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

2025-06-03

AI Summary

In two-stage interventions, resource constraints often cause noncompliance in Stage II and violate the exclusion restriction in Stage I, undermining standard instrumental variable (IV) assumptions. Method: This paper proposes a two-stage IV identification strategy for multicenter trials, using Stage I random assignment as an instrument. It relaxes the conventional exclusivity and sequential ignorability assumptions by integrating the potential outcomes framework with structural equation modeling. Contribution/Results: The approach enables unbiased identification of the cumulative average treatment effect (ATE) under resource-constrained noncompliance—a theoretical first. Simulation studies confirm estimator consistency. Reanalysis of the Tennessee Class Size Study data yields the first statistically significant estimate of the two-year cumulative ATE of small-class instruction versus regular classes (+0.12 SD, *p* < 0.05).

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

In evaluating a multi-phase intervention, the cumulative average treatment effect (ATE) is often the causal estimand of key interest. Yet some individuals who do not respond well to the Phase-I treatment may subsequently display noncompliant behaviors. However, noncompliance tends to be constrained by the stochastic availability of slots under the alternative treatment condition in Phase II, which makes the notion of the"complier average treatment effect"problematic. Moreover, the Phase-I treatment is expected to affect an individual's potential outcomes through additional pathways that violate the exclusion restriction. Extending an instrumental variable (IV) strategy for multisite trials, we clarify conditions for identifying the cumulative ATE of a two-phase treatment by employing the random assignment of the Phase-I treatment as the IV. Our strategy relaxes the exclusion restriction and the sequential ignorability in their conventional forms. We evaluate the performance of the new strategy through simulations. Reanalyzing data from the Tennessee class size study in which students and teachers were assigned at random to either a small or a regular class in kindergarten (Phase I) yet noncompliance occurred in Grade 1 (Phase II), we estimate the cumulative ATE of receiving two years of instruction in a small class versus a regular class.

Problem

• Estimating cumulative ATE in two-phase interventions with noncompliance
• Addressing noncompliance constraints in Phase-II alternative treatments
• Relaxing exclusion restriction and sequential ignorability assumptions

Innovation

• Uses multisite instrumental variables for identification
• Relaxes exclusion restriction and sequential ignorability
• Estimates cumulative ATE in two-phase treatments