The use of block maxima method of extreme value statistics to characterise blood glucose curves

Abstract

In contrast to regular statistics where the focus is on the most typical part of the data and the used metrics are describing that part (usually with the mean or median and variance and interquartile range) where most of the observations came from, there is a branch of statistics which focuses on the extreme events, i.e, the tails of the distributions. These are not simple outliers, like data entry errors, but real part of the data which are far from the central tendency and occur rarely, yet, have relevance and impact. Thus, in many application, they can’t be simply neglected. 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 have 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. This factor limited the use of extreme value statistics in biomedical field where available technology and costs are strong limitations at frequently 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, in particular the block maxima approach could be a possible way to characterize blood glucose curves. In addition to providing a metric for the state of the patient and therefore hopefully the associated risks, it allows the comparison of the performance of artificial pancreas systems. Block maxima method was used to model extreme values of a dataset containing measurements of a single patient with 476 complete days of data acquired with sampling frequency of 15 minutes. 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 3.47% and 4.96.10-7% respectively. Through these estimates it is possible to characterise each patient’s status and compare different controllers.