Extreme Value Theory in Medical Sciences: Modeling Total High Cholesterol Levels
The World Health Organization (WHO) estimated that more than 50% of the mortality and disability caused by the ischemic heart disease and stroke could be avoided by implementing simple measures at individual and national levels. Programs targeted to promote the control of the main risk factors for these pathologies, such as hypertension, hypercholesterolemia, smoking, and obesity, should be designed and implemented. In 2005, the Department of Pharmaceutical Care Services of the Portuguese National Association of Pharmacies developed a survey for assessing the cardiovascular risk of the Portuguese population that attended the pharmacies. Several parameters were measured, such as total cholesterol, blood glucose, and triglycerides levels. To the best of our knowledge, the studies performed so far in our country describe the mean behavior of the individuals. However, this approach is unable to address subjects who have very high levels of, for instance, total cholesterol. These individuals are located in the tail of the distribution and are the ones most at risk of developing a cardiovascular disease. An appropriate way to address this problem is to use extreme value theory (EVT). EVT has extensively been applied to model data of many scientific areas but seldom in medical sciences. In this article, we use the peaks over threshold (POT) method to model the sample of excesses above a sufficiently high value of total cholesterol. As usual in EVT applications, the levels of total cholesterol that are to be observed with a small probability are estimated by region.
AMS Subject Classification60G70 92C50
KeywordsCardiovascular diseases Extreme quantile estimation Generalized Pareto distribution Peaks over threshold Total cholesterol levels
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