发表机构
Department of Mathematics, Toronto Metropolitan University（多伦多都会大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对同期混杂下的动态治疗方案，提出无需敏感性参数的尖锐因果界，通过反向归纳获得期望结果的精确上下界，并推广了经典g-公式与Q-learning框架。
AI 中文摘要
我们研究了同期混杂下的动态治疗方案：在每个阶段，一个未测量的因素可能同时影响治疗和下一个观察到的状态，但对后续阶段没有进一步的直接影响。从观测分布、因果图以及对可能下一状态的指定结构限制出发，我们在每个状态-治疗对处构造了与此信息兼容的转移概率集合。这些局部集合不需要敏感性参数，可以通过反向归纳进行组合，以获得在任意给定治疗方案下期望结果的上下界。我们的主要结果表明这些界是尖锐的：它们的端点恰好是由与相同观测分布、因果图和结构限制兼容的因果模型所生成的最小和最大期望结果。相同的反向归纳方法给出了一个极大极小规则，通过最大化最坏情况下的期望结果来选择治疗。因此，对于这类具有同期混杂的模型，该框架推广了用于评估治疗方案的经典g-公式（Robins, 1986）和用于选择治疗方案的Q-learning框架（Murphy, 2003）。当局部转移概率可识别时，这两个递归可简化为这些经典方法。
英文摘要
We study dynamic treatment regimes under contemporaneous confounding: at each stage, an unmeasured factor may affect both treatment and the next observed state, but has no further direct effect on later stages. From the observational distribution, the causal graph, and specified structural restrictions on possible next states, we construct at each state--treatment pair the set of transition probabilities compatible with this information. These local sets require no sensitivity parameter and can be combined by backward induction to obtain lower and upper bounds on the expected outcome under any given treatment regime. Our main result shows that these bounds are sharp: their endpoints are exactly the smallest and largest expected outcomes generated by causal models compatible with the same observational distribution, causal graph, and structural restrictions. The same backward-induction method gives a maximin rule for choosing treatments by maximizing the worst-case expected outcome. Thus, for this class of models with contemporaneous confounding, the framework generalizes the classical g-formula of \citet{Robins1986} for evaluating treatment regimes and the Q-learning framework of \citet{Murphy2003} for selecting them. When the local transition probabilities are identified, the two recursions reduce to these classical methods.
Comments41 pages, 2 figures. Includes an appendix with proofs
