The research objective of this project is to develop new mathematical models and solution methodologies to study the design of optimal treatment plans for type 2 diabetes. The research will begin by investigating models for the management of cardiovascular risk using common drug treatment options such as cholesterol and blood pressure lowering medication. Algorithmic methods will be developed for computing optimal and approximate (near optimal) treatment guidelines in the presence of uncertainty about a patient's future health status. The models will consider multiple perspectives including a patient's quality adjusted lifespan, the costs of treatment, and the cost of diabetes related complications to the health system.
According to the American Diabetes Association, there are more than 20 million children and adults in the United States who have diabetes. Of the affected population, approximately 90 percent have type 2 diabetes. Currently, several risk models exist to predict the probability of complications related to type 2 diabetes, including cardiovascular complications such as heart attack and stroke; however, there has been limited investigation of how to use these models to make optimal treatment decisions. This project seeks to bridge this gap by furthering the basic knowledge of how to optimally treat type 2 diabetes over the course of a patient's lifetime. It is anticipated that discoveries from this research project will be transferrable to the treatment of other diseases.
This National Science Foundation sponsored project had three major goals. The first goal was to create new models for helping physicians decide on the optimal time to initiate preventive treatment for patients with type 2 diabetes. The second goal was to develop new algorithmic methods for solving these models and to develop insights into which medications to use and how best to prioritize treatment of various risk factors for diabetes complications including blood sugar, blood pressure, and cholesterol. The third and final goal was the dissemination of knowledge about new methodology and optimal treatment decisions for diabetes, through journal publications, course offerings at engineering and medical centers, undergraduate and graduate student involvement in research, student internships, and the development of teaching materials for high school mathematics students. The multi-disciplinary project team that carried out this work was comprised of researchers with expertise in engineering, medicine, and health services research. To achieve our first goal, we developed mathematical models for optimal control of drug treatment decisions for patients with type 2 diabetes. The models simulate the natural progression of diabetes over a patient's lifetime from diagnosis to end of life. Progression was defined by changes in a patient’s blood sugar, blood pressure, cholesterol, or health status defined by complications of diabetes such as heart attack, stroke, kidney failure, or blindness. Preventive treatment to mitigate the risk of these complications included the most commonly used medications for lowering blood sugar, blood pressure, and cholesterol. The models also included functions that defined treatment performance measures, including quality adjusted lifespan and lifetime cost of medical treatment. To achieve our second goal, we designed and tested varying algorithmic approaches to find optimal treatment strategies that are personalized to individual patient risk factors. We performed computational testing to measure and compare the performance of the algorithms. We further analyzed the models to develop a theoretical understanding of the factors that most influence the decisions to initiate medications, how these decisions change over time as patients age, and how adherence improving interventions can best be used over a patient’s lifetime to help avoid complications of diabetes. We used several data sources including a large data set of observations for patients followed for over a decade to estimate model parameters to perform our numerical experiments. Our results provide evidence that coordination of treatment decisions for cholesterol and blood pressure control has the potential to significantly increase quality adjusted lifespan and reduce total cost to the health system compared to published treatment guidelines which treat risk factors as independent. We also found that the best decisions are highly dependent on the side effects of medications, and thus an individual patient’s preferences should play a role in treatment decision making. Our efforts to achieve the third goal of the project resulted in a number of important outcomes. First, several stochastic models for the natural progression of diabetes have been developed as part of this project. These models provide a valuable test bed for future research. Second, several new algorithmic approaches have been developed as part of this project which may be useful for treatment problems in the context of other diseases and other decision making contexts. Third, our analysis has contributed important insights into medical decision making in the context of drug treatment decisions. Results of our research have been communicated to the medical community through scientific presentations and numerous journal publications in the fields of engineering and medicine. This project has made a contribution the development of human resources in the Science, Technology, Engineering, and Mathematics (STEM) field in several ways. First, two PhD students were part of the project team and completed theses based on research stemming from this project. Both have graduated and taken positions related to health systems engineering research. Second, undergraduate students periodically worked as members of the research team to gain experience in conducting research. Finally, research related to this project has been integrated into a high school mathematics textbook developed for an NSF sponsored project called MINDSET. The textbook contains a chapter on stochastic models which includes examples motivated by this project.
