Two-Phase Treatment with Noncompliance: Identifying the Cumulative Average Treatment Effect via Multisite Instrumental Variables

TL;DR

This paper develops a new instrumental variable approach to identify the cumulative average treatment effect in two-phase interventions with noncompliance, relaxing key assumptions and validated through simulations and real data reanalysis.

Contribution

It introduces a strategy that relaxes exclusion restriction and sequential ignorability assumptions for identifying cumulative ATE in multisite two-phase treatments.

Findings

The new method accurately estimates the cumulative ATE in simulations.

Reanalysis of the Tennessee class size study demonstrates practical applicability.

The approach provides robust estimates despite noncompliance and assumption violations.

Abstract

When evaluating a two-phase intervention, the cumulative average treatment effect (ATE) is often the primary causal estimand of interest. However, some individuals who do not respond well to the Phase I treatment may subsequently display noncompliant behaviors. At the same time, exposure to the Phase I treatment is expected to directly influence an individual's potential outcomes, thereby violating the exclusion restriction. Building on an instrumental variable (IV) strategy for multisite trials, we clarify the conditions under which the cumulative ATE of a two-phase treatment can be identified by employing the random assignment of the Phase I treatment 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. 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). Applying our new strategy, we estimate the cumulative ATE of receiving two consecutive years of instruction in a small versus regular class.