Mediation analysis is essential for decomposing the causal effect of a treatment into direct and indirect pathways. However, many practical settings rely on the stringent assumption that recanting witnesses, defined as treatment-induced mediator-outcome confounders, are either absent or fully known a priori. Such a requirement is often untenable, especially when these variables remain unobservable due to measurement difficulties or privacy constraints. In this paper, we leverage proximal causal inference to develop three novel identification strategies to address the challenge of identifying path-specific effects in the presence of unknown recanting witnesses. Building on this, we develop a semiparametric inference framework that derives the efficient influence function and proposes a proximal multiply robust estimator, which remains consistent if at least one set of nuisance models is correctly specified. When all nuisance models are correctly specified and converge at appropriate rates, the estimator is asymptotically normal and achieves the semiparametric efficiency bound. We provide a minimax optimization-based debiased machine learning procedure for point estimation and constructing valid confidence intervals. The performance of the proposed methods is demonstrated by simulation studies and a real data application.

翻译：摘要：中介分析对于将处理的因果效应分解为直接和间接路径至关重要。然而，许多实际场景依赖于一个严格假设，即翻供见证者（定义为由处理引起的中介-结果混杂因素）要么不存在，要么完全先验已知。这一假设往往难以成立，特别是当这些变量因测量困难或隐私限制而无法观测时。本文利用邻近因果推断，提出三种新型识别策略，以应对在未知翻供见证者存在时识别路径特异性效应的挑战。在此基础上，我们构建了一个半参数推断框架，推导出有效影响函数，并提出一种邻近多重稳健估计量——若至少一组干扰模型设定正确，该估计量将保持一致性。当所有干扰模型均正确设定且以适当速率收敛时，该估计量渐进正态且达到半参数效率界。我们提供了基于极小极大优化的去偏机器学习方法，用于点估计和构建有效置信区间。通过模拟研究和真实数据应用验证了所提方法的性能。