Research Projects

Individualized Medical Treatment Optimization for Chronic Diseases


This project involves the development of mathematical models for understanding the progression of biological factors that influence the risk of disease complications such as heart attack, stroke, and kidney failure. We are using massive national data sets based on electronic medical record (EMR) data to create these models for the purpose of studying optimization of drug treatment plans for managing risk factors for disease complications. Since models estimated based on EMR data are subject to unavoidable uncertainty as a result of patient heterogeneity, missing data, and conflicting estimates from different data sources, we are developing new robust optimal control models that can hedge against model uncertainty to make treatment decisions safer.  These types of models are an order of magnitude more difficult to analyze and solve than standard optimization models. To address this challenge we are developing new methods for computing optimal treatment policies to gain insight into the effects of model uncertainty on decision making. This project is in collaboration with investigators in Internal Medicine at University of Michigan and the Department of Health Science Research at Mayo Clinic. This project is supported by grant CMMI 1462060 from the National Science Foundation.

Optimal Design of Biomarker-Based Screening Strategies for Early Detection of Cancer


Recent discoveries of new molecular biomarkers are helping physicians identify early signs of chronic diseases, such as cancer. At the same time, these advances have made clinical decision making difficult because the available tests are not 100% reliable and sometimes cause false positive or false negative results. Since no single biomarker on its own is considered satisfactory, attention is turning to ways to combine biomarkers into composite tests with better predictive characteristics. This project is creating new data-driven optimization models for the design of personalized composite tests and dynamic and adaptive protocols for screening over a patient’s lifetime to optimally balance the competing goals of early disease detection and minimal harm from screening.  These problems are challenging because of their stochastic and combinatorial nature and the partially observable characteristics of early stage chronic diseases. Theoretical properties that provide insight into optimal screening strategies will be analyzed and used to design efficient algorithms and approximation methods for solving these problems using a combination of stochastic optimization and machine learning methods. This work is in collaboration with the Department of Urology at University of Michigan and it is supported by grant CMMI 1536444 from the National Science Foundation.Learn more by watching this YouTube video about the project: Science Nation Video.

Predictive Models for Precision Medicine


The ability to predict a patient’s health status and the potential outcome of medical tests, procedures and protocols, allows clinicians to make more effective decisions at the point of care. Observational data based on electronic medical records provide a valuable source of data that can be used to develop predictive models; however, observational data is  influenced by several sources of bias. This project involves the development of predictive models, primarily in the context of early detection and staging of cancer, that address challenges of verification bias and class imbalance. We are using a combination of statistical methods and optimization methods to address these challenges. My research group is collaborating with researchers in the Michigan Urological Surgery Improvement Collaborative (MUSIC). Watch this video for an example of our work in the context of radiologic imaging for prostate cancer and implementation of our work in the state of Michigan.

Links to Videos Describing Some of My Research Projects:

Statistical Models for Predicting CT and Bone Scan Imaging Outcomes for Prostate Cancer

Optimization Methods for Early Detection of Cancer Using Molecular Biomarkers

Simulation and Optimization of Patient Flow Through Cancer Centers

Research Opportunities: I am looking for PhD students and Postdoctoral Research Fellows to become involved in these research projects. Important prerequisites include an interest in the theory of optimization and stochastic models, advanced programming skills with C/C+ and/or mathematical software tools like CPLEX, Matlab, Python, and R. The work we do has two purposes: 1) To develop new methods for solving data-driven optimization models in healthcare and 2) To use these methods to have an impact on patient care. If you are interested in finding out more please contact me with a copy of your CV ([email protected]). There may also be opportunities for undergraduate and masters students with advanced knowledge of scientific computation and algorithm implementation.