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.
Mathematical device of algebraic model of constructive logic has been used for many years for multivariate analysis in medicine and biology. The resulting mathematical model is represented by a set of output components in the form of factors indicating the detection restrictions, which are united by the sign of con-junction (indicating joint influence). Each resulting component is characterized by a capacity, which is the es-sence of the number of rows in the table with the same factors and their intervals of definition. These capacities characterize the degree of influence of the resulting component on the overall result. The input table must not contain contradictions (when the goal is achieved and not achieved when the same values of the factors). For this purpose, the computer program provides for an exception to those target lines, which coincide with non-target rows. However, this is not always acceptable in cases of a large number of matching target lines and unit numbers of non-target rows or vice versa, because a large number of cases is excluded because of a single non-target rows or single target lines. These contradictions arise, primarily, due to the probabilistic nature of the cases. This is clearly seen in the monitoring of mortality. In this article the authors propose three ways optimum yield conflicting source data, based on the excess multiplicity of frequencies matching target and non-target cases and estimates of confidence intervals. The pro-posed methods are examined by analyzing data on deaths of persons aged 18 years and older, residents of the Tula region for 2007-2014 (total 208269 cases). An age cohort 45-54 years is a goal of study. The application of methods of optimum yield conflicting source data is a necessity, which not only im-proves the mathematical model, but, in some cases, is the only way to perform multivariate analysis. All pro-posed methods have their own scope of use, depending on the circumstances.
Multivariate analysis, including algebraic model of constructive logic, is often used in medical practice and biological research. To carry out such studies, it is necessary a array of source information (analyzed cases) and purpose, which is most often selected one of the values of the factors. At the same time, in the practice of analytical calculations there are cases when the target value cannot be set explicitly. The aim of this work is to provide a method of calculating target values for specific cases of morbidity and mortality. The proposed method is based on counting the number of instances of each value of each factor and their share in the total number of cases. The product of the assessed values of each involved factor, compared with the set of the threshold value, determines a value corresponding to the achievement of the goal. To confirm the proposed method on the array of 208269 deaths, the authors built a mathematical model using algebraic model of constructive logic. Evaluation of a mathematical model confirmed the performance of the proposed method of calculating the target value, since the simulation results are most consistent with known estimates obtained by other methods.
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.
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