Statistical Methodology and Applications to Engineering, Economics, and Health Analytics

拟议研究的长期目标是发展创新的统计方法，并将其与技术进步相结合，以解决工程、经济和卫生保健方面的基本问题。特别是在过去的七年里，随着2010年医疗改革立法的颁布，以及2015年的精准医疗倡议，美国医疗保健系统迎来了大数据时代。这个时代为数学（包括统计、计算和数据）科学及其与生物医学、工程和经济科学的相互作用带来了新的挑战和新的机遇。该项目将解决其中的一些挑战，其更广泛的影响包括(i)在工程、经济和金融、卫生和医学方面的直接应用，以及（ii）通过让研究生参与研究的各个阶段、开发新的高级课程和修订金融和风险建模、统计和数据科学、临床试验和生物统计学方面的课程，培训学术界、工业界和政府的下一代科学家。该项目大致分为三个领域。首先是在大数据时代发展有效和高效的选择后多重测试，其中通常使用一些机器学习/特征工程/变量选择算法来提取特征/变量，用于后续的假设生成和统计检验。本研究将通过解决有效的后选择推理的基础问题，解决生物医学大数据统计推断的可重复性问题和“复制危机”。初步调查已经开始，考虑了固定规模的样本，并将继续扩展到分组顺序设计，然后对多阶段制造过程、多组件系统和来自金融和生产网络的多个数据流进行顺序检测和诊断。第二个领域是梯度增强的统计基础，由于梯度增强在处理高维非线性和广义线性模型方面的有效性，它在第一个领域也有应用。第三个领域涵盖生物标志物引导的临床试验自适应设计，用于开发和测试个性化疗法，以及密切相关的顺序分析和强化学习中的上下文多臂强盗主题。这一领域的创新可以推动精准医疗计划的发展。还涉及创新的研究设计和对护理点试验和观察性研究的分析，以及开发移动保健平台和可穿戴设备，以改善和促进慢性病的循证管理。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。

A long-term objective of the proposed research is to develop innovative statistical methodologies and combine them with technological advances for resolving fundamental problems in engineering, economics, and health care. In particular, the past seven years have witnessed the beginning of a big data era in the US health care system, following the health care reform legislation enacted in 2010, and the Precision Medicine Initiative of 2015. This era poses new challenges and opens up new opportunities for the mathematical (including statistical, computational, and data) sciences and their interactions with the biomedical, engineering, and economic sciences. The project will address some of these challenges, and its broader impact includes (i) direct applications in engineering, economics and finance, health, and medicine, and (ii) training the next generation of scientists in academia, industry, and government by involving graduate students in all phases of the research and developing new advanced courses and revising the curriculum in financial and risk modeling, statistics and data science, and clinical trials and biostatistics.The project is broadly divided into three areas. The first is the development of valid and efficient post-selection multiple testing in the big data era, in which some machine learning/feature engineering/variable selection algorithms are typically used to extract features/variables for subsequent hypothesis generation and statistical testing. The proposed research will address the reproducibility issues and "replication crisis" with this data-dependent choice of features and hypotheses for statistical inference from biomedical big data by resolving foundational issues concerning valid post-selection inference. Initial investigations have already started by considering samples of fixed size, and will proceed with extensions to group sequential designs and then to sequential detection and diagnosis for multistage manufacturing processes, multicomponent systems, and multiple data streams from financial and production networks. The second area is the statistical foundation of gradient boosting, which also has applications to the first area because of its effectiveness in tackling high-dimensional nonlinear and generalized linear models. The third area covers biomarker-guided adaptive design of clinical trials for the development and testing of personalized therapies and in the closely related subject of contextual multi-armed bandits in sequential analysis and reinforcement learning. Innovations in this area can lead to advances toward the Precision Medicine Initiative. Also covered are innovative study designs and analyses of point-of-care trials and observational studies, and development of mobile health platforms and wearable devices to improve and facilitate evidence-based management of chronic diseases.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.