Estimation of the Number Needed to Treat, the Number Needed to be Exposed, and the Exposure Impact Number with Instrumental Variables
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使用工具变量估计需治疗人数、需暴露人数与暴露影响人数
- 研究问题
- 当暴露分组存在未测混杂且两组特征不同，如何估计分别针对总体、暴露组和未暴露组的三类疗效人数指标？
- 方法与思路
- 作者在潜在结果框架中将 NNT、EIN 和 NNE 定义为因果对比，再提出工具变量估计方法，辅以解析例子和模拟。
- 材料陈述的贡献
- 摘要称新估计量在模拟中体现一致性，解析置信区间覆盖率趋于名义水平，并应用于维生素 D 缺乏与死亡率分析。
- 阅读关注点
- 应核对工具变量识别各目标人群指标的条件、效应尺度与倒数转换，以及效应接近零时的估计和区间行为。
- 阅读边界
- 这是预印本，同行评审或期刊接收未核实。摘要未说明工具变量条件及弱工具处理，也未给出具体模拟或应用结果。
原文摘要
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.