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 Expose (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）定义为获得一个额外治疗获益所需治疗的平均患者数，是一种疗效指标。在观察性研究中，尤其流行病学领域，整体人群的NNT适用性存疑，因暴露组特征可能与未暴露组存在显著差异。为解决该问题，定义了分组疗效指数：暴露组的暴露影响指数（EIN）和未暴露组的需暴露人数（NNE）。各指数针对特定亚人群，回答不同的研究问题。观察性研究中，分组分配通常受未测量的混杂因素影响。依赖随机化或测量协变量充分控制混杂的现有估计方法，在此类情境下会导致真实NNT（EIN、NNE）的估计量不一致。基于Rubin潜在结果框架，我们明确定义NNT及其衍生指数为因果对比，并引入一种使用工具变量估计上述三种指数的新方法。我们给出两个分析实例及相应的模拟研究。模拟研究表明，与既有方法不同，新估计量具有一致性，且其置信区间符合名义覆盖率。最后，以维生素D缺乏对死亡率影响的真实数据为例进行说明。