Randomized Trials with Non-Compliance: Extending the Angrist-Imbens-Rubin Framework

随机对照试验（RCT）是临床和社会学研究中常用的一种设计，其中研究参与者被随机分配到研究治疗组或对照组作为比较。随机化作为消除治疗选择中的系统性偏差的独特手段，RCT理所当然地被奉为任何科学研究的黄金标准，尤其是那些涉及人类受试者的科学研究。然而，当RCT中的一些参与者不遵守随机分配，而是自行选择他们所选择的治疗方法时，就会出现一个具有挑战性但普遍存在的问题。这种自我选择损害了处理分配的客观性，从而削弱了实验的严谨性。一篇由Angrist， Imbens和Rubin（1996）撰写的开创性论文为在不服从的随机对照试验中得出有效因果推理的困难任务提供了宝贵的见解。然而，他们的工作主要集中在定量结果的平均值上，作为治疗效果的度量，因此不适用于其他常见的结果类型，如有序数据（例如肿瘤分级）。此外，尚不清楚他们的方法是否充分利用了每个参与者的现有信息。随着现代统计/数学工具（如经验过程、半参数理论和泛函分析）的出现，PI试图扩展Angrist-Imbens-Rubin （AIR）方法，目标是更广泛的效应大小测量或因果估计，并在统一的框架下研究它们的有效估计。PI还将开发用户友好的软件包，实现相应的推理程序，并让研究生参与该项目。该项目的成功完成将使研究人员拥有更多功能和更强大的工具，以解决随机对照试验中的不合规问题，随机对照试验是医学和社会学调查的支柱。具体来说，一般因果估计是由两个分支之间边际（潜在）结果分布的任意平滑对比来定义的。该公式统一了各种结果类型的看似不同的效应大小度量，如平均治疗效果（ATE）、曼-惠特尼效应（即治疗结果大于对照组结果的概率）、分位数治疗效果、分布治疗效果、胜率等。由于与不依从性相关的不可识别性，人们的兴趣集中在治疗效果的“局部”版本上，即对依从者亚群进行对比。这些都是AIR彻底研究过的本地ATE的自然延伸。在标准假设下，基于编译器结果分布的非参数估计，构造了局部处理效果的简单非参数插件估计。基于这些估算器的测试程序的工作特性也将被研究。最后，整个框架将在半参数理论术语中重新铸造，以优化估计和测试程序的统计效率。这项研究将为未来的扩展奠定基础，以适应基线协变量、审查结果和非二进制（可能与时间相关）治疗。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Randomized controlled trial (RCT) refers to a design commonly employed by clinical and sociological studies where study participants are randomly assigned to an investigational treatment arm, or to a control arm to serve as comparison. With randomization as the unique device to eliminate systematic bias in treatment choice, RCT has been rightfully enshrined as the gold standard for any scientific inquiry, especially those involving human subjects. A challenging yet pervasive issue arises, however, when some participants in an RCT do not comply with the random assignment and instead self-select into the treatment of their choice. This self-selection compromises the objectivity of treatment assignment and thereby weakens the rigor of the experiment. A seminal paper by Angrist, Imbens, and Rubin (1996) provided invaluable insight into the difficult task of drawing valid causal inference in RCTs plagued by non-compliance. However, their work is focused on the average of a quantitative outcome as the metric of treatment effect and thus does not apply to other commonly encountered outcome types such as ordinal data (for example, tumor grade). Moreover, it is unclear whether their approach has utilized the available information on each participant to the fullest extent. With the advent of modern statistical/mathematical tools such as empirical processes, semiparametric theory, and functional analysis, the PI seeks to extend the Angrist-Imbens-Rubin (AIR) approach by targeting a much wider scope of effect size measures, or causal estimands, and studying their efficient estimation under a unified framework. The PI will also develop user-friendly software packages implementing the corresponding inference procedures and involve graduate students in the project. Successful completion of this project will equip investigators with more versatile and powerful tools to address non-compliance in RCTs, the mainstay of medical and sociological investigations. Specifically, the general causal estimand is defined by an arbitrary smooth contrast in the marginal (potential) outcome distribution between the two arms. This formulation unifies seemingly disparate effect size measures for all kinds of outcome types, such as the average treatment effect (ATE), Mann-Whitney effect (i.e., probability of an outcome under treatment being greater than one under control), quantile treatment effect, distributional treatment effect, the win ratio, and so forth. Due to non-identifiability associated with non-compliance, interest is focused on a “local” version of treatment effects, that is, contrasts made on the sub-population of compliers. These are natural extensions of the local ATE thoroughly studied by AIR. Under standard assumptions, simple nonparametric plug-in estimators are constructed for the local treatment effects based on nonparametric estimators for the complier outcome distributions. The operating characteristics of testing procedures based on these estimators will also be investigated. Finally, the entire framework will be re-cast in semiparametric-theoretical terms to optimize the statistical efficiency of both the estimation and testing procedures. This research will lay the groundwork for future extensions to accommodate baseline covariates, censored outcomes, and non-binary (and possibly time-dependent) treatment.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.