In experimental and observational studies, there is often interest in understanding the potential mechanism by which an intervention program improves the final outcome. Causal mediation analyses have been developed for this purpose but are primarily restricted to the case of perfect treatment compliance, with a few exceptions that require exclusion restriction. In this article, we establish a semiparametric framework for assessing causal mediation in the presence of treatment noncompliance without 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 behaviour. We derive the efficient influence functions for the principal natural mediation effect estimands, which motivate a set of multiply robust estimators for inference. The semiparametric efficiency theory for the identified estimands is derived, based on which a multiply robust estimator is proposed. The multiply robust estimators remain consistent to the their respective estimands under four types of misspecification of the working models and is quadruply robust. We further describe a nonparametric extension of the proposed estimators by incorporating machine learners to estimate the nuisance parameters. A sensitivity analysis framework has been developed for address key identification assumptions-principal ignorability and ignorability of mediator. We demonstrate the proposed methods via simulations and applications to a real data example.

翻译：在实验和观察性研究中，研究者通常关注干预方案改善最终结果的潜在机制。因果中介分析虽为此目的而发展，但主要限于完美治疗依从的情况，少数例外则需满足排除限制假设。本文建立了一个半参数框架，用于评估存在治疗不依从但无需排除限制假设时的因果中介效应。我们提出一系列假设以识别整个研究人群的自然中介效应，进而识别以潜在依从行为为特征的子群内的主自然中介效应。推导出主自然中介效应估计量的有效影响函数，并由此提出多重稳健估计量进行推断。基于识别估计量的半参数效率理论，我们提出了一个多重稳健估计量。该估计量在四种工作模型设定错误的情况下仍能保持对其对应估计量的一致估计，具有四重稳健性。进一步通过引入机器学习方法估计干扰参数，提出了估计量的非参数扩展。建立了敏感性分析框架以处理关键识别假设——主可忽略性与中介变量可忽略性。通过模拟实验和真实数据案例验证了所提出方法的有效性。