"Treatment-confounder feedback" is the central complication to resolve in longitudinal studies, to infer causality. The existing frameworks for identifying causal effects for longitudinal studies with discrete repeated measures hinge heavily on assuming that time advances in discrete time steps or treatment changes as a jumping process, rendering the number of "feedbacks" finite. However, medical studies nowadays with real-time monitoring involve functional time-varying outcomes, treatment, and confounders, which leads to an uncountably infinite number of feedbacks between treatment and confounders. Therefore more general and advanced theory is needed. We generalize the definition of causal effects under user-specified stochastic treatment regimes to longitudinal studies with continuous monitoring and develop an identification framework, allowing right censoring and truncation by death. We provide sufficient identification assumptions including a generalized consistency assumption, a sequential randomization assumption, a positivity assumption, and a novel "intervenable" assumption designed for the continuous-time case. Under these assumptions, we propose a g-computation process and an inverse probability weighting process, which suggest a g-computation formula and an inverse probability weighting formula for identification. For practical purposes, we also construct two classes of population estimating equations to identify these two processes, respectively, which further suggest a doubly robust identification formula with extra robustness against process misspecification. We prove that our framework fully generalize the existing frameworks and is nonparametric.

翻译：“治疗-混杂因子反馈”是纵向研究中推断因果关系的核心难题。现有针对离散重复测量纵向研究的因果效应识别框架，高度依赖于时间以离散步长推进或治疗作为一种跳跃过程变化的假设，这使得“反馈”次数有限。然而，现代医学研究中的实时监测涉及功能性的时变结局、治疗和混杂因子，导致治疗与混杂因子之间存在不可数无穷多的反馈。因此需要更通用和先进的理论。我们将用户指定随机治疗策略下的因果效应定义推广至连续监测的纵向研究，并发展了一个识别框架，允许右删失和死亡截尾。我们提供了充分的识别假设，包括广义一致性假设、序贯随机化假设、阳性假设，以及专门为连续时间情形设计的新型“可干预性”假设。在这些假设下，我们提出了g-计算过程和逆概率加权过程，由此得到用于识别的g-计算公式和逆概率加权公式。出于实用目的，我们还分别构建了两类人群估计方程来识别这两个过程，进一步提出了具有额外稳健性（针对过程误设）的双重稳健识别公式。我们证明该框架完全推广了现有框架，并且是非参数的。