Investigating artificial neural networks versus regression models in predicting MI mortality based on climatic elements in Sanandaj
برومند صلاحی
1
(استاد آب و هواشناسی،گروه جغرافیای طبیعی، دانشکده علوم اجتماعی، دانشگاه محقق اردبیلی)
سید اسعد حسینی
2
(University of Mohaghegh Ardabili, Ardabil, Iran)
Kaweh Mohammadpour
3
(University of Kharazmi, Tehran, Iran)
کلید واژه: Climatic Parameters, Myocardial Infarction, Sanandaj City, Regression Model, ANNs,
چکیده مقاله :
To analyze the relationship between mortality due to Myocardial Infarction (MI) with climatic parameters and its prediction, the ability of artificial neural network models, and linear and nonlinear regression in Sanandaj was evaluated. The dependent variable is the total number of MI mortality. 54 months out of 60 in the sample period (2014-2018) were dedicated to training the ANNs model and, the remaining six months were given to test the ANNs model. By a selection of the monthly average temperature, a monthly average of maximum and minimum temperature, the average of the maximum and minimum air pressure measured at earth surface, the total number of sunny hours, and the number of days that their temperature is equal to or less than zero as input, a three-layer perceptron accompanied the didactic Levenberg-Marquardt algorithm and a hidden layer which contained 13 neurons and movable function of sigmoid tangent had the best possible output (the number of MI mortality). The results showed that in the relationship between the monthly MI mortality with the climatic parameters of Sanandaj, The relative error for multiple linear and nonlinear regression models is 22.3% and 22.1%, respectively, while for the ANNs model, it is 2.6%. The results also showed that according to the model error, using ANNs model as a nonlinear method in predicting and diagnosing the relationship between climatic parameters and mortality due to MI in Sanandaj could be considered an efficient and powerful tool in comparison with regression models.
چکیده انگلیسی :
To analyze the relationship between mortality due to Myocardial Infarction (MI) with climatic parameters and its prediction, the ability of artificial neural network models, and linear and nonlinear regression in Sanandaj was evaluated. The dependent variable is the total number of MI mortality. 54 months out of 60 in the sample period (2014-2018) were dedicated to training the ANNs model and, the remaining six months were given to test the ANNs model. By a selection of the monthly average temperature, a monthly average of maximum and minimum temperature, the average of the maximum and minimum air pressure measured at earth surface, the total number of sunny hours, and the number of days that their temperature is equal to or less than zero as input, a three-layer perceptron accompanied the didactic Levenberg-Marquardt algorithm and a hidden layer which contained 13 neurons and movable function of sigmoid tangent had the best possible output (the number of MI mortality). The results showed that in the relationship between the monthly MI mortality with the climatic parameters of Sanandaj, The relative error for multiple linear and nonlinear regression models is 22.3% and 22.1%, respectively, while for the ANNs model, it is 2.6%. The results also showed that according to the model error, using ANNs model as a nonlinear method in predicting and diagnosing the relationship between climatic parameters and mortality due to MI in Sanandaj could be considered an efficient and powerful tool in comparison with regression models.
Investigating artificial neural networks versus regression models in predicting MI mortality based on climatic elements in Sanandaj
Abstract
To analyze the relationship between mortality due to Myocardial Infarction (MI) with climatic parameters and its prediction, the ability of artificial neural network models, and linear and nonlinear regression in Sanandaj was evaluated. The climatic data used in this study include different elements related to statistics from 2014 to 2018. Its output the dependent variable is the total number of MI mortality. 54 months out of 60 in the sample period (2014-2018) were dedicated to training the network ANNs model and, the remaining six months were given to test the network ANNs model. By a selection of the monthly average temperature, a monthly average of maximum and minimum temperature, the average of the maximum and minimum air pressure measured at earth surface at the station surface, the total number of sunny hours, and the number of days that their temperature is equal to or less than zero as input, a three-layer perceptron accompanied the didactic Levenberg-Marquardt algorithm and a hidden layer which contained 13 neurons and movable function of sigmoid tangent had the best possible output (the number of MI mortality). The artificial neural network model is an efficient model in predicting the relationship between climatic elements and mortality rate due to Myocardial Infarction. The results showed that in the relationship between the monthly MI mortality with the climatic parameters of Sanandaj, The relative error for multiple linear and nonlinear regression models is 22.3% and 22.1%, respectively, while for the ANNs model, it is 2.6%. The results also showed that according to the model error, using ANNs model as a nonlinear method in predicting and diagnosing the relationship between climatic parameters and mortality due to MI in Sanandaj could be considered an efficient and powerful tool in comparison with regression models.
