=Paper= {{Paper |id=Vol-3702/paper27 |storemode=property |title=Use of Neural Network-based Models to Predict the Severity of Bronchial Asthma in Children |pdfUrl=https://ceur-ws.org/Vol-3702/paper27.pdf |volume=Vol-3702 |authors=Oleh Pihnastyi,Olha Kozhyna,Iuliia Karpushenko |dblpUrl=https://dblp.org/rec/conf/cmis/PihnastyiKK24 }} ==Use of Neural Network-based Models to Predict the Severity of Bronchial Asthma in Children== https://ceur-ws.org/Vol-3702/paper27.pdf
                         Use of Neural Network-based Models to Predict
                         theSeverity of Bronchial Asthma in Children
                         Oleh Pihnastyi1, Olha Kozhyna2 and Iuliia Karpushenko2
                         1 National Technical University "KhPI", 2 Kyrpychova, Kharkiv, 61002, Ukraine
                         2 Kharkiv National Medical University, 4 Nauky Avenue, Kharkiv, 61022, Ukraine



                                         Abstract
                                         Problem of early diagnosis of bronchial asthma in children is due to the heterogeneity of the disease. The
                                         time of onset of the first symptoms of the disease, their severity, and the possibility of controlling
                                         exacerbations are determined by the interrelation of a factors numerous. The aim of the study is to
                                         develop a method for predicting the severity of bronchial asthma based on the factors numerous for
                                         prediction. A clinical and paraclinical examination of 70 children with a diagnosis of bronchial asthma at
                                         the age from 6 to 18 years was carried out. 142 factors were analysed and the degree of interrelationship
                                         between them was determined. A model for predicting the degree of severity of bronchial asthma in
                                         children, the foundation of which is a neural network, is presented. A multilayer perceptron with an
                                         architecture containing one and two hidden layers was used to build the model. A comparative analysis
                                         of prediction results for models using neural network architecture with different number of nodes in
                                         hidden layers was performed. MSE (Mean Squared Error) values were calculated for training and test
                                         data set for architecture variants with different number of nodes in hidden layers. Comparative
                                         characteristics for models used for prediction of linear regression equation and models based on neural
                                         networks are presented. Quantitative results for predicting the severity class of the course of bronchial
                                         asthma are given. The results indicate the effectiveness of using neural network based models to predict
                                         outcomes that depend on a large number of factors.


                                         Keywords
                                         Correlation, perceptron, neural network, bronchial asthma, child 1


                         1. Introduction
                         Bronchial asthma is a noncommunicable disease that affects children. In 2019, the number of asthma
                         patients was 262 million and 455,000 deaths due to this disease were reported [1]. The
                         pathophysiological aspects of bronchial asthma are complex and diverse. Multifactoriality, the lack of
                         reliable monopredictors of development and the peculiarities of the course of bronchial asthma cause
                         the difficulty of diagnosing the disease in children [2]. The study of asthma pathogenesis mechanisms
                         and the development of new effective medical drugs are aimed at determining their prognostic value in
                         achieving control of disease symptoms. The problem of early diagnosis and timely prediction of the
                         course of the disease remains acute.
                             To predict the bronchial asthma development, linear regression models are frequently utilized [3].
                         The work of Yan Zhao et al identified factors (age, parental asthma, early frequent wheezing, allergic
                         rhinitis, eczema, allergic conjunctivitis, obesity and dust mite aeroallergen), and used a logistic
                         regression model to predict asthma in school-age children [4]. Author Amani F. Hamad et al developed
                         a model for predicting the risk of asthma in children using data on comorbid conditions among children
                         and parents [5]. The use of a binary logistic regression model has improved the accuracy of diagnosing
                         asthma in children and adults under 25 years of age in primary care by identifying the most valuable
                         combination of predictors based on clinical assessment [6]. Studying the association between birth
                         weight and asthma in children using univariate and multivariate logistic models identified factors
                         (premature birth, age, sex, race, family poverty, health insurance, smoking, maternal age) that play an
                         important role in the formation of diseases [7].

