The Number needed to treat (NNT) is an efficacy index defined as the average number of patients needed to treat to attain one additional treatment benefit. In observational studies, specifically in epidemiology, the adequacy of the populationwise NNT is questionable since the exposed group characteristics may substantially differ from the unexposed. To address this issue, groupwise efficacy indices were defined: the Exposure Impact Number (EIN) for the exposed group and the Number Needed to be Exposed (NNE) for the unexposed. Each defined index answers a unique research question since it targets a unique sub-population. In observational studies, the group allocation is typically affected by confounders that might be unmeasured. The available estimation methods that rely either on randomization or the sufficiency of the measured covariates for confounding control will result in inconsistent estimators of the true NNT (EIN, NNE) in such settings. Using Rubin's potential outcomes framework, we explicitly define the NNT and its derived indices as causal contrasts. Next, we introduce a novel method that uses instrumental variables to estimate the three aforementioned indices in observational studies. We present two analytical examples and a corresponding simulation study. The simulation study illustrates that the novel estimators are consistent, unlike the previously available methods, and their confidence intervals meet the nominal coverage rates. Finally, a real-world data example of the effect of vitamin D deficiency on the mortality rate is presented.

翻译：需治疗人数（NNT）是定义为获得一个额外治疗获益所需治疗的平均患者数的疗效指标。在观察性研究中，特别是在流行病学领域，基于人群的NNT的适用性存在疑问，因为暴露组特征可能与未暴露组存在显著差异。为解决这一问题，定义了分组疗效指标：针对暴露组的暴露影响人数（EIN）和针对未暴露组的需暴露人数（NNE）。每个指标针对特定亚群回答独特的研究问题。在观察性研究中，分组分配通常受到可能未测量的混杂因素的影响。依赖随机化或足够测量混杂因素控制的现有估计方法，在此类情境下会导致真实NNT（EIN、NNE）的估计量不一致。基于Rubin的反事实结果框架，我们明确定义NNT及其衍生指标为因果对比。随后，我们引入一种使用工具变量估计观察性研究中上述三个指标的新方法。我们提供了两个分析示例及对应的模拟研究。模拟研究表明，与现有方法不同，新估计量具有一致性，其置信区间达到名义覆盖率。最后，我们以维生素D缺乏对死亡率影响的真实数据示例进行展示。