We define dynamic treatment regimes and associated potential outcomes for data described by marked point processes (MPPs). These definitions motivate MPP analogues of the commonly used consistency, exchangeability, and positivity conditions that are sufficient for identifying effects in MPP data structures. The conditions are formulated based on martingale theory, which allows us to derive explicit identifying assumptions for data described by stochastic processes. The definitions and conditions align with well-established discrete-time results in important special cases. Thus, this work bridges the large literatures on survival (event history) analysis with counting processes in continuous time and causal inference with variables in discrete-time. After formulating a set of identification conditions, we derive and characterize marginal g-formulas. The g-formulas are generally different from those studied in related works, though they coincide in important special cases. We relate our findings to previous work on causal inference with (counting) processes, the classical survival literature, and the discrete-time causal inference literature.

翻译：我们定义了带标记点过程（MPPs）中数据的动态治疗方案及相应的潜在结果。这些定义推动了MPP中一致性、可交换性和积极性条件（这些条件在MPP数据结构中足以识别效应）的对应推广。这些条件基于鞅理论构建，使我们能够为随机过程描述的数据推导出显式的识别假设。在重要特例中，该定义和条件与成熟的离散时间结果保持一致。因此，本研究衔接了连续时间计数过程生存（事件史）分析与离散时间变量因果推断这两个庞大的文献领域。在构建一组识别条件后，我们推导并刻画了边际g公式。尽管在重要特例中一致，这些g公式通常不同于相关研究中的公式。我们将发现与先前关于（计数）过程因果推断的研究、经典生存分析文献以及离散时间因果推断文献进行了关联。