Primary Submission Category: Instrumental Variables
Identifying the Cumulative Average Effect of a Multi-Phase Treatment with Noncompliance by Leveraging Multisite Instrumental Variables
Authors: Guanglei Hong, Fan Yang, Zhengyan Xu, Xu Qin,
Presenting Author: Guanglei Hong*
When evaluating a multi-phase intervention, the cumulative average treatment effect (ATE) is often a causal estimand of primary interest. However, among individuals who do not respond well to the treatment in an earlier phase, some may subsequently display noncompliant behaviors. At the same time, exposure to the earlier-phase treatment is expected to both directly and indirectly influence an individual’s potential outcomes. Building on an instrumental variable (IV) strategy for multisite trials, we clarify the conditions under which the cumulative ATE of a multi-phase treatment can be identified by employing the randomization of the initial treatment assignment as the instrument. Our strategy relaxes both the conventional exclusion restriction and sequential ignorability assumptions. We assess the performance of the new strategy through simulation studies and clarify data requirements for estimation. Additionally, we reanalyze data from the Tennessee class size study, in which students and teachers were randomly assigned to either small or regular class types in kindergarten (Phase I) with noncompliance emerging in Grade 1 (Phase II) and again in Grade 2 (Phase III). Applying our new strategy, we estimate the cumulative ATE of receiving three consecutive years of instruction in a small versus regular class.
Â