                         CMIS-2024: Seventh International Workshop on Computer Modeling and Intelligent Systems, May 3, 2024,
                         Zaporizhzhia, Ukraine
                             pihnastyi@gmail.com (O. Pihnastyi); olga.kozhyna.s@gmail.com (O. Kozhyna); yv.karpushenko@knmu.edu.ua
                         (I. Karpushenko)
                             0000-0002-5424-9843 (O. Pihnastyi); 0000-0002-4549-6105 (O. Kozhyna); 0000-0002-2196-8817
                         (I. Karpushenko)
                                    © 2024 Copyright for this paper by its authors.
                                    Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

CEUR
                  ceur-ws.org
Workshop      ISSN 1613-0073
Proceedings
    Regression model relies on a non-invasive forecasting method and an expanded factors number. The
identification of predictors for model development consists of analysing the observed value dependence
on other factors. Because of the heterogeneity of childhood asthma, many predictors are considered:
wheezing after exercise; wheezing causing dyspnoea; cough during exercise; atopic dermatitis and
allergic sensitisation [8]. The use of CHART screening allows symptom-based identification of children
at high risk of developing asthma as early as 3 years of age, developed using predictive models [9, 10].
The difference between models is the absence in the model of quantitative factors characterising the
results of laboratory examinations. Linear regression four factors mode (hospitalisation, eczema,
parental atopy, the positive and negative predictive value of specific Ig E to inhalant allergens) was
studied in [11], which made it possible to increase the predictive value of the model. In [12], a simplified
methodology allowing to construct the observed value dependence on quantitative factors was
considered. When using a one-dimensional and three-dimensional model together instead of a four-
dimensional one, the computational complexity of the process of constructing regression models is
reduced. Another way to reduce the computational complexity is related to the use of approximate
methods for building regression models [13]. The works used the technique of constructing approximate
one- and two-parameter models (TSLP, severe, pillow feather, bronchial asthma in relatives of second
generation, allergic rhinitis, atopic dermatitis, domestic dust) and using their combinations to analyse
the degree of prognosis of the bronchial asthma course in children as a way of replacing multifactorial
linear regression models was proposed.
    To improve the accuracy of prognosis of the bronchial asthma course, models based on neural
networks have been proposed.
    To understand the heterogeneity of the disease and to identify asthma subtypes, cluster analysis was
used based on the definition of four distinguishing features: age of onset, allergic sensitisation, severity
and exacerbations in the previous year [14]. The authors M. Lovrić, I. Banić et al. applied neural
network based models to predict treatment outcomes in children with mild to severe asthma by changes
in asthma control, lung function (SPF1 and MEF50) and FENO values after 6 months of control
medication [15]. A research paper [16] presents machine learning algorithms for asthma phenotype
detection and prediction of clinical outcomes to find heterogeneous relationships between clinical
features and outcomes [16]. In [17] a review of algorithms of machine learning methods for predicting
asthma exacerbation was conducted to identify characteristic features of the disease course. Asthma
prediction on conventional blood biomarkers using an improved classifier (AGEC) with affinity graph
improves the accuracy of asthma prediction compared to five state-of-the-art prediction models [18].
An automatic machine learning model is used to develop a prediction model for severe asthma
exacerbation [19]. The presented model demonstrates the ability to identify children who are not at risk
of exacerbation. Data from retrospective electronic medical records (EMR) of patients were used to
identify asthma signs in children in paediatric hospitals in China. To improve the quality of asthma
diagnosis, models based on machine learning CatBoost, Naive Bayes, support vector machines (SVM)
have been developed and are constantly being improved [20].
    The aim of the study is to develop a method for predicting the severity of the bronchial asthma
course, based on the factors numerous for prediction. The vast majority of studies devoted to prognosis
of bronchial asthma in children are based on linear regression models that contain a small number of
regressors (no more than ten) and one observed parameter. The feature of the study of the bronchial
asthma severity is the dependence of the observed parameter on the factors numerous of regressors,
which have a small correlation coefficient between the observed value and the regressor. The use of
linear models based on a small number of regressors, as well as the lack of regression models for
classifying the severity of bronchial asthma, does not allow obtaining the required accuracy of
prediction results for clinical studies. In this regard, an urgent problem in conducting clinical research
is the construction of nonlinear prediction models containing several dozen regressors in the presence
of the required number of observable factors. The scientific novelty of this work is the construction of
a classification nonlinear model based on a neural network to predict the severity of bronchial asthma,
containing several dozen regressors.