Keywords: Climatic Parameters, Myocardial Infarction; Sanandaj City, Regression Model, ANNs. Artificial Neural Network, Modelling.
Introduction
Humans are affected by environmental climatic factors climate of the environment in any situation, and climatic variables affect many diseases and aspects of human health. In recent decades, much research has been done on the effect of climatic parameters on human mortality. Heart disease often occurs in people exposed to severe air pressure, extreme heat, or extreme cold. Cardiovascular disease will be a significant cause of death by 2030 (Rashidi et al. 2011). On a global scale, mortality rates associated with heat waves, high temperatures, high concentrations of air pollutants, and stressful climatic conditions have been investigated under future climate change scenarios.
Mortality due to acute myocardial infarction was associated with the occurrence of low temperatures in Brazil (Ferreira et al. 2019) and Taiwan (Li et al. 2021), and North China (Zhao and Cheng, 2019). Mortality due to cold temperature is high among the elderly in the urban area of Lisbon (Portugal) in winter (Rodrigues et al. 2021). The relationship between cardiovascular disease mortality and myocardial infarction with air temperature was investigated in China (Yang et al. 2017) and in Augsburg, Germany (Chen et al. 2019). The Research showed that there is a significant good relationship between diseases, especially cardiovascular disease mortality and myocardial infarction with air temperature (Braga et al. 2002; Vaneckova et al. 2008; Wolf et al. 2009; Esmaeili-Nadimi et al. 2014; Claeys et al. 2017; Saeidi et al. 2018; Dadbakhsh et al. 2018; Sharif Nia et al. 2021).
The prediction of mortality based on climatic variables is generally based on regression models. Regression models and time series are among the commonly used older models in this field. Therefore, there is a need to implement the new modeling approaches replace the old models. One of these models is artificial neural networks, whose main attraction is to development create a relationship between input and output data without considering a physical relationship. In this regard, the use of artificial neural networks (ANNs), especially in simulating the changes of climatic elements through general circulation models at the regional scale, has flourished. The ANNs model is a suitable model with high capacity widely used in predicting climate variables and can extract the law governing data (Dehghani and Ahmadi, 2009). The importance of artificial neural networks is that they can examine the processes that depend on different parameters and with different degrees of importance and then provide a convincing answer. Although nonlinear relationships between variables can be modeled by various regression models, the nature of these relationships is such that these models cannot analyze such relationships well. Artificial neural networks as a model for detecting nonparametric and nonlinear trends can find complex nonlinear relationships with hidden layers between dependent and independent variables and act more accurately than regression methods (Farajzadeh and Darand 2010).
Neural networks are suitable methods for prognosticating patients with heart failure and improving performance (Hearn et al. 2018). The ANNs model is effective in predicting asthma patients in Sanandaj City, Iran (Khorshiddoust et al. 2020). An ANNs algorithm was developed and validated for predicting heart failure mortality in Sweden (Mohammad et al. 2022). Hassanvand et al. (2022) used the artificial neural network model to investigate and evaluate the temperature of Aleshtar Al-Shatar city. Some Researchers also investigated the relationship between climatic variables with disease incidence and mortality and used ANNs and regression models for prediction of them and showed that ANNs model performs well in predicting acute MI (Itchhaporia et al. 1996; Eftekhar et al. 2005; Eggers et al. 2007; Lampen et al. 2011; Atkov et al. 2012; Wilbert- Madrigano et al. 2014; Kojuri et al. 2015; Gligorijević et al. 2017; Fahimi Nezhad et al. 2019; Vaičiulis et al. 2021; Marien et al. 2022).
There are different methods of predicting MI mortality, each of which has specific advantages and disadvantages. In previous studies, multiple linear and non-linear regression models were used in the diagnosis of diseases, which did not have acceptable accuracy and efficiency. The results of studies show that the ANNs model can be effective in predicting the mortality rate due to MI. In Sanandaj, mortality due to heart attack can be related to some climatic elements like many other diseases; therefore, in this paper, the efficiency possibility of using ANNs and analyzing their performance in comparison with multiple linear and nonlinear regression models to predict the mortality rate due to MI about climatic parameters in Sanandaj will be examined.
