CIF:Small:A Systems Approach to Statistics for N-of-1 Experimental Trials

随机实验可以说是20世纪统计学最重要的贡献，它提供了一个程序来确定干预对个体群体的价值。通过将个体随机分配到治疗组和对照组，统计分析可以确定干预效果的大小，并消除混淆的解释。然而，随机化实验得出的结论只涉及群体，而不是个人。当治疗具有异质性效应时，随机实验无法告知个体治疗是否对他们个人有效。相比之下，N-of-1试验试图通过让单个个体在不同的时间窗内应用随机治疗来解决这个问题。如果效果是即时和短暂的，则可以使用随机实验的标准工具来估计效果的大小和显著性。然而，N-of-1试验仍然非常有限，因为目前还没有一个通用框架来理解长期积累的效应或与个体有复杂相互作用的干预措施。该项目旨在为个人设计一种实验方法，使用工程系统的想法来构建一个复杂的框架，以理解这种复杂的N-of-1实验试验。预计这项工作最终可能会帮助护理人员为他们的病人找到新的治疗方法，最大限度地减少机器人系统的设计时间，为那些患有成瘾症的人提供新的工具，并为提高教育环境或体育技能提供一个框架。第一个推力铸造个人作为一个动力系统，并探讨应用动力系统识别技术的实验框架。第二个重点是应用在线学习和自适应控制工具将实验设计框架为最优控制问题，随着时间的推移设计干预计划以最大限度地提高结果。第三个重点是研究教育者、教练、治疗师和护理人员如何利用他们与前客户的经验来快速适应新客户的特殊需求。该奖项反映了NSF的法定使命，并通过使用基金会的智力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 experiments are arguably the most important contribution of twentieth-century statistics, providing a program to establish the value of interventions to populations of individuals. By randomly assigning individuals to treatment and control, statistical analysis can determine the magnitude of intervention effects and eliminate confounding explanations. However, randomized experiments yield conclusions about only populations, not individuals. When treatments have heterogeneous effects, a randomized experiment cannot inform an individual whether a treatment can work for them personally. In contrast, N-of-1 trials attempt to solve this problem by having a single individual apply random treatments in different time windows. If the effect is immediate and transient, standard tools from randomized experiments can be used to estimate the magnitude and significance of the effect. Yet, N-of-1 trials remain highly limited as there currently exists no general framework to understand effects that accumulate over long time periods or interventions that have a complex interaction with the individual. This project aims to devise a methodology of experiments for individuals, using ideas from engineering systems to build a sophisticated framework for understanding such complex N-of-1 experimental trials. It is anticipated that the work may eventually help caregivers find new treatments for their patients, minimize design time in robotic systems, provide new tools for those who suffer from addiction, and provide a framework for improving skills in educational settings or athletics.The work consists of three main thrusts. The first thrust casts the individual as a dynamical system and investigates the application of dynamical system-identification techniques in an experimental framework. The second thrust applies online-learning and adaptive-control tools to frame experiment designs as optimal-control problems, devising intervention plans over time to maximize outcomes. The third thrust studies how educators, coaches, therapists, and caregivers use their experience with former clients to quickly adapt to the specialized needs of new clients. The work conducted will draw on mathematical tools from machine learning, control theory, optimization, and signal processing.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.