The use of peak over threshold methods to characterise blood glucose curves

In contrast to regular statistics which focuses on the typical part of the data and use metrics to describe that part (usually the mean or variance), there is a branch of statistics which focuses on the extreme and thus rare events. The use of extreme value statistics allows us to fit models on this part of the data and like ,,regular" statistics, enables us to calculate estimates and predictions, but in this case for extreme values. These methods are frequently used in fields like meteorology and finance where the extreme events has large impact despite their rarity. Because of this rarity, however, only a small fraction of the data can be used so much higher sample size is required for such analysis – thus fields with a large amount of historical data have an advantage.This factor limited the use of extreme value statistics in biomedical field where available technology and costs are strong limitations at measuring most of the biomarkers until recently.Blood glucose level is one of the exceptions nowadays, as with recent advancements it can be monitored for relatively long time and with high frequency for a patient. Additionally, extreme values of blood glucose levels (both high and low) are associated with – chronic or acute – complications of diabetes.This paper aims to demonstrate that the use of extreme value statistics could be a possible way to characterize blood glucose curves. In addition to providing a metric for the state of the patient, it allows the comparison of the performance of artificial pancreas models.Peak over threshold method was used to model extreme values of a simulated dataset containing 1440 measurements of 99 patients with 250 mg/dl as threshold. Probabilities for exceeding the clinically relevant levels of 270 mg/dl (cognitive symptoms expected) and 600 mg/dl (diabetic hyperosmolar syndrome) were calculated and were 23.9% and 8.0 • 10
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% respectively in the region above the threshold (250 mg/dl). Through these estimates it is possible to compare different controllers.