The number needed to treat (NNT) is an efficacy and effect size measure commonly used in epidemiological studies and meta-analyses. The NNT was originally defined as the average number of patients needed to be treated to observe one less adverse effect. In this study, we introduce the novel direct and indirect number needed to treat (DNNT and INNT, respectively). The DNNT and the INNT are efficacy measures defined as the average number of patients that needed to be treated to benefit from the treatment's direct and indirect effects, respectively. We start by formally defining these measures using nested potential outcomes. Next, we formulate the conditions for the identification of the DNNT and INNT, as well as for the direct and indirect number needed to expose (DNNE and INNE, respectively) and the direct and indirect exposure impact number (DEIN and IEIN, respectively) in observational studies. Next, we present an estimation method with two analytical examples. A corresponding simulation study follows the examples. The simulation study illustrates that the estimators of the novel indices are consistent, and their analytical confidence intervals meet the nominal coverage rates.

翻译：需治数（NNT）是流行病学研究和荟萃分析中常用的疗效与效应量指标。NNT最初定义为观察到一例不良事件减少所需治疗的平均患者数。本研究引入了新颖的直接需治数与间接需治数（分别记为DNNT与INNT）。DNNT与INNT是疗效衡量指标，分别定义为从治疗直接效应与间接效应中获益所需治疗的平均患者数。我们首先基于嵌套潜在结果框架正式定义这些指标，随后系统阐述观察性研究中DNNT、INNT以及直接/间接需暴露数（DNNE/INNE）、直接/间接暴露影响数（DEIN/IEIN）的识别条件。继而提出包含两个实证案例的估计方法，并辅以相应的模拟研究。模拟结果表明：新指标的估计量具有一致性，其解析置信区间满足名义覆盖概率要求。