We consider Dynamic Treatment Regimes (DTRs) with one sided non-compliance that arise in applications such as digital recommendations and adaptive medical trials. These are settings where decision makers encourage individuals to take treatments over time, but adapt encouragements based on previous encouragements, treatments, states, and outcomes. Importantly, individuals may choose to (not) comply with a treatment recommendation, whenever it is made available to them, based on unobserved confounding factors. We provide non-parametric identification, estimation, and inference for Dynamic Local Average Treatment Effects, which are expected values of multi-period treatment contrasts among appropriately defined complier subpopulations. Under standard assumptions in the Instrumental Variable and DTR literature, we show that one can identify local average effects of contrasts that correspond to offering treatment at any single time step. Under an additional cross-period effect-compliance independence assumption, which is satisfied in Staggered Adoption settings and a generalization of them, which we define as Staggered Compliance settings, we identify local average treatment effects of treating in multiple time periods.

翻译：我们考虑在数字推荐和自适应医疗试验等应用中出现的单侧不服从的动态治疗方案。这类场景中，决策者会随时间推移逐步鼓励个体接受治疗，并根据先前的鼓励、治疗、状态和结果调整鼓励策略。关键问题在于，当个体被提供治疗方案时，可能基于未观测的混杂因素选择（不）遵从推荐。我们为动态局部平均处理效应提供了非参数识别、估计与推断方法——该效应定义为适当地定义的依从者子群体中多期治疗对比的期望值。基于工具变量和动态治疗方案文献的标准假设，我们证明可以识别出对应于任何单一时点提供治疗的治疗对比的局部平均效应。在满足交错采纳设置及其推广形式（我们将其定义为交错依从设置）的跨期效应-依从独立性附加假设下，我们进一步识别了多个时点持续治疗的局部平均处理效应。