Causal mediation analysis with random interventions has become an area of significant interest for understanding time-varying effects with longitudinal and survival outcomes. To tackle causal and statistical challenges due to the complex longitudinal data structure with time-varying confounders, competing risks, and informative censoring, there exists a general desire to combine machine learning techniques and semiparametric theory. In this manuscript, we focus on targeted maximum likelihood estimation (TMLE) of longitudinal natural direct and indirect effects defined with random interventions. The proposed estimators are multiply robust, locally efficient, and directly estimate and update the conditional densities that factorize data likelihoods. We utilize the highly adaptive lasso (HAL) and projection representations to derive new estimators (HAL-EIC) of the efficient influence curves of longitudinal mediation problems and propose a fast one-step TMLE algorithm using HAL-EIC while preserving the asymptotic properties. The proposed method can be generalized for other longitudinal causal parameters that are smooth functions of data likelihoods, and thereby provides a novel and flexible statistical toolbox.

翻译：随机干预下的因果中介分析已成为理解随时间变化效应（伴随纵向和生存结局）的重要研究方向。为应对复杂纵向数据结构中时变混杂因素、竞争风险和删失信息带来的因果与统计挑战，学界普遍期望将机器学习技术与半参数理论相结合。本文聚焦于随机干预定义下纵向自然直接效应与间接效应的目标化最大似然估计（TMLE）。所提出的估计量具有多重稳健性和局部有效性特征，能够直接估计并更新数据似然因子化所需的条件密度。我们利用高度自适应LASSO（HAL）和投影表征推导出纵向中介问题有效影响曲线的新估计量（HAL-EIC），并基于HAL-EIC提出一种在保持渐近性质的同时实现快速一步式TMLE的算法。该方法可推广至其他作为数据似然光滑函数的纵向因果参数，为因果推断提供了新颖灵活的统计工具集。