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ИНФОРМАТИКА, ВЫЧИСЛИТЕЛЬНАЯ
ТЕХНИКА И УПРАВЛЕНИЕ INFORMATION TECHNOLOGY, COMPUTER SCIENCE, AND MANAGEMENT
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Original article
UDC 004.11.6
https://doi.org/10.23947/2687-1653-2022-22-4-373-383
Determinants in Predicting Life Expectancy Using Machine Learning
Brou Kouame Amos, Ivan Smirnov
Peoples' Friendship University of Russia (RUDN), 6, Miklikho-Maklaya St., Moscow, Russian Federation И broukouameamos9@gmail.com
Abstract
Introduction. Life expectancy is, by definition, the average number of years a person can expect to live from birth to death. It is therefore the best indicator for assessing the health of human beings, but also a comprehensive index for assessing the level of economic development, education and health systems. From our extensive research, we have found that most existing studies contain qualitative analyses of one or a few factors. There is a lack of quantitative analyses of multiple factors, which leads to a situation where the predominant factor influencing life expectancy cannot be identified with precision. However, with the existence of various conditions and complications witnessed in society today, several factors need to be taken into consideration to predict life expectancy. Therefore, various machine learning models have been developed to predict life expectancy. The aim of this article is to identify the factors that determine life expectancy.
Materials and Methods. Our research uses the Pearson correlation coefficient to assess correlations between indicators, and we use multiple linear regression models, Ridge regression, and Lasso regression to measure the impact of each indicator on life expectancy. For model selection, the Akaike information criterion, the coefficient of variation and the mean square error were used. R2 and the mean square error were used.
Results. Based on these criteria, multiple linear regression was selected for the development of the life expectancy prediction model, as this model obtained the smallest Akaike information criterion of 6109.07, an adjusted coefficient of 85 % and an RMSE of 3.85.
Conclusion and Discussion. At the end of our study, we concluded that the variables that best explain life expectancy are adult mortality, infant mortality, percentage of expenditure, measles, under-five mortality, polio, total expenditure, diphtheria, HIV/AIDS, GDP, longevity of 1.19 years, resource composition, and schooling. The results of this analysis can be used by the World Health Organization and the health sectors to improve society.
Keywords: life expectancy, machine learning, machine learning models.
Acknowledgments. This paper has been supported by the RUDN University Strategic Academic Leadership Program.
For citation. Brou Kouame Amos, I. Smirnov. Determinants in Predicting Life Expectancy Using Machine Learning. Advanced Engineering Research, 2022, vol. 22, no. 4, pp. 373-383. https://doi.org/10.23947/2687-1653-2022-22-4-373-383
Научная статья
Детерминирующие факторы в прогнозировании ожидаемой продолжительности жизни с помощью машинного обучения
Бру Куамэ Амос, И. Смирнов
Российский университет дружбы народов (РУДН), Российская Федерация, г. Москва, ул. Миклухо-Маклая, 6 И broukouameamos9@gmail.com
Аннотация
Введение. Ожидаемая продолжительность жизни — это, по определению, среднее количество лет, которое человек может прожить от рождения до смерти. Таким образом, это лучший индикатор для оценки здоровья
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людей, а также комплексный индекс для оценки уровня экономического развития, систем образования и здравоохранения. В результате нашего обширного исследования мы обнаружили, что большинство существующих исследований содержат качественный анализ одного или нескольких факторов. Отсутствует количественный анализ множества факторов, что приводит к ситуации, когда невозможно точно определить преобладающий фактор, влияющий на продолжительность жизни. Однако при наличии различных состояний и осложнений, наблюдаемых сегодня в обществе, необходимо учитывать несколько факторов для прогнозирования ожидаемой продолжительности жизни. Поэтому были разработаны различные модели машинного обучения для прогнозирования продолжительности жизни.
Целью данной статьи является выявление факторов, определяющих продолжительность жизни. Материалы и методы. В нашем исследовании используется коэффициент корреляции Пирсона для оценки корреляций между показателями, и мы используем несколько моделей линейной регрессии, регрессию Риджа и регрессию Лассо для измерения влияния каждого показателя на ожидаемую продолжительность жизни. Для выбора модели использовали информационный критерий Акаике, коэффициент вариации и среднеквадратичную ошибку. Использовались R2 и среднеквадратическая ошибка.
Результаты исследования. На основании этих критериев для разработки модели прогнозирования ожидаемой продолжительности жизни была выбрана множественная линейная регрессия, поскольку эта модель получила наименьший информационный критерий Акаике 6109,07, скорректированный коэффициент 85 % и среднеквадратичное отклонение 3,85.
