AI 中文总结
本文将因果推断中个体化治疗规则的表现界研究扩展至时变设定，推导了基于未观测潜在结果的先知策略的精确界，覆盖二元与连续结局，并探讨连续潜在结果CDF的界。
AI 中文摘要
许多因果推断研究聚焦于动态治疗 regimes（Murphy, 2003; Robins, 2004; Schulte et al., 2015）的优化方法，这类规则依据不断演变的历史决定应分配何种治疗及时机。该研究隐含一种乐观态度，即通过充分调整或许能实现显著改进。此前另一类研究局限于点暴露设定，探讨任何个体化治疗规则可能达到的表现界。本文将其扩展至时变设定，推导基于每个受试者未观测到的潜在结果或“反应类型”选择最优治疗 regime 的先知策略表现的精确界。对于二元结局，下界（假设越高越好）即为基于观测历史的最优治疗 regime 所达到的期望结局；对于连续结局，下界可能严格超过基于观测协变量的最大值。在连续设定中，本文还考虑了先知连续潜在结果的累积分布函数（CDF）的界。
英文摘要
Much causal inference research is focused on methods for optimizing dynamic treatment regimes (Murphy, 2003; Robins, 2004; Schulte et al., 2015), which are rules for deciding which treatments should be assigned and when based on evolving history. There is a certain optimism underlying this endeavor that with enough tinkering we might realize consequential improvements. Another strand of research, previously confined to the point exposure setting, considers bounds on how well any individualized treatment rule could possibly do. Here, we extend to the time-varying setting sharp bounds on the performance of an oracle strategy that selects the best treatment regime for each subject based on their unobserved potential outcomes or `response type'. For binary outcomes, the lower bound (assuming higher is better) is simply the expected outcome attained by the optimal treatment regime based on observed history. For continuous outcomes, the lower bound may strictly exceed the maximal observed covariate based value. In the continuous setting, we also consider bounds on the CDF of oracle continuous potential outcomes.
