Predictive Modeling using ARX and ARMAX Models for Glycemic Control in Intensive Care Unit Patients

Several studies have been venturing into developing a model for controlling blood glucose among diabetes patients. It is because diabetes mellitus is a severe and common chronic disease affecting almost all populations in many countries. This study collected retrospective clinical data from five patients receiving insulin therapy in the ICU of HUSM. The auto-regressive with exogenous (ARX) and auto-regressive moving average with exogenous (ARMAX) model structure techniques were used to generate a model converter that best describes the glucose and insulin relationship of the subject. The simulation of ARX were started from model order (1,1,1) to model order (5,5,10) while, for ARMAX the simulation was started from model order (1,1,1,1) until model order (5,5,5,10). The three best model orders from ARX and ARMAX models were chosen. The best model fits for ARX and ARMAX were compared to identify the best model order in predicting the glucose-insulin system. The finding indicated that the ARX model recorded the best model fit for all patients in the 5
^th
model order. Meanwhile, the ARMAX model recorded patients with different medical backgrounds and produced a different model order. Besides, the ARMAX model was considered the best option for most of the patients in this study due to the highest model fit, time-delay and lowest percentage of peak error. A more extensive data set may be required to ensure the structure of the model precisely describe the glucose-insulin interaction of the patient.Clinical Relevance– This study establishes a prediction model of the glucose-insulin system that can assist clinicians in providing appropriate insulin value and consequently reduce the incidence of hypoglycemia and hyperglycemia.