Обсуждение и заключения. В конце нашего исследования мы пришли к выводу, что переменными, которые лучше всего объясняют ожидаемую продолжительность жизни, являются взрослая смертность, младенческая смертность, процент расходов, корь, смертность детей в возрасте до пяти лет, полиомиелит, общие расходы, дифтерия, ВИЧ/СПИД, ВВП, продолжительность жизни 1,19 года, состав ресурсов и обучение. Результаты этого анализа могут быть использованы Всемирной организацией здравоохранения и секторами здравоохранения для улучшения общества.
Ключевые слова: ожидаемая продолжительность жизни, машинное обучение, модели машинного обучения.
Благодарности. Работа выполнена при поддержке Программы стратегического академического лидерства РУДН.
Для цитирования. Бру Куамэ Амос, И. Смирнов. Детерминирующие факторы в прогнозировании ожидаемой продолжительности жизни с помощью машинного обучения. Advanced Engineering Research. — 2022. — Т. 22, № 4. — С. 373-383. https://doi.org/10.23947/2687-1653-2022-22-4-373-383
Introduction
Human life expectancy can be understood as a statistic used in demography to estimate the average age at which people in a given region and at a given time can be expected to live under current conditions [1]. Life expectancy is not only a statistical indicator of human health, but also a means of assessing the degree of economic, educational, health [2] and environmental development. It should be noted that the World Health Organization (WHO) considers life expectancy to be a key, if not the most important, indicator of health, reflecting the instruments of human existence [3-6]. In the majority of the world countries, life expectancy has in fact increased. Global life expectancy increased from 67.2 years in 2005 to 70.8 years in 20151. The United Nations and individual national governments now have the optimization of human life expectancy, health and well-being as their main objective [7-8]. The UN has been a strong promoter of human health by providing sanitary remedies, which ^ greatly improves the urban environment and helps developing countries2. In the African region of the World Health "S Organization, life expectancy is 61.2 years, while in the European region, it is 77.5 years, giving a ratio of 1.3 between ,o the two regions [9]. Analysis of the disparities in life expectancy between developed and developing countries will -k enable the United Nations to improve its health promotion and humanitarian assistance activities. It will also tn enable governments of different nations to establish more effective policies to increase life expectancy and
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ve improve living standards. States would be able to significantly increase the life expectancy of their population by investing more in the health care system [7]. According to [10], the increase in life expectancy in the United States as a function of per capita income is substantially related to the increase in income level. According to some researchers, the relevant factors affecting life expectancy are mainly environmental, social and economic factors. These vary according to location and involve economic development, medical and health requirements. Existing research has
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1 United Nations Statistical Yearbook, 2017 edition. United Nations, New York; 2017.
2 United Nations Economic and Development website: https://www.un.org/chinese/esa/health.htm (accessed: 9 February, 2021)
given rise to debates about the factor that determines life expectancy. In [11], the author analysed life expectancy in Tibet, China, and found the main factors determining life expectancy. The author in [12], thought that social economy played an important role in determining life expectancy in the early stages of development. However, it was replaced by diet and lifestyle when economic development reached a certain level. The article [13] considered that the determining factor in the evolution of life expectancy in Eastern Europe was lifestyle.
In the end, several studies have identified numerous factors influencing life expectancy. However, few studies compared economic development with environmental factors to analyse the intensity of their impact on life expectancy. Several studies are trying to find out the determining factor of life expectancy. It must be said that there are several. Epidemiological studies in developed countries reveal large differences in life expectancy that are often highly complex. A current study in the United States suggests that 10 to 38 % of the differences in life expectancy can be explained by work-related stress. Life expectancy depends on many factors such as economic status, regional changes in education, gender disparities, physical and mental illnesses, alcohol consumption, GDP, health care spending, and many other demographic factors. Life expectancy has actually increased during the 20th and 21st centuries in industrialized countries [14-20]. The improvement in life expectancy in Europe is followed by a population growth in the over-50 age group. There were 179 million people aged 50 or over in all EU Member States in 2008, and 195 million in 2014, with women accounting for about 55 % of the total [21-24].