2. Problem statement
90 children aged from 6 to 18 years were involved in the study of the course of bronchial asthma: the
main group is 70 children diagnosed with bronchial asthma; the control group is 20 children. The
average age of children with bronchial asthma was 11 years. For each patient, information on 142 factors
that could be the cause of bronchial asthma was collected, processed and analysed. The study is carried
out in compliance with scientific ethics and biomedical standards [21]. Parents were interviewed about
the patients' symptoms characteristic of bronchial asthma, as well as the patients' medical history. The
survey data were added to the patient's materials. Clinical features of the disease and the results of
laboratory methods of investigation were studied.
   In this study, a prediction model based on a neural network was developed to predict the severity of
the disease course. Selection criteria were introduced to select the m-factors of the model
                                ry xm → max, rxm xv → min,                                        (1)
где ry xm is correlation coefficients between model factors model factor X m and the observed parameter
Y ; rxm xv are correlation coefficients between factors X m and X  :

              (
            1 n
                         )(           )
               X ki − m xk X i − m x
 rx k x v =
            n i =1
                      xk  xv
                                        ,  xk =
                                                   1 n
                                                      (
                                                   n i =1
                                                                   )             1 n
                                                          X k i − m xk 2 , m xk =  X ki , k = 1..K.
                                                                                 n i =1
                                                                                                          (2)


           1 n
                  (       )(
              X ki − m xk Yi − m y)
           n
   ry xk = i =1
                     xk  y
                                      ,    y =
                                                   1 n
                                                     
                                                   n i =1
                                                         (         )           1 n
                                                          Yi − m y 2 , m y =  Yi ,  = 1..Z .
                                                                               n i =1
                                                                                                          (3)

Experimental data of laboratory clinical changes, which were used to calculate correlation coefficients
ry x m , rxm xv are presented in [22]. The numerical characteristics of the selected set of factors in
accordance with the criteria (1) are given in Table 1.

Table 1
Numerical the factors characteristics
   Code     Regressor name                                                           mx , m у          x ,  y
     X1       Atopic dermatitis                                                      0.0562            0.2303
     X2       Bronchial asthma in relatives of second generation                     0.0658            0.2479
     X3       Allergic rhinitis                                                      0.4494            0.4974
     X4       Sheep wool                                                             0.5217            0.6507
     X5       Domestic dust                                                          2.2319            1.1312
    X6        Pillow feather                                                         0.7536            0.8059
    X7        Dog hair                                                               0.5362            0,8090
    X8        Bronchial asthma in father                                             0.0864            0.2810
    X9        Age                                                                   11.0674            3,6220
    X 10      CD25 10*3 cells                                                        0.6937            0.3087
    Y1        SEVERE PERSISTENT                                                      0.0444            0.2082
    Y2        MODERATE PERSISTENT                                                    0.3111            0.4657
    Y3        MILD PERSISTENT                                                        0.3111            0.4562
    Y4        INTERMITTENT                                                           0.3333            0.4740



   The calculated correlation coefficients values between the model factors rx m x v , as well as between
the model factors and the observed value are also ry  x m presented in Table 2.
       Table 2
        Correlation coefficients values rx m x v , ry  x m
                       X1       X2       X3         X4    X5     X6    X7      X8      X9     X 10
         X1               - 0.08        0.08      0.03 0.26      0.6 0.11      0.08    0.03    0.17
         X2           -0.08     -       0.10      0.21 0.25      0.29 0.00    -0.09    0.16   -0.22
         X3            0.08 0.10            -     -0.01 0.27     0.09 -0.19    0.24    0.16   -0.03
         X4           -0.03 0.21        -0.01        - 0.16      0.34 0.20     0.02    0.00   -0.17
         X5            0.26 0.25        0.27      0.16      -    0.19 0.12    -0.05    0.17   -0.07
         X6            0.06 0.29        0.09      0.34 0.19         - 0.11    -0.05    0.04    0.08
         X7            0.11 0.00        -0.19     0.20 0.12      0.11     -   -0.17   -0.02   -0.07
         X8            0.08 0.09         0.24     0.02 -0.05    -0.05 -0.17       -    0.12   -0.05
         X9           -0.03 0.16         0.16     0.00 0.17      0.04 -0.02   -0.12       -   -0.22
         X 10         -0.17 -0.22       -0.03     -0.17 0.07     0.08 -0.07   -0.05   -0.22       -
         Y1            0.23 0.44         0.31      0.31 0.32     0.38 0.20    -0.10    0.18   -0.20
         Y2           -0.12 -0.22        0.23     -0.29 0.01    -0.28 -0.14    0.32   -0.17   -0.28
         Y3            0.02 -0.22       -0.08     -0.05 -0.14   -0.11 0.16    -0.05   -0.01    0.11
         Y4           -0.12 0.44         0.12      0.08 -0,11   -0,18 0,20    -0,05   -0,22   -0,18


