Melnykova Nataliia
Abstract
The article covers the formalization of time-dependent and time-independent data of various origins of the investigated object, which are necessary for personalization of patient’s data in the process of seeking an individual approach to choosing a treatment strategy. This allowed to simulate the warehouse of the state of the object being studied in time, as the Euclidean warehouse. The mathematical model of states` warehouse is constructed, which is a vector-matrix form for the recording of a system of differential equations of the first order. The analysis is made of the application of methods of cluster analysis, Bayesian approach and decision trees for finding personalized decisions about treatment and improvement of the general state of the patient.
Keywords: The Mathematical Model of States` Warehouse; The Formalization of Personalization Data; Big Data Processing
Introduction
The problem of personalization is one of the vectors of the development of many problem areas. This is evident in business, education, consulting and marketing research, and especially in medicine. Personalization is actual by the importance of decision-making by respondents in the process of solving problems, taking into account the individual characteristics of the investigated object. In the health system, all processes of research and determination of a patient’s state require a maximum assessment of the quality of his personalized data as well as the sources of their receipt [1,3,5].
The search for a personalized approach to the treatment of medical information is characterized by a number of problems, namely: uncertainty of the presented data, data classification and data consolidation, determination of the current state of the patient, definition of the strategy of personalized treatment, assessment of the reliability of the decisions, assessment of the emergence of risks. So, for the qualitative processing of medical data and the acquisition of personalized solutions for forecasting the dynamics of changes, it is necessary to consolidate knowledge about the patient using the modern technologies Big Data, Data Science and Mashing Learning [2, 6, 9].
Nowadays, the health care system is slowly integrating personalized medicine into clinical practice [1,4]. The evidence suggests that in some cases, personalized medicine is not actively promoted at the state. A recent public survey showed that only four out of ten consumers know about personalized medicine, and only 11% of patients say their physician discusses or recommends individual treatment options [5, 7]. Following these trends in the clinical adoption of personalized solutions, there are new challenges faced by health care providers when they adapt to new requirements, practices and standards related to this area [2, 8, 10].
Some large medical centres are trying to develop “intelligent” programs that can solve certain problems that arise during the examination and diagnosis of patients, namely: definition diagnose, narrowing the range of diseases in differential diagnosis, determine the minimum set of diagnostic tests (for example, expert systems of installation Diagnoses Internist, BPLab, SpeseLabs Medical, Meditech, A & D, Omron, CardioVita, etc.) [9, 11, 13]
The making of personalized medical decisions for choosing a treatment and choosing a method for diagnosing diseases can be transformed into classification or predictive problems in machine learning. There, the optimal solution for a person is a decision-making rule that gives a better future clinical outcome or maximizes diagnosis and accuracy [16, 17]. However, there are problems with the analysis of complex medical data. On the one hand, statistical simulations are necessary to address their inherent complications, such as lack of data, loss of patient data for follow-up. On the other hand, new data types and larger heterogenic data sizes require innovation that combines statistical simulation, domain knowledge and information technology. The research concerns the assessment of an optimal personalized rule for choosing a treatment, an assessment of the optimal individualized rule for choosing the diagnosis of diseases and the methods for selecting variables in the absence of data [8, 14, 15].
Materials and Methods
Formalization of personalized medical data of a patient based on the analysis of parameters of a state of different origin.
The problem of personalization of the data of the investigated object requires a distinct strategy for determining the main stages of processing information, namely: definition of the most important individual characteristic, processing personalized patient’s data, data consolidation, classification of the general patient’s condition, the presence of the relationship between the values of the most important signs and the classification of patients, definition of personal medical decisions taking into account existing medical protocols of treatment, analysis of the results of treatment, prediction of patient’s states, determination of the patient’s rehabilitation strategy.
The definition of the necessary individual characteristics for solving the problem of personalization depends on the key factors of the identification of the object. The basic parameters are taken account of its general state with its definite characteristics for the formal representation of the investigated object in medicine.
Experts are analysing the patient’s condition during treatment, have recognized that an important indicator of recovery is the positive dynamics of changes in the main indicators of the general state in time, namely: the results of microbiological studies, temperature indices, the analysis of the spread of inflammatory processes, etc. This suggests that time is an important criterion for analysis.