Data and research method
In this research, meteorological data statistics of the Sanandaj synoptic station have been used (Table 1). First, information about the mortality rate due to heart attacks in Sanandaj was collected. The data included various monthly parameters related to the statistical years 2014 to 2018 (Data for 2019-2022 were not available). After preparing the information, the data were analyzed. First, the parameters affecting the mortality due to MI were determined, and then the relevant matrix was prepared to enter the artificial neural network model. Variables such as mean monthly temperature, mean minimum and maximum monthly temperature, average monthly minimum and maximum station air pressure (QFE), total hours of sunshine, and several days with minimum temperature, equal to or below zero, and the output of the models is the total number of monthly deaths due to MI in Sanandaj city (Khorshiddoust et al. 2020). In this process, out of the 60 months of the current statistical period (2014-2018), 54 months were used for training, and the remaining six months were used in the model test phase. Then, the data were entered into the ANNs model and were also entered into multiple linear and nonlinear regression models to evaluate the performance of the models in predicting the rate of mortality due to MI. The steps of designing and implementing artificial neural networks have been done in MATLAB software programming environment. SPSS, and Excel software have been used to design graphs and regression models.
Table 1. Characteristics of the synoptic station under study
Period | Lon (E) | Lat (N) | Altitude (m) | Station type |
2014-2018 | 47 00 | 20 35 | 1373.4 | Synoptic |
Study area
The city of Sanandaj, the capital of Kurdistan province with an area of 3688.6 hectares, is located in the west of Iran and the mountainous region of Zagros and has a cold and semi-arid climate. The altitude of this city varies from 1450 to 1538 meters above sea level. The city has mild summers and cold winters (Figure 1).
Fig. 1 Geographical location of Sanandaj City
Artificial Neural Network model
ANNs are one of the most successful data mining techniques that can predict nonlinear relationships between phenomena through linkage models inspired by human brain behavior and in recent times, ANNs have become a useful model for pattern recognition and prediction in many fields (Farajzadeh and Darand 2010; Abiodun et al. 2018). These networks are constructed by simple imitating of the biological nervous system and have a high degree of flexibility and correct-ability in adapting to existing data. Artificial neural networks can be equipped to be organized and find the order and coordination within this data and, based on a series of evidence, predict the occurrence and magnitude of a phenomenon. The typical structure of an ANNs usually consists of 4 layers (Figure 2).
Fig. 2 The typical structure of an ANNs (Holmgren et al. 2019)
In terms of network type, artificial neural networks are also divided into two groups: feedforward and feedback neural networks. In this paper, due to the generalizability of the results, feedforward networks and multilayer perceptron structure (MLP) were used. The most important advantage of the artificial neural network over other methods is the ability of the network to learn from its environment (Khorshiddoust et al. 2020).
Multiple linear and nonlinear regression model
Simple regression and correlation coefficients are not very valid in cases where the function variables are affected by several other variables (Rezaei et al. 1998). Multiple regression can be used to measure the correlation of an independent variable (mortality due to MI) with several dependent variables (air temperature, air pressure, sunshine hours, etc.). Unlike linear regression, which is limited to linear models, in nonlinear regression, models with arbitrary criteria between independent and dependent variables can be established. Due to the excessive variety of nonlinear models, there is no specific formula for estimating the parameters, so it is done using numerical methods. Due to a large number of nonlinear models, it is impossible to estimate the parameters of all models with analytical methods. However, with the help of numerical methods and complex algorithms, this is possible (Ismailian 2006). In this study, the data were entered into regression models as they were entered into the artificial neural network model. Thus, the inputs of the ANNs model mentioned were considered dependent variables, and the network output was considered an independent variable (Khorshiddoust et al. 2020)..
