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、结局以及称为中介变量的中间变量之间的因果机制。该方法最初针对固定时间点的中介变量和结局变量而开发，后通过对中介变量和结局变量的评估时间进行离散化处理，被扩展至纵向数据框架。然而，纵向研究中的过程通常定义在连续时间中，并在不规律且受试者特定的访视时间点进行测量。这在痴呆症研究中尤为典型，例如，当关注队列中计划访视时测量的脑部与认知变化。因此，我们提出一种方法，用于估计时间固定暴露（$X$）、随时间重复测量的中介过程（$\mathcal{M}_t$）和结局过程（$\mathcal{Y}_t$）之间的因果机制，同时考虑存在时变混杂过程（$\mathcal{L}_t$）的情况。我们考虑三类因果估计量：自然效应、路径特异性效应以及自然效应的随机干预模拟，并给出可识别性假设。我们采用基于微分方程的动态多变量模型进行估计。通过模拟研究探索了该方法的性能，并以3C脑衰老研究为背景的两个实际案例进行说明：（1）通过抑郁症状和认知功能评估教育水平对功能依赖的影响，以及（2）评估遗传因素对认知功能的潜在影响（该影响可能由血管性脑损伤中介，并被神经退行性变所混杂）。