Using non-stationary extreme value analysis to characterize blood glucose curves

Introduction: The application of extreme value statistics provides a novel way to characterize the risk of high blood glucose levels. Its statistical methodology works well for dependent data, but the impact of non-stationarity is unclear.Material and Methods: 14.7 million blood glucose measurements from 225 patients were analyzed with stationary and nonstationary extreme value models. In case of the latter, the location parameter was allowed to vary with time using spline expansion to allow for a flexible, data-driven functional form.Results: Estimated scale and shape parameters were almost identical (correlation > 0.99) and estimated location was also similar (correlation =0.9). One-year return level and estimated time spent in a year above the clinically relevant threshold of 600 mg/dl was also very similar, and estimated time spent above 400 mg/dl was similar with the exception of a single patient, who had much higher value with the stationary model.Discussion and Conclusion: Non-stationary extreme values models can be applied to analyze blood glucose measurements with the aim of measuring the risk of hyperglycaemia. Obtained results are similar to those with stationary models, but whether it is possible (and if so, to what extent) that the estimated longterm trend in location picks up some effect of true extremity requires further investigation.