Estimating Complier Average Causal Effects with Mixtures of Experts

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.