Two-phase treatment with noncompliance: identifying the cumulative average treatment effect via multisite instrumental variables
研究两阶段干预中，利用第一阶段随机分配作为工具变量，在放宽传统排除限制和序贯可忽略性假设下，识别累积平均处理效应，并应用于田纳西州班级规模研究。
Abstract 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 behaviours. 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 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 reanalyse 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.