We consider causal mediation analysis with confounders subject to nonignorable missingness in a nonparametric framework. Our approach relies on shadow variables that are associated with the missing confounders but independent of the missingness mechanism. The mediation effect of interest is shown to be a weighted average of an iterated conditional expectation, which motivates our Sieve-based Iterative Outward (SIO) estimator. We derive the rate of convergence and asymptotic normality of the SIO estimator, which do not suffer from the ill-posed inverse problem. Essentially, we show that the asymptotic normality is not affected by the slow convergence rate of nonparametric estimators of nuisance functions. Moreover, we demonstrate that our estimator is locally efficient and attains the semiparametric efficiency bound under certain conditions. We accurately depict the efficiency loss attributable to missingness and identify scenarios in which efficiency loss is absent. We also propose a stable and easy-to-implement approach to estimate asymptotic variance and construct confidence intervals for the mediation effects. Finally, we evaluate the finite-sample performance of our proposed approach through simulation studies, and apply it to the CFPS data to show its practical applicability.

翻译：我们考虑了在非参数框架下，混杂因子受到不可忽略缺失影响时的因果中介分析。我们的方法依赖于与缺失混杂因子相关但与缺失机制独立的影子变量。研究显示，感兴趣的中介效应是迭代条件期望的加权平均，这启发了我们提出的基于筛法的迭代向外（SIO）估计量。我们推导了SIO估计量的收敛速度和渐近正态性，该估计量不受病态逆问题的影响。本质上，我们证明了渐近正态性不受干扰函数非参数估计量慢收敛速度的影响。此外，我们证明该估计量在特定条件下具有局部有效性，并达到了半参数效率界。我们精确刻画了缺失导致的效率损失，并识别出效率损失不存在的情景。我们还提出了一种稳定且易于实现的方法来估计渐近方差，并构建中介效应的置信区间。最后，通过模拟研究评估所提方法的有限样本性能，并将其应用于CFPS数据以展示其实用性。