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

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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.