Mediation analysis aims to decipher the underlying causal mechanisms between an exposure, an outcome, and intermediate variables called mediators. Initially developed for fixed-time mediator and outcome, it has been extended to the framework of longitudinal data by discretizing the assessment times of mediator and outcome. Yet, processes in play in longitudinal studies are usually defined in continuous time and measured at irregular and subject-specific visits. This is the case in dementia research when cerebral and cognitive changes measured at planned visits in cohorts are of interest. We thus propose a methodology to estimate the causal mechanisms between a time-fixed exposure ($X$), a mediator process ($\mathcal{M}_t$) and an outcome process ($\mathcal{Y}_t$) both measured repeatedly over time in the presence of a time-dependent confounding process ($\mathcal{L}_t$). We consider three types of causal estimands, the natural effects, path-specific effects and randomized interventional analogues to natural effects, and provide identifiability assumptions. We employ a dynamic multivariate model based on differential equations for their estimation. The performance of the methods are explored in simulations, and we illustrate the method in two real-world examples motivated by the 3C cerebral aging study to assess: (1) the effect of educational level on functional dependency through depressive symptomatology and cognitive functioning, and (2) the effect of a genetic factor on cognitive functioning potentially mediated by vascular brain lesions and confounded by neurodegeneration.

翻译：中介分析旨在揭示暴露、结局及中间变量（称为中介变量）之间的潜在因果机制。该方法最初针对固定时间点的中介变量与结局变量开发，后通过离散化中介变量与结局变量的评估时间点，被扩展至纵向数据框架。然而，纵向研究中的动态过程通常定义在连续时间中，并在研究对象特异性、非规则随访时间点进行测量——这正是痴呆症研究中关注的关键问题：在队列研究的计划访视中测量的脑部与认知变化。为此，我们提出一种方法论，在存在时间依赖性混杂过程（$\mathcal{L}_t$）时，估计时间固定暴露（$X$）、中介过程（$\mathcal{M}_t$）与结局过程（$\mathcal{Y}_t$）之间的因果机制。我们考虑三类因果估计量：自然效应、路径特异性效应及自然效应的随机干预模拟量，并给出可识别性假设。基于微分方程构建动态多变量模型进行参数估计。通过模拟研究验证方法性能，并基于3C脑老化队列研究的两项实证案例展示方法应用：（1）评估教育水平通过抑郁症状与认知功能对功能依赖性的影响；（2）评估遗传因素通过血管性脑损伤（潜在中介）与神经退行性变（潜在混杂）对认知功能的因果效应。