Thus, the separation of time-dependent and time-independent data forms a set of data that is necessary to personalize patient data in the process of seeking an individual approach to choosing a treatment strategy.
Using the theory of functional analysis, time-dependent data can be formalized as a set of At, whose elements are subsets of the parameters of the patient’s individual parameters: :
(1)
where
namely:
(2)
It is possible to form the property of time-dependent indicators of the object under study, at the stage of analysis of the results of studies of the patient’s state. That is, time-dependent data at a certain point in time take constant indicators that, under the influence of the application of personalized decisions on treatment, determine the change in the patient’s state.
Considering that patient data is characterized by heterogeneity, which complicates the process of processing, there is a need for formalizing the patient’s physical state (FS) taking into account time-dependent and time-independent data.
(3)
The time index:
The differential operator of the patient’s physical state
(4)
Based on the patient’s physical state, this measurement will provide the necessary data to identify the treatment anomalies and identify trends. To do this, we aggregate the various parameters that indicate the progress in health of individual patients: the length of stay in a hospital, the dynamics of changes in health state or recovery, the level of recovery of physical activity, return to work, mortality, etc. Taking into account the personalized data of the patient during the process of care of the state, and it values, we can simulate the warehouse of the state of the investigated object in time, as the Euclidean space, where each pair of elements a1,a2, corresponds to the real number (a1,a2 ), that satisfies conditions (axioms of scalar product):
(5)
Construction of the model of the space of states of the investigated object (the patient)
Considering the fact that the state warehouse of the investigate object is represented as the Euclidean space, one can simulate the mathematical model of the state warehouse as a multidimensional system in the time domain. Consequently, the mathematical model of the states warehouse is represented by the state equation, which is the vector-matrix form of the recording of the system of differential equations of the first order, that due to the change of the individual characteristics of the object during the treatment process.
The state equation has the form –
(6)
Where 
– the vector of the dimension of warehouse n, which includes the variables of the object, which uniquely determine its state;
– the vector of control of the dimension m, which displays the signals that influence the system from the outside, based to the proposed solutions to determine the therapeutic scheme of treatment; A, B– the matrices of parameters, which include the parameters of the system, the dimension of which respectively n x n, n x m.
The equation of state and structure completely describes management of the investigate object, the state vector includes the object variables that uniquely describe his state.
Using of the decision making system for finding personalized solutions
Considering the characteristics of Big data of heterogeneous origin (results of hardware and laboratory research and outpatient survey) to provide search, storage and analysis of personalized data, by means of intellectual analysis methods, will allow to determine optimal doctors practical recommendations, to define rules of association between the basic concepts and to identify trends diseases. Optimization of the process of integration and analysis of data of various nature can lead to new knowledge and solutions, the study of new hypotheses, the discovery of hidden patterns. This, in turn, will allow to improve the process of making medical decisions on the definition of personalized treatment schemes [4, 6].
Using new approaches to formalizing consolidated personalized patient data, as a model of states warehouse of patient, and applying cluster analysis methods, Bayesian approach and decision trees, will allow to offer individual treatment decisions and improve the general state of the patient [2].
The requirement for a balanced decision tree is reduced, when designing a decision-making support system that focuses on finding and rendering the necessary information according to the user’s request.
Results
The application of methods for processing medical data has shown that one of the effective methods for evaluating and processing medical information is the goal tree method, which is aimed at obtaining a complete and relatively stable structure of goals, problems, functions, directions. This is, such a structure that will change little during a certain a period of time with inevitable changes occurring in any system that is being improved. The results of the analysis of the applying the intellectual analysis methods of personalized data are shown in Fig. 1
Fig.1. The results of the analysis of the applying the intellectual analysis methods of personalized data
Conclusion
The availability of effective storage, access and modification of information about the state of the object (patient), as well as association with the actual flow data about the investigated situational problem, will allow to develop the structure of medical data. To do this, we need to define the structure of personalized data. To solve such a class of problems, we need to formalize the process of identifying a patient’s condition by constructing a model of the space of its states.
Thus, the purpose of the article is to construct a model of consolidated personalized medical data of the patient based on the analysis of various types of its parameters, as well as to construct a model of the space of the patient’s states taking his individual characteristics during the treatment process.
References
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