Date of Award
Doctor of Philosophy
Derrick K. Rollins
Type 2 diabetes is one of the greatest burdens on the health care industry today. This condition is characterized by poor control of blood glucose concentration (BGC). In order to help those afflicted with type 2 diabetes better control their BGC, the goal of this research is to develop a device that can noninvasively measure BGC. There are several statistical issues that must be addressed before such a device can be developed. The first is to identify inputs that appear to infer BGC and choose a model that can use these inputs to accurately predict BGC. Due to its ability to assign unique dynamics to each input, the Wiener network model is used to predict BGC for each subject. However, there are several challenges to fitting a Wiener network model that can accurately predict BGC, including estimating a large number of parameters, the nonlinearity of the parameters, the stiffness of the least squares objective function for fitting this model, and possible overfitting. Thus an algorithm is designed to fit a Wiener network model where the correlation between predicted and observed BGC is maximized under supervised learning. However, such models were fit with frequent BGC measurements every five minutes. For a non-insulin dependent person, there may only be four BGC measurements per day, which for a week of data or less, implies that there are fewer observations than parameters. Thus, in order to calibrate a noninvasive device, some parameters were held fixed to reduce parameterization, and a novel scheme was devised to estimate the remaining model parameters. Finally, a method of predicting future BGC should be devised that could be used to warn the user if their BGC is going to be too low or too high in the near future. Time series models that use only outputs, such as autoregressive models, to predict BGC into the future performed well in the very near future, but performance degraded quickly as time increased. By utilizing the Wiener network model and previous measurements of BGC, a k-steps ahead prediction model is devised that predicts BGC 5k minutes into the future. This is used to calculate approximate (1-α) 100% forecast intervals for BGC up to one hour into the future.
Beverlin, Lucas, "The Use of Advanced Statistical Concepts and Analysis to Improve Nonlinear Dynamic Glucose Modeling" (2011). Graduate Theses and Dissertations. 10071.