For many years, algebraic constructive logic model is used for multivariate analysis in medicine and biology. The classic version of this model includes the exclusion of contradictory accounts, i.e. when the target is achieved and not achieved in the presence of the same values of the factors. In this case, the lines as appropriate to achieving target, and its failure are removed, including significant proportions. Another feature of this algorithm is the partial overlap of the intervals to determine the factors resulting in components in achieving a target and not achieving despite the exclusion of contradictory accounts. The authors explain this by the fact that the classical algorithm generates the detection limits of the factors in resulting components with some capture values that are related to the lines of not achieving the target (up to inappropriate values). To some extent this reduces the accuracy of the mathematical model. A further feature of the algorithm is the necessary to optimize mathematical model by excluding re-coating lines. This is acceptable, but not optimal. This requires additional procedures at the final stage of formation of the mathematical model. The proposed version of the algebraic model of constructive logic allows to eliminating the above drawbacks. This is achieved the measure of approximation and a way of combining the cases in the resulting components. The proposed algorithm was tested using specially designed software that allows to exclude controversial cases and to form a mathematical model. Testing showed that the proposed algorithm is better than the classic version and meets the objectives of multivariate analysis in medicine and biology.
Algebraic model of constructive logic is developed in Russia and is used for many years in medicine and biology for multivariate analysis and for building expert systems. In the process of improving the algorithm of the algebraic model of constructive logic and software, the methods of the study of population health with the use of these models are improved. The tasks of providing a compact representation of the mathematical model are solved, the version of algorithms and programs with different reaction to incomplete source data is created, an analytical and methodological support of research is developed. The article presents the results of practical work to improve the working methods of the study of population health. It covers the issues of verification of source data, an obtainment a compact mathematical models, the valuation and completeness of the source data, the main highlight of the resulting components, the exclusion of inconsistencies in the source data, the absorption of the analyzed factors, the principles of the analysis of the factors in mathematical models and principles of construction of expert systems. The authors showed that the classical and modernized versions of the algebraic model of constructive logic have their applications and are not exclusive of each other. This article also provides recommendations and explanations that facilitate the realization of analytical studies using algebraic models of constructive logic.
Mathematical device of algebraic model of constructive logic has been used for many years for multivariate analysis in medicine and biology most often to identify causal relationships. This mathematical apparatus can be used for more complex analysis schemes for the purpose of determining the contingent of patients who require this method of treatment. The proposed method is a two-step analysis using algebraic model of constructive logic with different specified purposes and subsequent analysis of the resulting final components of the mathematical model. As a result, it is possible to identify restrictions and to quantify the number of patients who need to analyzed method of treatment. The proposed method is explained by an analytical study of hyperbaric oxygen therapy in oncological pathology. Analysis of the results revealed 7,87-39,35% of patients requiring hyperbaric oxygen therapy. The authors revealed the restrictions presented resulting final components of the mathematical model in the form of limits of detection of the combined factors. The equity analysis of values of the resulting components of the mathematical model is associated with the need to calculate the maximum possible total power of the resulting components of the mathematical model, used in expert systems.
The article presents the analysis results of 182897 rates of deaths of the adult population in the Tula region since 2007 to 2013, which were obtained by means of software, in the frame of the international project. To ensure high validity of data, the automatic determination of the initial reason to deaths, automatic transposition of the lines of the reasons to deaths for recovering the logical sequence, posthumous diagnostics were used. The Analysis of the age cohorts was carried out based on the graphs constructed for each age cohort schedule with the imposed trend. Mortality monitoring made by Public Health of the Tula region, as well as measures control allowed to reduce the mortality in cohort 45-54 age which resulted in the displacement of the high mortality of this cohort in a cohort of older age 55-64. Little progress in reducing mortality in men compared with women was identified. There is a steady decline in mortality, which requires detailed analysis of the age groups 25-34, 35-44 men and 20-24, 35-44 women and the development of control actions. To further reduce mortality, it is advisable to focus on the age cohort 55-64. Received and verified data is the basis for a detailed analysis by class of diseases.
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