Estimating dynamic treatment regimes (DTRs) from retrospective observational data is challenging as some degree of unmeasured confounding is often expected. In this work, we develop a framework of estimating properly defined "optimal" DTRs with a time-varying instrumental variable (IV) when unmeasured covariates confound the treatment and outcome, rendering the potential outcome distributions only partially identified. We derive a novel Bellman equation under partial identification, use it to define a generic class of estimands (termed IV-optimal DTRs), and study the associated estimation problem. We then extend the IV-optimality framework to tackle the policy improvement problem, delivering IV-improved DTRs that are guaranteed to perform no worse and potentially better than a pre-specified baseline DTR. Importantly, our IV-improvement framework opens up the possibility of strictly improving upon DTRs that are optimal under the no unmeasured confounding assumption (NUCA). We demonstrate via extensive simulations the superior performance of IV-optimal and IV-improved DTRs over the DTRs that are optimal only under the NUCA. In a real data example, we embed retrospective observational registry data into a natural, two-stage experiment with noncompliance using a time-varying IV and estimate useful IV-optimal DTRs that assign mothers to high-level or low-level neonatal intensive care units based on their prognostic variables.
翻译:在这项工作中,我们制定了一个框架,用于对定义得当的“最佳”DTR进行适当评估,并使用一个时间变化工具变量(IV),在无法计量的共变混混混了治疗和结果,仅部分确定潜在结果分布时,用追溯观测数据估算出一个新型的Bellman方程式(DTRs),在部分识别下得出一个新型的Bellman方程式,用它来定义一个通用的估量类别(确定为四至最佳的变量),并研究相关的估算问题。然后,我们扩展了四至最佳框架,以解决政策改进问题,提供四至完善的DTRs,保证其性能不会比事先设定的基准DTRs差,而且可能更好。 重要的是,我们的四级改进型DTRs框架为严格改进DTRs(在未测定的假设下是最佳的)实用性假设(UNCARCa)。我们通过广泛模拟了四至四级的四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级四级八级八级八级八级八级四级四级四级四级八级八级八级八级八级四级八级级级级级级级级级级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级八级内的最佳数据数据数据数据的最佳数据数据,我们仅为最佳次级次级次级次级次级次级次级次级次级次级次级次级次级次级次级次级