In experimental and observational studies, there is often interest in understanding the mechanism through which an intervention program improves the final outcome. Causal mediation analyses have been developed for this purpose but are primarily considered for the case of perfect treatment compliance, with a few exceptions that require the exclusion restriction assumption. In this article, we consider a semiparametric framework for assessing causal mediation in the presence of treatment noncompliance without the exclusion restriction. We propose a set of assumptions to identify the natural mediation effects for the entire study population and further, for the principal natural mediation effects within subpopulations characterized by the potential compliance behavior. We derive the efficient influence functions for the principal natural mediation effect estimands and motivate a set of multiply robust estimators for inference. The multiply robust estimators remain consistent to their respective estimands under four types of misspecification of the working models and are efficient when all nuisance models are correctly specified. We further introduce a nonparametric extension of the proposed estimators by incorporating machine learners to estimate the nuisance functions. Sensitivity analysis methods are also discussed for addressing key identification assumptions. We demonstrate the proposed methods via simulations and an application to a real data example.

翻译：在实验研究和观察性研究中，人们常关注干预项目改善最终结局的作用机制。因果中介分析为此目的而发展，但主要针对完全治疗依从的情况，少数例外需要排除限制性假设。本文考虑在无排除限制性假设下，针对治疗非依从性评估因果中介效应的半参数框架。我们提出一组假设以识别整体研究人群的自然中介效应，并进一步识别以潜在依从行为为特征定义的子群内的主自然中介效应。推导了主自然中介效应估计量的有效影响函数，并激发了一组用于推断的多重稳健估计量。这些多重稳健估计量在工作模型存在四种错误设定时仍能保持对各自目标参数的一致性，且当所有干扰模型均正确设定时具有有效性。我们进一步引入机器学习方法估计干扰函数，将所提估计量扩展至非参数形式。同时讨论了用于解决关键识别假设的敏感性分析方法。通过模拟研究和真实数据实例验证了所提方法。