We propose a new Bayesian non-parametric (BNP) method for estimating the causal effects of mediation in the presence of a post-treatment confounder. We specify an enriched Dirichlet process mixture (EDPM) to model the joint distribution of the observed data (outcome, mediator, post-treatment confounders, treatment, and baseline confounders). The proposed BNP model allows more confounder-based clusters than clusters for the outcome and mediator. For identifiability, we use the extended version of the standard sequential ignorability as introduced in \citet{hong2022posttreatment}. The observed data model and causal identification assumptions enable us to estimate and identify the causal effects of mediation, $i.e.$, the natural direct effects (NDE), and indirect effects (NIE). We conduct simulation studies to assess the performance of our proposed method. Furthermore, we apply this approach to evaluate the causal mediation effect in the Rural LITE trial, demonstrating its practical utility in real-world scenarios. \keywords{Causal inference; Enriched Dirichlet process mixture model.}

翻译：我们提出了一种新的贝叶斯非参数（BNP）方法，用于在存在事后混杂变量时估计中介效应的因果作用。通过设定富化的狄利克雷过程混合模型（EDPM）来对观测数据（结果变量、中介变量、事后混杂变量、处理变量及基线混杂变量）的联合分布进行建模。所提出的BNP模型允许基于混杂变量的聚类数量多于基于结果变量和中介变量的聚类数量。为保证可识别性，我们采用了由 \citet{hong2022posttreatment} 引入的扩展版标准序贯可忽略性假设。基于观测数据模型与因果识别假设，我们能够估计和识别中介效应的因果作用，即自然直接效应（NDE）和间接效应（NIE）。通过模拟研究评估了所提出方法的性能，并进一步将该方法应用于Rural LITE试验中因果中介效应的评估，验证了其在真实场景中的实用价值。\关键词{因果推断；富化狄利克雷过程混合模型}