Dynamic Local Average Treatment Effects

TL;DR

The study addresses identifying and estimating Dynamic Local Average Treatment Effects in adaptive trials with one-sided noncompliance. It develops nonparametric identification for When-to-Treat LATEs and Dynamic Mixture LATEs, and shows Always-Treat LATEs are not identifiable without extra cross-period restrictions, introducing Staggered Compliance as a practical condition to recover them and extend to many periods. The authors propose automatically debiased machine learning estimators based on Neyman orthogonality and Riesz representers, enabling valid inference with flexible ML nuisances. They further generalize the framework to multi-period settings, provide explicit identification formulas, and validate the approach through synthetic experiments demonstrating accurate estimates and nominal coverage, with clear guidance for policy evaluation in dynamic treatment regimes.

Abstract

We consider Dynamic Treatment Regimes (DTRs) with One Sided Noncompliance that arise in applications such as digital recommendations and adaptive medical trials. These are settings where decision makers encourage individuals to take treatments over time, but adapt encouragements based on previous encouragements, treatments, states, and outcomes. Importantly, individuals may not comply with encouragements based on unobserved confounders. For settings with binary treatments and encouragements, we provide nonparametric identification, estimation, and inference for Dynamic Local Average Treatment Effects (LATEs), which are expected values of multiple time period treatment effect contrasts for the respective complier subpopulations. Under One Sided Noncompliance and sequential extensions of the assumptions in Imbens and Angrist (1994), we show that one can identify Dynamic LATEs that correspond to treating at single time steps. In Staggered Adoption settings, we show that the assumptions are sufficient to identify Dynamic LATEs for treating in multiple time periods. Moreover, this result extends to any setting where the effect of a treatment in one period is uncorrelated with the compliance event in a subsequent period.

Figures (12)

• Figure 1: Directed Acyclic Graphs that adhere to the exclusion restrictions in Assumption \ref{['assume:2_consistency']}. Encouragements $Z$, treatments $D$, states $S$, and long term outcomes $Y$ are represented by gray circles to indicate that they are observed variables. $U$'s are unobserved confounders, and are illustrated using a white circle to indicate that they are unobserved. Edges (arrows) pointing from one random variable to another indicates that the latter is allowed to be a function of the former. The node $S_0$ should be thought of as sending edges to all observed random variables.
• Figure 2: Causal graph depicting a scenario with endogenous entry into an adaptive stratified trial. The variable $S_0$ should be thought as having outgoing edges to all the observed variables (gray).
• Figure 3: RMSE, Bias and Coverage on Synthetic Data with two periods.
• Figure 4: RMSE, Bias and Coverage on Synthetic Data with three periods.
• Figure 5: RMSE, Bias and Coverage on Synthetic Data with two periods and gradient boosted forests for all classification models.

Theorems & Definitions (34)

• Definition 1: Intervention Counterfactuals
• Definition 2: Shorthand Notation of Central Intervention Counterfactuals
• Definition 3: Dynamic LATE
• Definition 4: Dynamic Mixture LATE
• Definition 5: Heterogeneous Dynamic LATE
• Definition 6: Heterogeneous Dynamic Mixture LATE
• Theorem 1: Identification of Dynamic LATEs
• Theorem 2: Identification of Heterogeneous Dynamic When-to-Treat LATEs
• Proposition 1
• Theorem 3