  Understanding the causal impact of medical interventions is essential in
healthcare research, especially through randomized controlled trials (RCTs).
Despite their prominence, challenges arise due to discrepancies between
treatment allocation and actual intake, influenced by various factors like
patient non-adherence or procedural errors. This paper focuses on the Complier
Average Causal Effect (CACE), crucial for evaluating treatment efficacy among
compliant patients. Existing methodologies often rely on assumptions such as
exclusion restriction and monotonicity, which can be problematic in practice.
We propose a novel approach, leveraging supervised learning architectures, to
estimate CACE without depending on these assumptions. Our method involves a
two-step process: first estimating compliance probabilities for patients, then
using these probabilities to estimate two nuisance components relevant to CACE
calculation. Building upon the principal ignorability assumption, we introduce
four root-n consistent, asymptotically normal, CACE estimators, and prove that
the underlying mixtures of experts' nuisance components are identifiable. Our
causal framework allows our estimation procedures to enjoy reduced mean squared
errors when exclusion restriction or monotonicity assumptions hold. Through
simulations and application to a breastfeeding promotion RCT, we demonstrate
the method's performance and applicability.