According to some sources, the level of economic development has a significant effect on life expectancy. Indeed, studies have shown that people who are financially well off and those from wealthy families tend to have a higher life expectancy [25, 26]. For some researchers, other economic development variables such as GDP per capita [27, 28], urbanisation rate [29] and level may affect life expectancy to different degrees. Some studies show that environmental factors are determinants of life expectancy [29]. Indeed, according to [29, 30], most environmental factors, such as ecological resilience and environmental sustainability, are positively correlated with life expectancy, while some factors, including biodiversity, are negatively correlated with life expectancy. In [31], current environmental conditions influence the life expectancy of the population at birth, while cumulative changes in circumstances continue to influence the remaining life expectancy of the population at different ages over time. J. O. Anderson in [32] thought that people living in an environment with high levels of particulate pollutants over a long period of time had higher cardiovascular morbidity, and that there was some degree of dose dependence. Other researchers have studied the impact of different environmental variables on life expectancy. A. Wuffle [33] compared the average temperature of all US states. The results showed that the lower the average temperature in November, the ^ higher the life expectancy of the population in those states [34-36]. E
Therefore, through machine learning, we will determine the factors that influence life expectancy. Machine § learning (ML) can be understood as a discipline that lies at the intersection of mathematics, statistics and computer science. Machine learning has played an important role in the development of artificial intelligence (AI). Thus, artificial intelligence, through machine learning, helps companies to prevent problems and increase profits. In the field of health, s machine learning is still surprising researchers. It is now the most widely used tool for prediction and forecasting. « Machine learning, which represents a cutting-edge technology due to its predictive accuracy in several problems, E is widely used to increase life expectancy by reducing the mortality rate [17]. Indeed, given that several elements ^ impact on life expectancy, the multiple regression model is of paramount importance and corresponds to the g exploration of the specific relationship and level of impact between several factors and life expectancy. ^
This paper uses multiple linear regression models and Pearson's correlation coefficient to examine the relationship between several variables on life expectancy and provide more help for future research on both sides. These models are s also used as a basis for suggestions to states for improving life expectancy in order to achieve a development of human g
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Materials and Methods
The World Health Organization (WHO) Global Health Observatory (GHO) data repository tracks health status and « many other related factors for all countries. The datasets are made available to the public for analysis of health data. ^
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Data on life expectancy and health factors for 193 countries were collected on the same WHO website and the corresponding economic data were collected on the UN website. From all categories of health-related factors, only the ^ most representative critical factors were selected. It has been observed that in the last 15 years, the health sector has ^ undergone enormous development, resulting in improved human mortality rates, especially in developing countries, compared to the last 30 years. Therefore, in this project, we considered data from the year 2000 to 2015 for 193 countries for further analysis. The individual data files were merged into a single dataset. Initial visual inspection of the data revealed some missing values. As the datasets were from WHO, we did not find any obvious errors.
Our dataset had missing data, and the missing data were for population, hepatitis B and GDP. Imputation of missing 375 data using the *mice* function in the R package of the same name.
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Each variable is associated with an imputation model, conditional on the other variables in the data set: if we have Xk variables, the missing data for the variable Xt will be replaced by the predictions of a model created from the other variables.
The final file is composed of 22 attributes, the target variable "life expectancy" and various other social factors, such as total expenditure on life, population, education and health factors, such as BMI, measles, etc. These data are available on Kaggle [18]. All predictors were then divided into several broad categories: vaccination-related factors, mortality factors, economic factors, and social factors.
Data mining
The objective of this section is to gain a better understanding of the data by extracting information from the data. We mainly want to determine the relationship between the variables.
The correlation matrix, visualized using a heat map (as shown in Figure 1), is one of the best ways to understand the correlation between variables. It is plotted using the R library "Reshape2" and shows us the strength of the linear relationships between the variables. The linear relationship between the outcome and the characteristics can be estimated by a correlation matrix. In multivariate analysis, it plays an important role, as it elaborates the relationship between the different components [19]. Looking at Figure 1, we can see that:
the target variable Life expectancy is strongly correlated (positively or negatively) with:
- Adult mortality (-0.70);
- HIV/AIDS (-0.56);
- Composition of income resources (0.72);
- Schooling (0.75).
There is also a very low correlation between the target variable Life Expectancy and Population (-0.02) or no correlation at all.
The child deaths variable is extremely positively correlated with deaths under five years of age (1.00).
The GDP variable and the percentage of expenditure are positively correlated (0.90).
The Hepatitis B variable is moderately positively correlated with Polio and Diphtheria (0.49) and (0.61).
The variables diphtheria and polio are strongly positively correlated (0.67).
The HIV/AIDS variable is negatively correlated with resource composition (-0.25).
