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

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.