CAREER: Optimization in the Race to a Liquid Biopsy

这项教师早期职业发展计划(Career)赠款将通过帮助开发针对早期癌症的准确血液测试来促进科学进步，促进国民健康和福利。迄今为止的进展是由于数据收集技术(特别是下一代DNA测序)的进步，以及分析这些新数据的计算能力的进步。剩下的关键任务是优化液体活检的设计，谨慎地在准确性和成本之间进行权衡。该奖项支持为这些优化问题设计的算法的开发，以及与医学研究人员和从业者的跨学科合作，以应用这些算法。随附的研究与教育相结合的计划将有助于向学生、学术医学界和私人公司传播这项工作，以及更广泛地对数学和生物学交叉的兴趣。这项研究拨款将研究一系列新的优化问题，这些问题统一了(A)目前构思的非适应性测试设计中出现的离散优化问题，(B)支持不同形式适应性测试的在线优化问题，以及(C)纳入液体活检特有的重要实践约束。这类问题包含或扩展了许多经典问题，包括主动序列假设检验、最优决策树、子模块函数排序和可分解子模块最大化，这些都是运筹学、统计学和计算机科学中的核心问题。这项工作的预期结果是一种具有可证明的近似保证和线性运行时的通用优化方法。这种方法将立即适用于液体活检的设计，并将通过公开数据的数值实验进行验证。更广泛地说，研究工作将有助于优化和统计学的交叉培养，跨越主动学习、近似算法和高维统计。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.