The thinness variable 10 ... 19 years is very strongly positively correlated with the thinness variable 5 ... 9 years (0.94).
The variable Schooling and the income composition of resources are very strongly correlated (0.8).
MATRIX OF CORRELATION
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0.10 0.46 -0.30 -0.11 0.35 № 0.08 -0.08 0.30 -0.11 0.21 0.14 0.20 -0.14
0 02 -0.02 -0 01 ■0.04 -0.03 -0.12 0.27 -0.07 ^ -0.04 -0.08 -0.03 -0.03 -0.03
■0 05 | 0.30 0,7 4.43 4.25 •0.12 022 Q 0,/ ■0.22 -0.28 -0.23 020 4.29 025
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Fig. 1. Visualisation of the correlation matrix by heat map (figure by authors)
By examining the correlation coefficients in Figure 1, we detect potential predictors of life expectancy. For each numerical variable that is potentially predictive of life expectancy, we will run a simple linear regression between it and the life expectancy variable, display the Pearson correlation coefficient and its P
y = ax + b. y is the dependent variable and x is the independent variable. a and b are the model parameters (a is the slope of the fitted line and b is the intercept).
From the result of this exploratory analysis on our data, we concluded that adult mortality, HIV/AIDS, BMI, income composition, and education are the most important factors in predicting life expectancy. This selection was made on the basis of the Pearson correlation coefficient and p-value (as shown in Figures 2, 3, 4, 5, 6).
- The correlation between the variable infant mortality, GDP, alcohol, percentage of expenditure, hepatitis B, measles, under-five deaths, polio, total expenditure, diphtheria, population, age 1-19, age 5-9, and life expectancy is statistically significant as their p-values are less than 0.001, but the linear relationship between these variables is weak with a Pearson correlation coefficient of less than 0.5. Under these conditions, the variables child deaths, GDP, alcohol, percentage of expenditure, hepatitis B, measles, under-five deaths, polio, total expenditure, diphtheria, population, leanness 1-19 years, leanness 5-9 years, cannot be considered as a predictor of life expectancy.
- There is a strong negative correlation between the variables Adult Mortality and Life Expectancy with a Pearson correlation coefficient of -0.7 and statistically significant since the p-value is less than 0.001. In other words, as adult mortality increases, life expectancy decreases. Under these conditions, the adult mortality variable can be considered a predictor of life expectancy.
- There is a negative correlation between the variables HIV/AIDS and life expectancy with a Pearson correlation coefficient of -0.56 and statistically significant since the p-value is less than 0.001. As the number of people affected by HIV/AIDS increases, life expectancy decreases. Under these conditions, the HIV/AIDS variable can be considered a predictor of life expectancy.
- There is a positive correlation between the BMI and life expectancy variables with a Pearson correlation coefficient of 0.56 and statistical significance since the p-value is less than 0.001. Under these conditions, the BMI variable can be considered a predictor of life expectancy.
- There is a strong positive correlation between the variables Income composition of resources and life expectancy
with the Pearson correlation coefficient of 0.69 and statistically significant as the p-value is less than 0.001. The graph
shows that as the composition of income increases, life expectancy increases. Under these conditions, the variable
Income composition of resources can be considered as a predictor of life expectancy. m
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- There is a strong positive correlation between the variables Education and Life Expectancy with a Pearson m correlation coefficient of 0.72 and statistically significant as the p-value is less than 0.001. The graph shows that the g higher the education, the higher the life expectancy. Under these conditions, the education variable can be considered a
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Pearson's coefficient of correlation is -0.56 with P value 7.670715201361051e-238
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Fig. 2. Correlation between life expectancy and HIV/AIDS variable (figure by authors)
Pearson's coefficient of correlation is -0.7 with P value 0.0
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Fig. 3. Correlation between life expectancy and the adult mortality variable (figure by authors)
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Fig. 5. Correlation between life expectancy and the BMI variable (figure by authors)
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Fig. 6. Correlation between life expectancy and the education variable (figure by authors)
Based on the results of the Pearson correlation, we detect the variables that have an influence on life expectancy. However, the Pearson correlation is not sufficient to determine the predictors of life expectancy. For this purpose, we will run several regression models to select the one with the smallest AIC, the highest fit, and the smallest mean square error, R2 and the smallest root mean square error (RMSE).
