When evaluating a two-phase intervention, the cumulative average treatment effect (ATE) is often the primary causal estimand of interest. However, some individuals who do not respond well to the Phase I treatment may subsequently display noncompliant behaviors. At the same time, exposure to the Phase I treatment is expected to directly influence an individual's potential outcomes, thereby violating the exclusion restriction. Building on an instrumental variable (IV) strategy for multisite trials, we clarify the conditions under which the cumulative ATE of a two-phase treatment can be identified by employing the random assignment of the Phase I treatment as the instrument. Our strategy relaxes both the conventional exclusion restriction and sequential ignorability assumptions. We assess the performance of the new strategy through simulation studies. Additionally, we reanalyze data from the Tennessee class size study, in which students and teachers were randomly assigned to either small or regular class types in kindergarten (Phase I) with noncompliance emerging in Grade 1 (Phase II). Applying our new strategy, we estimate the cumulative ATE of receiving two consecutive years of instruction in a small versus regular class.

翻译：在评估两阶段干预措施时，累积平均处理效应通常是主要的因果估计目标。然而，部分对第一阶段处理反应不佳的个体可能在后续阶段表现出非依从行为。同时，接受第一阶段处理预计会直接影响个体的潜在结果，从而违背排他性约束。基于多中心试验的工具变量策略，我们明确了在何种条件下，可通过将第一阶段处理的随机分配作为工具变量来识别两阶段处理的累积平均处理效应。该策略同时放宽了传统排他性约束和序贯可忽略性假设。我们通过模拟研究评估了新策略的性能。此外，我们重新分析了田纳西州班级规模研究的数据，在该研究中，学生和教师在幼儿园阶段（第一阶段）被随机分配到小班或常规班级，而一年级（第二阶段）出现了非依从现象。应用新策略，我们估计了连续两年接受小班教学相较于常规班级教学的累积平均处理效应。