Evaluating the performance of models
To evaluate the performance of estimation and forecasting models, there are various performance indicators in this study, coefficient of determination (R2), root means squared error (RMSE), mean absolute error (MAE), relative error (RE), mean squared error (MSE) and correlation coefficient (R) has been used (Sedaghatkerdar and Fattahi, 2008; Sedaghatkerdar and Fattahi, 2008; Karamooz et al. 2006; Khalili et al. 2007).
a. Coefficient of determination (R2):
This is a dimensionless coefficient, and its best value is one. Equation 1 shows how to calculate it (Sedaghatkerdar and Fattahi, 2008):
(1)
b. Root mean squared error (RMSE) and mean absolute error (MAE):
These indicators indicate the model error rate. The best value of them is zero, and they are calculated through the following equations 2 & 3. (Sedaghatkerdar and Fattahi, 2008):
(2)
(3)
In the above relations, XK is the observational value, YK is the estimated value, and K is the number of data.
c. Relative error (RE) and mean square error (MSE):
To calculate these indicators, the following equations 4 & 5 are used, which can change from zero to infinity (Karamooz et al. 2006):
(4)
(5)
In the above relation, Obsi and Fori are the observed and predicted values of MI mortality, and n is the total number of observational data, respectively.
d. Correlation coefficient (R):
This coefficient expresses the degree of correlation between the predicted results of the model and the actual data, which is calculated based on Equation 6.
(6)
is the actual value, 
is the average of the actual values, 
is the predicted value, and 
is the mean of the predicted value. The closer it is to one, the closer the predicted values are to the actual values (Khalili et al. 2007).
The annual distribution of deaths due to MI in Sanandaj by age and sex are presented in Figures 3 and 4 during the statistical period. The highest and lowest frequency of MI belonged to 954 men and 760 women, respectively. The highest rate of MI occurred in the age group of 60 years and above (1369 people). Of the total number of MI, the highest rate occurred in 2017 (386 people), with men having the highest rate with 199 people compared to women (187 people). Regarding distribution of MI among age groups, ages over 60 years with a frequency of 316 people had the highest deaths. In terms of sex distribution, in the age group over 60 years, the mortality rate of women is 162 more than men (154). The lowest annual death rate due to heart attacks is related to 2018. The mortality rate in terms of sex distribution in 2018 shows that mortality is higher for men than women (133 vs. 120). The mortality rate in the age group of 20 and under 20 years is zero, and no deaths due to MI have occurred at these ages.
Fig. 3 The rate of MI mortality in terms of total mortality and gender
Fig. 4 The rate of MI mortality in concern with age (2014-2018)
The monthly average of climatic variables used in this study in the statistical period under study is summarized in Table (2). Accordingly, the average monthly temperature of the studied period in The Sanandaj synoptic station is equal to 14.4 degrees Celsius and the average minimum and maximum monthly temperatures are equal to 6.3 and 22.5 degrees Celsius, respectively.
Table 2. The Mean Monthly climatic variables in Sanandaj synoptic station in (2014-2018)
The Mean temperature (c) | The mean of maximum temperature (c) | The mean of minimum temperature (c) | The mean of QFE minimum pressure (hPa) | The mean of QFE maximum pressure (hPa) | The Mean sunshine (hours) | N. of days with a temperature equal to or less than zero (n) | Mean of mortality (n) |
14.7 | 22.5 | 6.4 | 864 | 865.7 | 262 | 10 | 29 |
According to studies, the average minimum monthly temperature had the most effect on the rate of MI. The time series trend of the mean monthly minimum temperature and the total number of monthly deaths due to MI is presented in Figure (5). As can be seen, by decreasing the minimum temperature, the mortality rate due to MI has increased. However, this trend is untrue in all statistical years studied, especially in late 2018. In the cold months of the year, the number of people vulnerable to a heart attack in Sanandaj is higher, and after each severe cold, the rate of heart attack has increased. In addition to temperature, the rate of MI is related to other climatic variables such as air pressure, the number of days with a minimum temperature and below zero, and sunny hours.
Fig. 5 Time series of the monthly mean minimum temperature of Sanandaj in relation to MI (2014-2018)
In connection with the monthly changes of temperature parameters (average, minimum, maximum) with the rate of mortality due to MI (Figure 6), it can be said that with the decrease and increase of air temperature, the mortality rate has increased and decreased, respectively. In a general trend, the increase in mortality due to MI is associated with low air temperatures.
Fig. 6 Monthly changes of temperature parameters with the rate of MI mortality (2014-2018)
In the artificial neural network method, the results showed that by selecting the parameters of mean monthly temperature, mean minimum temperature and mean maximum monthly temperature, mean minimum and maximum air pressure (QFE), totals hours of sunshine, and number of days with a minimum temperature equal to and below zero as input, a three-layer perceptron model with a latent layer and 13 neurons and a tangent sigmoid movable function in the latent layer and the Levenberg–Marquardt algorithm (LM) training algorithm, the best possible output (monthly number of mortality due to MI) and the network, in this case, gives the best possible result. The structure of the model designed schematically in Figure (7), along with its optimal training parameters to predict the number of MI about climatic variables in Sanandaj, is given in Table (3), and this model is proposed to predict the number of MI about the climatic variables of Sanandaj in future research.