    To build a model for predicting the severity of bronchial asthma in children, a multilayer perceptron
consisting of several layers of neurons, each of which is connected with the previous layer (from which
it receives input data) and the subsequent layer (which it, in turn, affects), was used in this study. The
task of classifying the severity of the course of bronchial asthma Y depending on the values of input
factors X m . Softmax activation function was used to form the output parameters. This approach
guarantees that the output nodes take values from 0 to 1, and the sum of all values of the output nodes
is equal to one, which can be associated with the probability of the degree of the bronchial asthma course
Y .

3. Bronchial asthma severity prediction model
Linear models is studied in [23, 24] to predict of the disease course of bronchial asthma:
                                                M
                                Yi = w0 +  wm X mi ,  = 1..Z .                                   (4)
                                                m =1
Overcoming the limitation of a linear model of type (4) is achieved by including a nonlinear
transformation mechanism in the presented model [25]:
                                                       M        
                                    Yi = f  w0 +  wm X mi ,                               (5)
                                                      m =1      
where f (x ) - nonlinear transformation function. When using analytical methods to calculate the
coefficients w0 , wm in the linear regression model (4) and transformed linear regression model (5),
as a rule, for each observed factor is performed independently [26]. On the other hand, the model
coefficients are functions dependent on the values of the regressors X m and the observed parameter Y
:
                    w0 = w0 (Y , X 1 ,..., X M ), wm = wm (Y , X 1 ,..., X M ).             (6)
Increasing the accuracy of predicting the values of the observed parameters is achieved by switching to
numerical methods to calculate the coefficients w0 , wm which depend on all the observed parameters
Y :
              w0 = w0 (Y1 ,...,YZ , X 1 ,..., X M ), wm = wm (Y1 ,...,YZ , X 1 ,..., X M ).   (7)
Thus, the transition from the model consisting of -equations with independent coefficients (5) to the
model represented by the system of -equations is made:
                                                   M            
                                 1i
                                 Y    =   f   w
                                              10 +    w1m X mi ,
                                                  m =1          
                                ........
                                
                                                    M             
                                 i
                                 Y     =   f  0  wm X mi ,
                                              w   +                                            (8)
                                                   m =1           
                                ........
                                
                                                    M             
                                Y Zi = f  wZ 0 +  wZm X mi .
                                                   m =1           
In common, a unique transformation function Yi = f  (x ) can be chosen for each observed quantity
Y . Although the last system of equations contains nonlinear transformation functions for the output
parameter, by introducing the inverse function of the f −1 ( y ) = x for the reciprocal-ambiguous function
 y = f (x) system of equations (8) is transformed into a linear system of equations for the transformed
observables YT relative to input factors X m :
                                      M
                      T 1i
                      Y      = w10  +    w1m X mi ,
                                     m =1
                     ........
                     
                                      M
                     YTi = w0 +  wm X mi ,             YTi = f −1 (Yi ).                  (9)
                                     m =1
                     ........
                     
