Investigation of Regression Models of Glycemic Dynamics under Conditions of Measurement Uncertainty

Abstract

In the course of the research, it was analyzed that there are currently many widespread methods of invasive detection of glycemia. However, such methods can lead to infectious diseases. To minimize the risk of infection, research into the non-invasive method of determining glycemia, which can be used for medical purposes, is gaining popularity. The article describes the most common of these methods currently used.The article deals with the statistical substantiation of procedures for identifying the parameters of the glycemic dynamics model in the uncertainty of the measurement results. The heterogeneity of glycemic dynamics is ensured by the factor stimulating insulin secretion by exogenous glucose (glucose loading). The purpose of the article is to substantiate the choice of regression model of change in the level of glycemia with significant restrictions on the volume of primary measurement information, which cause uncertainty of nonlinear changes of the model at normative glucose loads.For the first time, polynomial regression analysis was applied to identify variants of polynomial regression recovery in incomplete measurement experiments for existing methods of type 2 diabetes, as well as models for the identification of diabetic conditions. Implementation of such dependencies can confirm the presence of stochastic relationships between the factors of influence and response of the organism. Three models are identified that should be prioritized in identifying the diabetic condition. It is shown in the paper that the research problems are reduced to the procedure of polynomial regression restoration as a model of glycemic dynamics depending on the number of possible variants. The analysis of the model shows that the main elements that influence the result are the sum of the regressors with a certain coefficient and the sum of the random remainder of the result of the calculation, which satisfies the conditions of interdependence and normality of probability distribution. One basic model, which is most suitable for the problems of recognizing the parametric model of glycemic dynamics in verifying the validity of statistical hypotheses, was also identified. The paper deals with a polynomial model of function by types of parametric uncertainty regarding the functional relationship between the factors of influence and reaction of the organism. The paper presents, as an example, the estimation of polynomial regressions that model the uncertainty of changes in glycemic levels for alternative conditions.