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

TL;DR

This paper develops methods for identifying and making valid inferences about treatment effects in randomized trials that use covariate-adaptive randomization and face imperfect compliance, providing practical estimation strategies.

Contribution

It characterizes the identified sets for ATE and ATT under covariate-adaptive randomization and imperfect compliance, and proposes consistent estimators and confidence intervals for these parameters.

Findings

Sample analog assignment frequencies improve efficiency for ATE bounds.

Using true assignment probabilities enhances ATT bounds estimation.

The methods are applicable to non-i.i.d. data under covariate-adaptive randomization.

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.