                     Y = w + M w X ,
                      TZi       Z0     Zm mi
                                     m =1
   As the next step to build non-linear models for calculating the observed parameters Y uses a multi-
layer architecture in which each k level (layer, k = 1..L ) is represented by a separate system of
equations:
                                                                                                                          ML            
                         M                                                                     Y     = f     wY 10 +  wY 1m H Lmi ,
                                                                       M   −                       1 i      Y                          
  H 11i = f 1  w110 +  w11m X mi ,
                                                                          k   1
                                               H k1i = f k  wk10 +  wk1m H (k −1)mi ,                              m =1           
                        m =1                                       m =1                    ........
                         M                                                                   
  H 12i = f 1  w120 +  w12m X mi ,                               M k −1                                                         
                                               H k 2i = f k  wk 20 +  wk 2m H (k −1)mi ,
                                                                                                                            ML
                                     
                        m =1                                        m  =1                    Y  i =  f Y 
                                                                                                                  wY  0 +    wYm H Lmi , (10)
  ........                                                                                                              m =1            
                                             ........                                           ........
                             M                                           M k −1            
   H 1M1i = f 1  w1M1 0 +  w1M1m X mi ,  H kM i = f k  wkM 0 +  wkM m H (k −1)mi , 
                                                                                                Y = f  w +  w H .
                                                                                                                            ML
                           m =1                 k              k              k
                                                                              m =1                  Zi       Y  YZ 0          YZm Lmi 
                                                                                                                         m =1           
     Procedure for calculating the coefficients wkM k 0 , wkM k m , wYZ 0 , wYZm requires a prepared dataset
for training the neural network, in which each row of values of input factors X m corresponds to the
string of values of the observed parameters Y . One way to calculate the coefficients wkM k 0 , wkM k m ,
wYZ 0 , wYZm is the method of error back propagation. The coefficients are calculated by the method of
successive approximation. Stopping of calculations occurs when the accuracy of calculation of the
values of the observed parameters Y reaches the specified accuracy or the number of approximations
has exceeded the maximum permissible specified value. In direct propagation, intermediate values of
variables are sequentially calculated and stored in the computational graph defined by the computational
procedure. The calculation is performed sequentially from the input layer to the output layer. In back
propagation, the gradients of intermediate variables and parameters are sequentially computed and
stored. The computation is performed in reverse order sequentially from output layer to output layer.
   A multilayer perceptron with an architecture containing a single M-M1-Z (L=1) and two M-M1-M2-
Z hidden layers (L=2), where M- number of input factors in the prediction model; Mk – the nodes
number in k hidden layer; Z- the nodes number in the output layer. The architecture of the neural
network is shown in Fig. 1. The values of the neural network nodes are calculated in accordance with
the system of equations (10).




                a) 10-M1-4 (L=1)                                   b) 10- M1-M2-4 (L=2)

Figure 1: Neural network architecture in a model for predicting the severity of the course of bronchial
asthma: (a) one M-M1-Z hidden layer (L=1); (b) two M-M1-M2-Z hidden layers (L=2).

For the hidden layer nodes, let us represent the activation function as a Sigmoid-function
                                                         1
                                        f1 ( x ) =                .                                (11)
                                                   1 + exp( − x )
As the activation function for the last (output) layer, choose Softmax function:
                                                      exp( − x  )
                                     f Y ( x  ) = Z               .
                                                                                                   (12)
                                                      exp( − x )
                                               =1
    This approach normalises the values of the output parameters of the bronchial asthma severity
prediction model, optimises the discrete output spaces and treats these values as the probability of a
patient having a disease corresponding to the bronchial asthma severity classification. The key point is
the application of a probabilistic approach that allows discrete categories to be treated as examples of
samples from a probability distribution. Thus, the use of softmax activation function for the output layer
allowed us to transform the values of the output layer of the neural network into actual discrete
probability distributions of bronchial asthma severity.
    As the method of initialisation of model weights and bias, the normal law distribution of values with
distribution parameters N (0,1). As shown by numerical experiments, the method of initialisation of
weights plays an important role in the construction of the prediction model, allows to accelerate the
convergence of training and improve the quality of the model. When training the neural network in the
prediction model, the following model hyperparameters are set: learning rate is lr = 0.001 , maximum
number of epochs is epochmax = 20000 , the size of the packet used in training is batch = 1 .