Fig. 7 The structure of the model designed schematically (MLP) for the relationship between MI and climatic elements in Sanandaj
Table 3. Optimal training parameters used in the neural network for the relationship between MI and climatic elements in Sanandaj
3-layer perceptron | Type of network |
13 | The number of neurons in the hidden layer |
Tansig | The movable function of hidden layers |
Pureline | The movable function of the output layer |
1000 | Number of repetitions |
0.005 | Performance Target |
0.90 | Correlation coefficient |
2.62 | Mean relative percentage error |
LM | Learning Algorithm |
The data were entered into multiple linear and nonlinear regression models just as they were entered into the ANNs. The results of predicting all three models are shown in Figure (8). In Figure (8), the actual and predicted number of MI are compared using ANNs models and multiple linear and nonlinear regression. As can be seen, the data predicted using artificial neural networks are almost identical to the actual data, so it is relatively difficult to distinguish it from the actual data which shows the significant superiority of the ANNs model designed over multiple linear and nonlinear regression models in predicting the mortality rate due to MI in the Sanandaj. The designed artificial neural network could predict the number of MI with actual data with an error of 2 people per month so that the correlation between the predicted and actual data in this model reached 0.99, which is significant with the actual data at the level of 0.01.
Fig. 8 Comparison of predicted and observed rates of MI mortality due to climatic factors
Multiple linear and nonlinear regression models with correlations of 0.05 and 0.07, respectively, were placed after the artificial neural network model (Table 4) so that the maximum difference between their predictions and actual data was 12 and 10 people per month, respectively, which is a huge difference. It can be said that multiple linear and nonlinear regression models cannot predict the number of MI in Sanandaj and are in no way comparable to ANNs. The results of the performance evaluation of each model with different evaluation indicators are presented in Table (4), and their error comparison is shown in Figure (9). As can be seen, the values of root mean squared error, mean squared error, mean absolute error, and relative error, in the ANNs model, have less error, and correlation and determination coefficient are higher than in the two models of linear and nonlinear multiple regression which indicates the high accuracy of ANNs in predicting MI mortality.
Fig. 9 Error comparison and performance evaluation of linear, nonlinear multiple regression and ANNs model with different evaluation indicators in Sanandaj
Table 4. Results of analysis models performance using different evaluation criteria in Sanandaj
| R | R2 | MAE | MSE | RMSE | RE |
Artificial Neural Networks | 0.99 | 0.99 | 1 | 1.3 | 0.7 | 3.6 |
Linear regression | 0.05 | 0.003 | 8.7 | 85.8 | 42.9 | 22.3 |
Nonlinear regression | 0.07 | 0.005 | 8 | 75.5 | 37.8 | 22.1 |
Conclusion
The results showed that according to the model error, using ANNs model as a nonlinear method in predicting and diagnosing the relationship between climatic parameters and mortality due to MI in Sanandaj could be considered an efficient and powerful tool in comparison with regression models. The results also showed that in the artificial neural network model, by selecting the appropriate inputs and determining its different structures and according to the nature of the variable under study, it is possible to design different models that are most effective. The results show that there is a nonlinear relationship between the monthly MI mortality with the climatic parameters of Sanandaj, which can be measured only by ANNs and linear regression models, and linear and nonlinear regression models are not efficient in this field and are not able to detect this relationship. This finding is consistent with the study of Khorshiddoust et al. 2020. The relative error for multiple linear and nonlinear regression models is 22.3% and 22.1%, respectively, while for the ANNs model, it is 2.6%. The ANNs can more accurately diagnose and identify the correlation between climatic variables and MI mortality and its prediction in Sanandaj and have a remarkable ability in this field. In the end, it should be said that various variables play a role in the occurrence of Myocardial Infarction (MI) mortality, which can be mentioned as economic, social, psychological, physiological, geographical, etc. variables. Among the geographical factors, climatic elements play an essential role in the occurrence of Myocardial Infarction (MI) mortality, which is discussed in this article. It is expected that in future research, in addition to climatic elements, researchers will consider other variables that are effective in the occurrence of Myocardial Infarction (MI) mortality.
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