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Methodology
In order to determine the variables that predict life expectancy, different regression models are used, namely, multiple linear regression, rigid regression and lasso regression. We will then examine the criteria for selecting (p - 1) explanatory variables from the k available explanatory variables. These criteria are: Mallows' Cp criterion, the coefficient of determination, R2 The Bayesian information criterion (BIC), the Akaike information criterion (AIC).
Multiple linear regression
Multiple linear regression is an immediate generalization of simple linear regression. In multiple linear regression, the function F that we want to estimate no longer depends on a single variable, but on several. If we have n pairs of the
form (Xi = (XjA, xi2, ........, xi/m) eRm, yt eRm), with yi the result obtained for the observation 'Xi = (x^, xi2, ........,
xi,m), then the function we wish to estimate will be of the general form below :
F (Xi = (xw, xit2,........, xitm) = a1xi>1 + a^ + ...+ amXi?m + o^. (1)
The objective is to estimate the vector A = a1, a2 , ..., am, a0 so that the function F is as close as possible to yt .
As with simple linear regression, the least squares method can be used to find the vector A, and the function to be minimized will be defined as follows:
E = Zi=1[yt - F ^ ........, xi,m)]2. (2)
One of the most difficult aspects of abundant regression algorithms is to determine how to converge to the configurations (a1t a2 , ..., am, a0) that yield errors £ = yt - yt and avoid the trap of over-learning.
The best-known approach to minimizing the error calculation function E while avoiding over-learning is the introduction of the concept of regularization.
There are two regularizations widely used with regression models: the Lasso regularization and the Ridge regularization.
Lasso and Ridge regression
Lasso regression is a regression model in which the selection and regulation of variables take place simultaneously. This method uses a penalty that affects the value of the regression coefficients. With Lasso regularization, the error function to be minimized becomes:
Elusso = I,?=1[yi - F (xU1, xi:2,........, xUm)]2 + Kn=0 I at|. (3)
The difference between E and Ehasso is that in Ehasso we have added the term 1Zi=o I ^tl2 to further sanction solutions with values of (a1t a2 , ..., am, a0).
Ridge regression is a regularised regression algorithm that performs an L2 regularisation by adding an L2 penalty, which is equal to the square of the magnitude of the coefficients. With Ridge regularization, large values of (a1t a2 , ..., am, a0) are more protected, and the error function to be minimized becomes:
ERidge = Z?=1[yi - F (xw, xw,........, xt,m)]2 + IZma2. (4)
We note that in both the Lasso and Ridge regularization cases, when the value I is set to 0, then E = Ehasso = Emdge.
Mallows' Cp criterion
Mallows' Cp is a selection criterion between several regression models. It compares the accuracy and bias of the full model with those of models containing a subset of predictors. Mallows' Cp criterion is defined from the following formula:
Cp = '-IT - (n -2p). (5)
But the problem is that we can no longer estimate S2 by s2 = ^^ because Cp would always be equal to p and then it
would no longer be interesting [9]. So, in practice, we estimate S2 by the s2 of the model that involves all k explanatory variables of the available model, then we choose among the models the one for which Mallows' Cp criterion is closest to p.
The coefficient of determination R2
The website R2 is the simplest to use. However, with the introduction of new variables, it increases monotonically .ru even if they are weakly correlated with the explained variable. It is therefore advisable to turn to the use of other criteria 3 such as the adjusted fl2adjusted criterion, Mallows' Cp, the AIC and AICc criteria, the BIC criterion. § The adjusted coefficient of determination R2 is the evolved version of the coefficient of determination R2.
The adjusted R2 determines the amount of variance of the dependent variable, which can be explained by the
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The Bayesian information criterion BIC
The Bayesian Information Criterion (BIC) is derived from the Akaike Information Criterion (AIC) and is defined by : BIC = -2 log ( L) + k log (n). It is more parsimonious than the AIC criterion because it penalises the number of variables present in the model more. According to [9], the AIC was introduced to retain the variables relevant to the forecast, whereas the BIC criterion aims at selecting the statistically significant variables in the model.
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The Akaike Information Criterion (AIC)
The Akaike Information Criterion (AIC) is a mathematical method that is applied to models estimated by a maximum likelihood method to assess how well a model fits the data from which it was generated. AIC is applied to analysis of variance, multiple linear regression, logistic regression and Poisson regression. The AIC criterion is defined by :
AIC = 2K - 2Log (L), (6)
where L is the maximised likelihood and k is the number of model parameters. With this criterion, the deviance of the model -2 log ( L) is penalised by two times the number of parameters.
Therefore, the AIC represents a compromise between bias, which decreases with the number of parameters, and parsimony, the desire to describe the data with as few parameters as possible.
