Chaotic time series prediction for glucose dynamics in type 1 diabetes mellitus using regime-switching models

Abstract

In patients with type 1 diabetes mellitus (T1DM), glucose dynamics are influenced by insulin reactions, diet, lifestyle, etc., and characterized by instability and nonlinearity. With the objective of a dependable decision support system for T1DM self-management, we aim to model glucose dynamics using their nonlinear chaotic properties. A group of patients was monitored via continuous glucose monitoring (CGM) sensors for several days under free-living conditions. We assessed the glycemic variability (GV) and chaotic properties of each time series. Time series were subsequently transformed into the phase-space and individual autoregressive (AR) models were applied to predict glucose values over 30-minute and 60-minute prediction horizons (PH). The logistic smooth transition AR (LSTAR) model provided the best prediction accuracy for patients with high GV. For a PH of 30 minutes, the average values of root mean squared error (RMSE) and mean absolute error (MAE) for the LSTAR model in the case of patients in the hypoglycemia range were 5.83 (± 1.95) mg/dL and 5.18 (± 1.64) mg/dL, respectively. For a PH of 60 minutes, the average values of RMSE and MAE were 7.43 (± 1.87) mg/dL and 6.54 (± 1.6) mg/dL, respectively. Without the burden of measuring exogenous information, nonlinear regime-switching AR models provided fast and accurate results for glucose prediction.