Multidimensional Mathematical-Statistical Modeling of Complex Medical Systems

The dissertation is devoted to the development of the methodology and technology of multidimensional mathematical-statistical modeling of complex medical systems. The work substantiates the application of modern methods of multivariate statistics — correspondence analysis, log-linear analysis, logistic regression, discriminant analysis, classification trees, survival analysis, dynamic time series analysis, and factor analysis — for solving the tasks of optimizing feature grouping, building classification models, forecasting disease outcomes, and studying the mechanisms of biomedical processes. The research covers a wide range of medical objects: severe traumatic brain injury, hepatitis, heroin addiction, alcoholism, ataxias, and epidemic processes.

The work addresses the problem of insufficient use of multidimensional methods in medical research: according to the author, only 12.8% of works at the Military-Medical Academy are based on multidimensional methods of data processing, while 81.8% of works are limited to univariate methods. A universal algorithm for the technological implementation of mathematical-statistical modeling of complex medical objects has been proposed, including stages from creating a general concept to model exploitation, as well as a system of quality criteria for models. The results have been trialed on typical medical objects and implemented in practical healthcare, the educational process, and the scientific work of a number of medical institutions.

Relevance of the Topic. At present, the value and appropriateness of applying mathematical methods in such "non-strict" sciences as biology and medicine are no longer questioned. However, the problem consists in the fact that in most cases the objects of medical research are complex medical systems with numerous elements in their composition and connections between them, determining the internal structure of the system. Such systems (objects, processes) are formed and function under the influence of numerous variable and mutually interacting factors of the environment. The study of such systems is distinguished by the collection of a significant number of primary "raw" data that do not have the form of perfected information and, even less, are either regularities or knowledge. Their analysis (traditional "discussion") is impossible without prior multifaceted processing. One of the directions of such processing is the method of multidimensional mathematical-statistical modeling, which is understood as the transformation of primary empirical data about a complex system into rigorous mathematical-statistical objects, which then appear as models of real or assumed systems. Multidimensional mathematical-statistical modeling implies the application of the method of multivariate statistics to medical material as "raw material," the subject of processing, and its results — mathematical-statistical objects — inevitably acquire the status of medical indicators. They are formed as a result of the interpretation of mathematical-statistical objects from the standpoint of the content of a complex medical system, which constitutes the essence of one of the important stages of modeling medical systems (Bailey N., 1970; Maksimov G.K., Sinitsyn A.N., 1983; Enyukov I.S., 1986; Gubler E.V., 1990; Marchuk G.I., 1991; Dyuk V.A., 1997; Ginkin A.A., 1999; Maksimova T.G., 2000; Klimenko N.B., 2001; Maksimov A.G., Maksimova T.G., Maksimov G.K., 2001; Abdulkerimov Kh.T., 2003; Cattell R.B., 1966; Soh D.R., Oakes D., 1984; Greenacre M.J., 1988; Lim T.S., Loh W.Y., Shih Y.S., 1997).

At present, all grounds exist for the application of methods of multidimensional mathematical-statistical modeling. The theory and practice of adequate coding of medical data have been developed. Modern technical and software tools of informatization provide the possibility of creating electronically readable databases in volumes sufficient for obtaining reliable results. The availability of corresponding applied software packages for mathematical-statistical processing and analysis of data allows the application of multidimensional mathematical methods and procedures by specialists of subject areas who are far from fundamental knowledge of applied mathematics. Multidimensional mathematical-statistical models of complex medical systems created on this basis make it possible to move from intuitive representations of a physician about medical processes and systems to mathematically grounded quantitative analysis and modeling.

However, such a possibility is insufficiently utilized. From the analysis of reports on research work performed at the Military-Medical Academy, as well as materials from candidate and doctoral dissertations submitted to the fundamental library of the academy, it follows that only in 12.8% of works are the conclusions based on multidimensional methods of processing research data adequate to the purpose, tasks, and materials of the research. In 81.8% of works, adequate univariate methods of mathematical-statistical description of research objects and proof of statistical significance of differences in derived quantities (arithmetic mean values and frequencies) and laws of distribution of random variables are used. Despite this, the nature of primary data from most studies provides the possibility of using more substantive and richer in their diversity multidimensional methods of mathematical statistics. Moreover, 5.4% of the studies we examined contain fundamental errors in the application of the mathematical-statistical apparatus that is not adequate to the collected data, and consequently, the conclusions in these cases do not correspond to reality.

