Stochastic Seasonal Models for Glucose Prediction in the Artificial Pancreas

Abstract

Background: Linear empirical dynamic models have been widely used for glucose prediction. The extension of the concept of seasonality, characteristic of other domains, is explored here for the improvement of prediction accuracy. Methods: Twenty time series of 8-hour postprandial periods (PP) for a same 60g-carbohydrate meal were collected from a closed-loop controller validation study. A single concatenated time series was produced representing a collection of data from similar scenarios, resulting in seasonality. Variability in the resulting time series was representative of worst-case intrasubject variability. Following a leave-one-out cross-validation, seasonal and nonseasonal autoregressive integrated moving average models (SARIMA and ARIMA) were built to analyze the effect of seasonality in the model prediction accuracy. Further improvement achieved from the inclusion of insulin infusion rate as exogenous variable was also analyzed. Prediction horizons (PHs) from 30 to 300 min were considered. Results: SARIMA outperformed ARIMA revealing a significant role of seasonality. For a 5-h PH, average MAPE was reduced in 26.62%. Considering individual runs, the improvement ranged from 6.3% to 54.52%. In the best-performing case this reduction amounted to 29.45%. The benefit of seasonality was consistent among different PHs, although lower PHs benefited more, with MAPE reduction over 50% for PHs of 60 and 120 minutes, and over 40% for 180 min. Consideration of insulin infusion rate into the seasonal model further improved performance, with a 61.89% reduction in MAPE for 30-min PH and reductions over 20% for PHs over 180 min. Conclusions: Seasonality improved model accuracy allowing for the extension of the PH significantly.