The rigour would dictate that all models compared should derive from the same 'complete' model included in the list of models compared.
The best model is the one with the lowest AIC. When the number of parameters k is large compared to the number of observations n, i.e., if N/k < 40, it is recommended to use the corrected AIC. The corrected Akaike information criterion, AICc, is defined by:
AICc = AIC + ^^ (7)
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Results
Our analysis has shown that life expectancy increases over the years, and that it is on average higher in developed countries than in developing countries.
This study has also led us to the conclusion that the model chosen for the selection of life expectancy predictors is multiple linear regression (Table 1), as this model obtained the lowest Akaike information criterion of 6109.07, an adjusted coefficient of 85% and an RMSE of 3.85. R2 of 85 % and an RMSE of 3.85.
These measures were better than those of the Lasso and Ridge regression models. According to this model and following the p-value of less than 2.2e-16, all variables are significant, except for: Alcohol, Hepatitis B, Measles, Population, Slimness.1.19, Slimness.5.9. This means that we can do without these variables to explain life expectancy. However, applying the Akaike information criterion to the multiple linear regression model, the variables that best explain life expectancy are: adult mortality, infant deaths, percentage of expenditure, measles, under-five deaths, polio, total expenditure, diphtheria, HIV/AIDS, GDP, thinness. 1.19 years, income composition, and school enrolment.
Table 1
Models Adjusted R2 RMSE
Multiple Linear Regression 0.85 3.85
Lasso Regression 0.82 3.85
Ridge Regression 0.82 3.91
Conclusion
Before analysing this data set, we had the impression that life expectancy could be increased if we had more money. This is because it takes money to be healthy and to receive appropriate medical treatment. Moreover, if a country is economically developed (GDP), all its citizens can afford appropriate medical treatment. This would mean that life expectancy depends largely on economic factors. However, after analysing this dataset, we have concluded that life expectancy is mainly affected by adult mortality, infant mortality, percentage of expenditure, measles, under-five mortality, polio, total expenditure, diphtheria, HIV/AIDS, GDP, wasting. 1.19 years, income composition, and schooling. This makes sense because if a person is educated enough to recognize health problems, they can make appropriate lifestyle changes, including but not limited to diet and exercise, which would ideally extend their life expectancy. Education can change a person's perception and help them understand the benefits of being fit and its impact on health. In addition, a higher level of education could be linked to a higher income, and a higher income would mean higher spending on health and fitness. Thus, education is directly or indirectly a good predictor of life expectancy. Various machine learning models have been used for training. Among these models, the multiple linear model has proven to be very effective in determining both the coefficient of determination and the errors. This model can therefore be used for the prediction of life expectancy.
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Received 14.09.2022. Revised 17.10.2022. Accepted 18.10.2022.
About the Authors:
Brou Kouame Amos, postgraduate of the Information Technology Department, Peoples' Friendship University of Russia (RUDN) (6, Miklikho-Maklaya St., Moscow, 117198, RF), broukouameamos9@gmail.com
Smirnov, Ivan V., associate professor of the Information Technology Department, Peoples' Friendship University of Russia (RUDN) (6, Miklikho-Maklaya St., Moscow, 117198, RF), Cand.Sci. (Phys.-Math.), associate professor, g
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ORCID, Scopus, smirnov-iv@rudn.ru g
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Claimed contributorship: <p
Brou Kouame Amos: basic concept formulation; research objectives and tasks; data pre-processing; analysis of ty research results. I. V. Smirnov: work control; the text revision; correction of the conclusions.
Conflict of interest statement
The authors do not have any conflict of interest.
All authors have read and approved the final manuscript.
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Бру Куамэ Амос, аспирант кафедры «Информационные технологии» Российского университета дружбы b
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народов (117198, РФ, г. Москва, ул. Миклухо-Маклая, 6), broureino9@gmail.com g
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Смирнов Иван Валентинович, доцент кафедры «Информационные технологии», Российского « университета дружбы народов» (117198, РФ, г. Москва, Миклухо-Маклая, 6), кандидат физико-математических наук, доцент, Scopus, ORCID, smirnov-iv@rudn.ru и
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Заявленный вклад соавторов: ^
К. А. Бру: формирование основной концепции, цели и задачи исследования, предварительная обработка л данных и анализ результатов исследований, подготовка текста, формирование выводов, сбор данных и
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доработка текста. И. В. Смирнов: контроль за работой, доработка текста и корректировка выводов. К
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