CAREER: Optimization in the Race to a Liquid Biopsy

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This Faculty Early Career Development Program (CAREER) grant will promote the progress of science and advance the national health and welfare by aiding in the development of accurate blood tests for early-stage cancer. Progress to date is due to advances in data collection technology (next-generation DNA sequencing, in particular), and in computational power for analyzing this new data. The critical task remaining is optimizing the design of liquid biopsies to carefully trade off between accuracy and cost. This award supports the development of algorithms designed for these optimization problems, and interdisciplinary work with medical researchers and practitioners to apply these algorithms. The accompanying plan for integrating research with education will aid in the dissemination of this work, and more broadly, interest in the intersection of mathematics and biology, to students, the academic medical community, and private companies.This research grant will study a new family of optimization problems that unifies (a) discrete optimization problems that occur in non-adaptive test design as it is conceived today, (b) online optimization problems supporting different forms of adaptive testing, and (c) the incorporation of important practical constraints unique to liquid biopsies. This family of problems subsumes or extends a number of classic problems including active sequential hypothesis testing, optimal decision trees, submodular function ranking, and decomposable submodular maximization, which are core problems in operations research, statistics, and computer science. The expected outcome of this work is a generic optimization approach with provable approximation guarantees and a linear runtime. Such an approach will be immediately applicable to the design of liquid biopsies, and will be validated with numerical experiments on publicly available data. More broadly, the researched work will contribute to the cross-fertilization of optimization and statistics, spanning active learning, approximation algorithms, and high-dimensional statistics.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.