We study time-dependent mediators in survival analysis using a treatment separation approach due to Didelez [2019] and based on earlier work by Robins and Richardson [2011]. This approach avoids nested counterfactuals and crossworld assumptions which are otherwise common in mediation analysis. The causal model of treatment, mediators, covariates, confounders and outcome is represented by causal directed acyclic graphs (DAGs). However, the DAGs tend to be very complex when we have measurements at a large number of time points. We therefore suggest using so-called rolled graphs in which a node represents an entire coordinate process instead of a single random variable, leading us to far simpler graphical representations. The rolled graphs are not necessarily acyclic; they can be analyzed by $\delta$-separation which is the appropriate graphical separation criterion in this class of graphs and analogous to $d$-separation. In particular, $\delta$-separation is a graphical tool for evaluating if the conditions of the mediation analysis are met or if unmeasured confounders influence the estimated effects. We also state a mediational g-formula. This is similar to the approach in Vansteelandt et al. [2019] although that paper has a different conceptual basis. Finally, we apply this framework to a statistical model based on a Cox model with an added treatment effect.survival analysis; mediation; causal inference; graphical models; local independence graphs

翻译：我们采用Didelez [2019]基于Robins和Richardson [2011]早期工作提出的治疗分离方法，研究生存分析中的时变中介变量。该方法避免了中介分析中常见的嵌套反事实和跨世界假设。治疗、中介变量、协变量、混杂因素和结局之间的因果模型由有向无环图表示。然而，当存在大量时间点的测量数据时，有向无环图往往变得非常复杂。因此，我们建议使用所谓的“卷曲图”，其中节点表示整个坐标过程而非单个随机变量，从而得到更为简化的图形表示。卷曲图不一定无环；可通过$\delta$-分离进行分析，这是该类图中适用的图形分离准则，类似于$d$-分离。特别地，$\delta$-分离是一种图形工具，用于评估中介分析的条件是否满足，或未测量的混杂因素是否影响估计效应。我们还提出了中介$g$-公式，这与Vansteelandt等人[2019]的方法类似，尽管该论文的概念基础不同。最后，我们将此框架应用于基于Cox模型并加入治疗效应的统计模型。