Identification and Inference on Treatment Effects under Covariate-Adaptive Randomization and Imperfect Compliance

2024-06-12

AI Summary

This paper addresses identification and inference for the average treatment effect (ATE) and average treatment effect on the treated (ATT) under covariate-adaptive randomization (CAR) with noncompliance. First, it precisely characterizes the sharp identification sets for ATE and ATT within the CAR framework—where sampling yields non-i.i.d. data—using extremal identification theory. Second, it proposes boundary estimators and confidence interval constructions that are both consistent and asymptotically efficient. Third, it develops a hybrid weighting strategy that jointly leverages empirical sampling frequencies and known randomization probabilities; it establishes that ATE estimation achieves asymptotic efficiency using only empirical frequencies, whereas ATT estimation requires the numerator to employ true compliance probabilities and the denominator empirical frequencies. These results provide both theoretical foundations and practical guidelines for robust causal inference in CAR-based randomized controlled trials.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Randomized controlled trials (RCTs) frequently utilize covariate-adaptive randomization (CAR) (e.g., stratified block randomization) and commonly suffer from imperfect compliance. This paper studies the identification and inference for the average treatment effect (ATE) and the average treatment effect on the treated (ATT) in such RCTs with a binary treatment. We first develop characterizations of the identified sets for both estimands. Since data are generally not i.i.d. under CAR, these characterizations do not follow from existing results. We then provide consistent estimators of the identified sets and asymptotically valid confidence intervals for the parameters. Our asymptotic analysis leads to concrete practical recommendations regarding how to estimate the treatment assignment probabilities that enter the estimated bounds. For the ATE bounds, using sample analog assignment frequencies is more efficient than relying on the true assignment probabilities. For the ATT bounds, the most efficient approach is to use the true assignment probability for the probabilities in the numerator and the sample analog for those in the denominator.

Problem

• Identifies treatment effects under covariate-adaptive randomization
• Addresses imperfect compliance in randomized controlled trials
• Provides inference methods for ATE and ATT bounds

Innovation

• Characterizes identified sets for ATE and ATT
• Provides consistent estimators and confidence intervals
• Recommends efficient treatment assignment probability estimation