Primary Submission Category: Instrumental Variables
Design-based nested instrumental variable analysis
Authors: Zhe Chen, Bo Zhang, Xinran Li,
Presenting Author: Zhe Chen*
Two binary instrumental variables (IVs) are nested if individuals who comply under one binary IV also comply under the other. This situation often arises when the two IVs represent different intensities of encouragement or discouragement to take the treatment-one stronger than the other. In a nested IV structure, treatment effects can be identified for two latent subgroups: always-compliers and switchers. Always-compliers are individuals who comply even under the weaker IV, while switchers are those who do not comply under the weaker IV but do under the stronger one. In this article, we introduce a novel pair-of-pairs nested IV design, where each matched stratum consists of four units organized in two pairs. Under this pair-of-pairs design, we develop design-based inferential methods for estimating the always-complier sample average treatment effect (SATE) and switcher SATE. In a nested IV analysis, IV assignment is randomized within each IV pair; however, whether a study unit receives the weaker or stronger IV may not be randomized. To address this complication, we then propose a novel partly biased randomization scheme and study design-based inference under this new scheme. Using extensive simulation studies, we demonstrate the validity of the proposed method and assess its power under different scenarios. Applied to PLCO trial data, we identified 52.2% always-compliers and 26.7% switchers, with sigmoidoscopy showing potential benefit for always-compliers but not switchers.