The method of building the hyperplane which separates the convex hulls in the Euclidean space is proposed. The algorithm of prediction of the presence of severity in patients based on this method is developed and applied in practice to predict the presence of severity in patients with acute pancreatitis. 1. Introduction During the last decades, pronounced tendency to the relentless increase in morbidity in acute pancreatitis is observed. Thus, the depth of pathomorphological pancreatic parenchyma lesions can vary from the development of edematous pancreatitis up to pancreatic necrosis. However, accurate predicting of the probable nature of the lesion of the pancreas in the early stages of acute pancreatitis is one of the most difficult problems of modern pancreatology. Diagnostic and the predictive probability of existing laboratory and instrumental diagnostic markers and rating scales does not exceed 70–80% [1–3]. Such situation is a major difficulty in selecting the adequate treatment strategy in the initial stages of acute pancreatitis. Thus the search for new methods of accurate predicting of acute pancreatitis’ severity becomes an urgent problem. Development of mathematical approaches for prediction in medicine was developed by Fisher, the father of the linear discriminant analysis [4]. Currently, there are many approaches to solving this problem: cluster analysis, the construction of predictive tables, image recognition, and linear programming. Fundamentals of building the prognostic tables and Wald serial analysis are described in [5]. Cluster analysis is commonly used for solving the tasks of medical prediction. In the paper [6], the procedure of cluster analysis with a study of the indices of the daily variability of cardiac rhythm in patients with the ischemic disease of heart is examined. In [7] using national data from the Scientific Registry of Transplant Recipients authors compare transplant and wait-list hospitalization rates. They suggest two marginal methods to analyze such clustered recurrent event data; the first model postulates a common baseline event rate, while the second features cluster-specific baseline rates. Results from the proposed models to those based on a frailty model were compared with the various methods compared and contrasted. Three major considerations in designing a cluster analysis are described in [8]. The first relates to selection of the individuals. The second consideration is selection of variables for measurement and the third consideration is how many variables to choose to enter into a cluster analysis.
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