Complier General Causal Effect in Randomized Controlled Trials with One-Sided Noncompliance

Abstract

A randomized controlled trial (RCT) is widely regarded as the gold standard for assessing the causal effect of a treatment or intervention, assuming perfect implementation. In practice, however, randomization can be compromised for various reasons, such as one-sided noncompliance. In this paper, we first systematically study the likelihood-based identifiability in an RCT with one-sided noncompliance. This foundational analysis naturally gives rise to the complier general causal effect (CGCE) as the primary estimand. We further develop two estimators for the CGCE: a simple estimator that requires no nonparametric procedures, and an efficient estimator that achieves the semiparametric efficiency bound. Our theoretical analysis shows that, achieving semiparametric efficiency requires only the nuisance estimators to converge in $L_2$-norm, with no restriction on their convergence rates. This rate-free property opens the door to employing many more modern machine learning methods while still guaranteeing efficiency. Comprehensive simulation studies and a real data application are conducted to illustrate the proposed methods and to compare them with existing approaches.