Primary Submission Category: Instrumental Variables
Nested Instrumental Variables Design: Switcher Average Treatment Effect, Identification, Efficient Estimation and Generalizability
Authors: Rui Wang, Yingqi Zhao, Oliver Dukes, Bo Zhang,
Presenting Author: Rui Wang*
Instrumental variables (IV) are a commonly used tool in estimating causal effect from non-randomized data. A prototype of an IV is a randomized trial with no compliance where the randomized treatment assignment serves as an IV for the nonignorable treatment uptake. Under a monotonicity assumption, a valid IV nonparametrically identifies the average treatment effect among a non-identifiable complier subgroup, whose generalizability is often under much debate. In many studies, there could exist multiple versions of an IV, for instance, different nudges to take the treatment in different study sites in a 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 the identification of the average treatment effect among two latent subgroups: always-compliers and switchers, who are defined based on the joint potential treatment uptake under two versions of a binary IV. We derive the conanical gradient for the SWitcher Average Treatment Effect (SWATE) and propose efficient estimator. We then propose formal statistical tests of the principal ignorability assumption based on comparing the conditional average treatment effect among the always-compliers and that among the switchers under the nested IV framework. We apply our method to the Prostate, Lung, Colorectal and Ovarian Cancer (PLCO) Screening Trial.