Existing causal methods for time-varying exposure and time-varying confounding focus on estimating the average causal effect of a time-varying binary treatment on an end-of-study outcome, offering limited tools for characterizing marginal causal dose-response relationships under continuous exposures. We propose a scalable, nonparametric Bayesian framework for estimating marginal longitudinal causal dose-response functions with repeated outcome measurements. Our approach targets the average potential outcome at any fixed dose level and accommodates time-varying confounding through the generalized propensity score. The proposed approach embeds a Dirichlet process specification within a generalized estimating equations structure, capturing temporal correlation while making minimal assumptions about the functional form of the continuous exposure. We apply the proposed methods to monthly metro ridership and COVID-19 case data from major international cities, identifying causal relationships and the dose-response patterns between higher ridership and increased case counts.

翻译：现有针对时变暴露和时变混杂的因果方法主要专注于估计时变二元治疗对研究终点结局的平均因果效应，在连续暴露条件下刻画边际因果剂量反应关系的工具十分有限。我们提出一种可扩展的非参数贝叶斯框架，用于估计包含重复结局测量的纵向边际因果剂量反应函数。该方法以任意固定剂量水平下的平均潜在结局为目标，通过广义倾向性得分处理时变混杂。该框架将狄利克雷过程规范嵌入广义估计方程结构中，在捕捉时间相关性的同时，对连续暴露的函数形式仅作极简假设。我们将所提方法应用于国际主要城市的月度地铁客流量与COVID-19病例数据，识别出高客流量与病例数增加之间的因果关系及剂量反应模式。