Taking the above into account, the object, subject, goal, and tasks of the research have been formulated.

Object of research — typical medical systems of study in selected areas of medicine, characterized by a multitude of individual features of their state, on the one hand, and adequate multidimensional mathematical-statistical methods for their description, on the other.

Subject of research — methodological and technological aspects of multidimensional mathematical-statistical modeling of typical medical systems: determination of mathematical-statistical characteristics and indicators of system properties, their interpretation and analysis, drawing conclusions about the regularities of system behavior.

Goal of research.

Development of a methodology, technology (principles, methods, algorithms), and scientific-practical recommendations for the application of mathematical-statistical methods for modeling complex medical systems.

Tasks of research.

1. Based on the study of historical and methodological questions of the use and application of quantitative methods in biomedical, economic, and other research, to evaluate the range of modern multidimensional mathematical-statistical methods of analysis and modeling and to identify those of them that most adequately describe complex medical systems.

2. To determine the tasks of medical research solved with the help of multidimensional mathematical-statistical methods and the range of practical applications of the results of multidimensional mathematical-statistical modeling of complex medical systems.

3. To substantiate and develop principles and algorithms of mathematical-statistical modeling and analysis of complex medical systems using multidimensional mathematical-statistical methods and software-technical means of informatization for the technological implementation of methods.

4. To propose criteria for the quality of results of mathematical-statistical modeling of complex medical systems.

5. To conduct a trial of technological algorithms for the application of the newest multidimensional methods of mathematical-statistical modeling and analysis of complex medical systems on typical medical objects and systems studied in various areas of medicine.

Scientific novelty of the research.

For the first time, the technology of mathematical-statistical modeling and analysis of complex medical systems has been substantiated and developed using the methods of correspondence analysis, log-linear analysis, logistic regression, discriminant analysis, classification trees, survival analysis, dynamic time series analysis, and factor analysis.

It has been shown that with the help of multidimensional mathematical-statistical methods, the following tasks of scientific inquiry in the field of medicine can be solved:

- optimization of feature grouping and compression of the information space of a phenomenon described by qualitative features;

- clarification of known and identification of new assumptions concerning quantitative and qualitative characteristics of leading clinical symptoms and syndromes in pathological states;

- determination of the set and weight of clinical features that could be used for differential diagnosis of homogeneous or similar in nature pathological processes;

- determination of the quality of the relationship between disease outcomes and various symptoms and syndromes, as well as treatment schemes and standards; determination of the degree of dependence of the duration of life, treatment, rehabilitation, remission on the features determining them;

- revealing the internal factor structure of the studied biomedical process and the mechanisms of its change.

The assertion has been substantiated that the primary indication for the application of methods of multidimensional mathematical-statistical analysis and modeling of medical systems and processes is the adequacy of the model to the studied medical system.

Methods for comparative evaluation of statistical significance and information capacity of mathematical models of medical systems constructed with the help of various mathematical-statistical methods have been developed.

Algorithms for forming the sequence of stages of mathematical-statistical processing and analysis of research data of complex medical objects and constructing their multidimensional models have been proposed.

Criteria for the quality of results of mathematical-statistical modeling of complex medical systems have been proposed.

Practical significance of the research.

The results of the work are used in practical healthcare, in the educational process, and in the scientific work of a number of medical universities and research institutes.

The developed and trialed technology of modeling complex medical systems can be applied in various branches of medicine, including military medicine, to solve the following tasks:

- dimensionality reduction, optimization of grouping, and study of the relationship of categorized features;

- creation of classification models and study of the degree of influence of features included in the model on the quality of classification;

- modeling the probability of an alternative outcome and assessing the influence of dichotomous predictive features on increasing the chance or risk of the predicted outcome;

- studying the dynamic characteristics and modeling the function of an object's stay in the state of interest to the researcher;

- modeling the dynamics of epidemic processes;

- dimensionality reduction of the multidimensional object of research and revealing the mechanisms of the dynamics of its internal structure.

