Instrumental variables (IV) are a commonly used tool to estimate causal effects from non-randomized data. A prototype of an IV is a randomized trial with non-compliance where the randomized treatment assignment serves as an IV for the non-ignorable treatment received. Under a monotonicity assumption, a valid IV non-parametrically identifies the average treatment effect among a non-identifiable complier subgroup, whose generalizability is often under debate. In many studies, there could exist multiple versions of an IV, for instance, different nudges to take the same treatment in different study sites in a multi-center clinical trial. These different versions of an IV may result in different compliance rates and offer a unique opportunity to study IV estimates' generalizability. In this article, we introduce a novel nested IV assumption and study identification of the average treatment effect among two latent subgroups: always-compliers and switchers, who are defined based on the joint potential treatment received under two versions of a binary IV. We derive the efficient influence function for the SWitcher Average Treatment Effect (SWATE) and propose efficient estimators. We then propose formal statistical tests of the generalizability of IV estimates based on comparing the conditional average treatment effect among the always-compliers and that among the switchers under the nested IV framework. We apply the proposed framework and method to the Prostate, Lung, Colorectal and Ovarian (PLCO) Cancer Screening Trial and study the causal effect of colorectal cancer screening and its generalizability.

翻译：工具变量（IV）是常用的从非随机数据中估计因果效应的工具。一个典型的IV例子是存在不依从性的随机试验，其中随机化的治疗分配作为不可忽略实际接受治疗的工具变量。在单调性假设下，有效的IV能够非参数地识别不可识别的依从者亚组中的平均处理效应，但其可推广性常受争议。在许多研究中，IV可能存在多个版本，例如多中心临床试验中不同研究站点为促使患者接受相同治疗而采取的不同推动策略。这些不同版本的IV可能导致不同的依从率，为研究IV估计的可推广性提供了独特机会。本文提出一种新颖的嵌套IV假设，研究两个潜在亚组（始终依从者和切换者）的平均处理效应的识别问题，这两个亚组基于二元IV两个版本下的联合潜在治疗接受行为定义。我们推导了切换者平均处理效应（SWATE）的有效影响函数，并提出高效估计量。随后基于嵌套IV框架，通过比较始终依从者与切换者的条件平均处理效应，提出了IV估计可推广性的正式统计检验方法。我们将该框架和方法应用于前列腺癌、肺癌、结直肠癌和卵巢癌（PLCO）筛查试验，研究结直肠癌筛查的因果效应及其可推广性。