何以比率衡量的功效，也会产生误导性的结果。然而，通过预后效应混合相对反应 (RR) 和中位数 (RoM) 生存时间比率，隐藏在显而易见的混杂/隐蔽因素，将在 RCT 中给出因果推断。
• 3.子组中的影响不应在对数尺度上混合，因为它会为整个总体创建一个人为的估计值，该估计值会根据总体划分为子组的方式而变化。

当前的计算机包实现包含所有这些疏忽。概率，包括生存曲线概率，在每个治疗组内按患病率自然平均。子组可混合估计 (SME) 原则通过首先对每个治疗组内的概率（而不是它们的对数）进行平均，然后根据严格的数学推导计算子组及其混合物中的比率功效的同时置信区间来修复疏忽，最终提供因果推断应用程序的形式。