The proposed technology and algorithms for developing mathematical-statistical models of complex medical systems can be used in the creation of automated monitoring, diagnostic, and prognostic systems for the state of complex medical systems, as well as in the development of the theory and practice of evidence-based medicine.

Basic provisions to be defended.

1. The main condition for the wide application of multidimensional methods of mathematical-statistical analysis and modeling of complex medical systems is the availability of the corresponding informatization infrastructure, including the composition, structure, and level of interface of applied software packages for statistical analysis of research results and the development of technical means of informatization.

2. The proposed technology of multidimensional mathematical-statistical analysis and modeling of complex medical systems may include the following methods: correspondence analysis for exploratory analysis, compression of primary information, optimization of groupings of qualitative features, and study of the relationship between them; log-linear, discriminant, and logistic regression analysis for building classification models; the classification trees method as an alternative to other classification methods in case of their low efficiency; survival analysis in modeling time-to-event data, the main features of which are possible data incompleteness and non-conformity of their distribution to the normal law; time series analysis, whose possibilities have been significantly expanded by software and technical means of informatization; factor analysis with the aim of revealing the mechanisms of the dynamics of biomedical phenomena, etc.

3. The developed universal algorithm of the technology of multidimensional mathematical-statistical analysis and modeling of complex medical objects is ensured by solving the following tasks of medical research: creation of a general modeling concept; information-logical modeling at the verbal level; selection of a mathematical-statistical model; model verification; creation of an operational prototype of the model; exploitation of the model. The named procedures are invariant to the goal, tasks of the research, and the nature of data in a specific area of medicine.

4. General criteria for the quality of multidimensional mathematical-statistical models of complex medical systems are: statistical significance of the model — not less than 95%; information or classification capacity of the model — not less than 70%; significance level of predictive features included in the model — not less than 70%; conformity of the distribution of residuals (the difference between observed and predicted values of the studied feature) to the normal law; acceptable level of forecast errors; possibility of application and interpretation of the model by a specialist in the subject area and mass implementation of the model.

Implementation of the Work.

The main results of the research are used in the educational and scientific work of departments and scientific laboratories of the VMA, in the scientific and practical work of the Russian Neurosurgical Institute named after Prof. A.L. Polenov, the Research Institute of Childhood Infections, and the LORNI. They have been implemented in methodological recommendations "Forecasting Early Outcomes of Severe Traumatic Brain Injury" and a number of educational-methodological publications: "Package of Applied Programs STATGRAPHICS on a Personal Computer," "Multivariate Methods of Statistical Analysis of Categorized Data of Medical Research," "Control Tasks on the Application of Computing Technology and Mathematical-Statistical Methods for Analysis of Results of Medical Research," "Application of the Theory of Experimental Planning in Medical Research (including a Personal Computer and the Statistica for Windows Statistical Software Package)," "Mathematical-Statistical Processing of Data of Medical Research." Two priority certificates for inventions have been obtained.

Trial of the Work.

The results of the research were reported at: the Inter-University Conference "Flight Safety and Human Factor," St. Petersburg, 1998; the All-Army Scientific Conference dedicated to the 200th anniversary of the Military-Medical Academy "Problems of Management of the Medical Service in Armed Conflicts and Local Wars," St. Petersburg, 1998; the All-Russian Conference "Medical Informatics on the Threshold of the 21st Century," St. Petersburg, 1999; the All-Russian Conference "Military Science and Education for the City," St. Petersburg, 1999; the Jubilee Scientific-Practical Conference "Naval and Radiation Hygiene: Results, Achievements, and Prospects for Development," St. Petersburg, VMA, 2000; the International Scientific-Practical Conference "Current Problems of Correctional Psychology, Medicine, and Pedagogy," St. Petersburg, 2001; the IV International Symposium "Modern Minimally Invasive Technologies," St. Petersburg, 2001; the Scientific-Practical Conference with International Participation "Prevention and Rehabilitation in Psychology, Medicine, and Pedagogy," St. Petersburg, 2002.