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 statistically consistent, unlike the previously available methods, and their analytical confidence intervals' empirical coverage rates converge to their nominal values. Finally, a real-world data example of an analysis of the effect of vitamin D deficiency on the mortality rate is presented.

翻译：治疗所需人数（NNT）是一种疗效指标，定义为获得一次额外治疗获益所需治疗的平均患者数。在观察性研究（特别是流行病学领域）中，由于暴露组特征可能与未暴露组存在显著差异，基于总体人群的NNT的适用性受到质疑。为解决此问题，学界定义了分组疗效指标：针对暴露组的暴露影响数（EIN）和针对未暴露组的暴露所需人数（NNE）。每个定义指标针对特定亚人群，因而能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无法测量的混杂因素影响。现有估计方法依赖随机化或假设已测量协变量足以控制混杂，在此类情境下将导致对真实NNT（EIN、NNE）的估计不一致。基于Rubin潜在结果框架，我们明确定义NNT及其衍生指标作为因果对比量。随后，我们提出一种利用工具变量估计观察性研究中上述三个指标的新方法。我们通过两个解析案例和相应的模拟研究进行验证。模拟研究表明：与既有方法不同，新提出的估计量具有统计一致性，其解析置信区间的经验覆盖率收敛于名义水平。最后，本文以维生素D缺乏对死亡率影响的真实数据分析为例进行演示。