In animal behavior studies, a common goal is to investigate the causal pathways between an exposure and outcome, and a mediator that lies in between. Causal mediation analysis provides a principled approach for such studies. Although many applications involve longitudinal data, the existing causal mediation models are not directly applicable to settings where the mediators are measured on irregular time grids. In this paper, we propose a causal mediation model that accommodates longitudinal mediators on arbitrary time grids and survival outcomes simultaneously. We take a functional data analysis perspective and view longitudinal mediators as realizations of underlying smooth stochastic processes. We define causal estimands of direct and indirect effects accordingly and provide corresponding identification assumptions. We employ a functional principal component analysis approach to estimate the mediator process and propose a Cox hazard model for the survival outcome that flexibly adjusts the mediator process. We then derive a g-computation formula to express the causal estimands using the model coefficients. The proposed method is applied to a longitudinal data set from the Amboseli Baboon Research Project to investigate the causal relationships between early adversity, adult physiological stress responses, and survival among wild female baboons. We find that adversity experienced in early life has a significant direct effect on females’ life expectancy and survival probability, but find little evidence that these effects were mediated by markers of the stress response in adulthood. We further developed a sensitivity analysis method to assess the impact of potential violation to the key assumption of sequential ignorability. Supplementary materials accompanying this paper appear on-line.

在动物行为研究中，一个共同的目标是研究暴露与结果之间的因果路径，以及介于两者之间的中介因素。因果中介分析为此类研究提供了原则性方法。尽管许多应用涉及纵向数据，但现有的因果中介模型并不直接适用于在不规则时间网格上测量中介的设置。在本文中，我们提出了一种因果中介模型，该模型同时适应任意时间网格和生存结果上的纵向中介。我们采取功能数据分析的视角，并将纵向中介视为底层平滑随机过程的实现。我们相应地定义了直接和间接影响的因果估计值，并提供了相应的识别假设。我们采用功能主成分分析方法来估计中介过程，并提出了一种灵活调整中介过程的生存结果的 Cox 风险模型。然后我们推导出一个 g 计算公式来使用模型系数来表达因果估计值。该方法应用于安博塞利狒狒研究项目的纵向数据集，以研究野生雌性狒狒早期逆境、成年生理应激反应和生存之间的因果关系。我们发现，早年经历的逆境对女性的预期寿命和生存概率有显着的直接影响，但几乎没有证据表明这些影响是由成年期压力反应标志物介导的。我们进一步开发了一种敏感性分析方法来评估潜在违规对顺序可忽略性关键假设的影响。本文附带的补充材料出现在网上。