CONSTRUCTION OF A REGRESSION MODEL FOR A SMALL SAMPLE OF MULTIDIMENSIONAL DATA ON THE EXAMPLE OF PATIENTS' RECOVERY TIMES FROM COVID-19 - KAMINSKIY, ROMAN; SHAKHOVSKA, NATALIA; DMYTRIV, GALYNA (Herald of Khmelnytskyi National University. Technical sciences, 2025)
Building a mathematical model, in particular, a regression model of the influence of individual indicators of the patient's condition on the recovery period is of utmost importance for making treatment decisions in various situations. This includes the recovery process in the event of a coronavirus infection. The material for analysis and modeling was presented by data on the recovery period of 19 patients with Covid-19 and a description of the physical and medical-physiological indicators of their health at the time of recovery, that is, a small sample of multidimensional data. This medical data was neatly formatted by medical personnel into a 19 × 30 table, in which the first column contains the duration of recovery (hospital stay in bed days), and the remaining columns are filled with data - individual examination results of each of these patients. The results of this study are presented by solutions to the following three problems. The first task concerned the determination of the correspondence of the parameters of a univariate sample of recovery terms to the terms of the general population – generally accepted recovery terms. In the second task, based on the correlation matrix, multicollinearity was eliminated by removing individual indicators. In addition, it was found that the closeness of the relationship between the indicators of medical and biological indicators and the recovery terms is insignificant. The third task consisted in constructing a regression model, the factors of which were the indicators that remained after the elimination of collinearity. The constructed model has a high closeness of connection with the original data, but the coefficients of the model turned out to be insignificant. The reasons for this situation can be considered both the selection of medical and physiological indicators themselves and the discrepancy in the number of signs of the sample size. In general, it can be stated that the presented indicators do not have a significant impact on the duration of recovery.
Keywords: small sample; multivariate data; correlation analysis; regression model; COVID-19