4. Аnalysing the results
When building the prediction model, the sample for training the neural network is divided into two sets
of data. The first dataset directly serves for training the neural network and makes up 80%, the second
dataset (test dataset), which makes up 20%, is used to verify the prediction accuracy. The training
process of the neural network with different architectures is shown in Fig. 2. Quantitative indicators
characterising the quality of the neural network training process are presented in Table 3.
                         a) 10-15-4 (L=1)                                  b) 10-25-4 (L=1)




                         c) 10-10-10-4 (L=2)                               d) 10-15-15-4 (L=2)

Figure 2: Neural network training results for different architectures with one hidden layer M-M1-Z
(L=1) and two hidden layers M-M1-M2-Z (L=2); the loss function for the lerning dataset (loss) and the
loss function for the test dataset (test loss) is black line; the prediction accuracy is red line.

Table 3
Learning rates of neural network for different architectures
                           regression      10-15-4      10-25-4            10-10-10-4        10-15-15-4
                             model            (L=1)        (L=1)                 (L=2)             (L=2)
 loss value, MSE              0.0713      5.77e-07     1.06e-07              3.94e-07          0.16e-07
 best test loss value, MSE    0.5051        0.2607       0,2061                0.2674            0.2473
 best test accuracy                         0.4444       0.6677                0.4556            0.5556
 best test epoch value                       11027         2214                 11905              2635

    A test dataset was used to determine the prediction accuracy. The severity of the disease
corresponded to the value of the predicted class having the maximum probability value. Table 3 shows
the comparative analysis of the training results of the neural network with one and two hidden layers
and different number of nodes in the hidden layer. When carrying out the comparative analysis, the
random sequence of numbers used in the initialisation of the neural network weights was a fixed
sequence of numbers. As would be expected, increasing the number of nodes for a neural network with
both one and two hidden layers results in a significant decrease in MSE. Similar behaviour is observed
for the MSE values corresponding to the test dataset. The decrease in MSE values leads to an increase
in the prediction accuracy determined with the test dataset. As a comparison of the prediction quality,
Table 3 presents the MSE value for the prediction model based on the linear regression model [27].
    The coefficients of the linear regression equation for the above model are given in Table 4, for the
calculation of which the same data set was used as for training the neural network. The MSE value for
the test dataset in the neural network based prediction models is half that for the prediction model using
the linear regression equation. Particular attention should be paid to the strong difference in the MSE
values obtained for the training dataset. The latter fact clearly demonstrates the property of the neural
network to approximate the values for the test dataset. It is expected that as the sample size for training
the neural network increases, a similar trend will be observed for the MSE values obtained for the test
dataset of the dataset.

Table 4
Linear regression mode coefficients for the value Severe Persisten [27].

      №                           MSE              X0           X1        X2          X3        X4       X5            X7      X8             X9        X10 X12




                                                   0.1617

                                                                0.1493

                                                                         0.4965

                                                                                      -0.1139

                                                                                                0.3788

                                                                                                         0.0314

                                                                                                                      0.0259

                                                                                                                               0.0775

                                                                                                                                              0.0791

                                                                                                                                                       -0.0029

                                                                                                                                                                  0.0004
      17                56        0.267



         To quantify the quality of prediction of the bronchial asthma course, Table 5 and Table 6
present the prediction values obtained for a model based on a neural network with a 10-15-4
architecture consisting of an input layer with ten nodes (model input factors X m , Table 2),
output layer with four nodes (observed model parameters Y , Table 2) and one hidden layer with
fifteen nodes.

Table 5
Model prediction results for the training dataset
                     initial                                                                                      predict
                                                                                                         PERSISTENT
                                                                                                         MODERATE
           PERSISTENT




                                                                                  PERSISTENT




                                                                                                                                        PERSISTENT
                         MODERATE
                         PERSISTENT


                                      PERSISTENT




                                                                                                                                                                  MITTENT
             SEVERE




                                                        MITTENT



                                                                                    SEVERE




                                                                                                                                                                   INTER
                                                                                                                                           MILD
                                                         INTER
                                         MILD




 N#


 1            0              0           1                  0                        0.0                 0.0289                    0.9415                        0.0294
 2            0              1           0                  0                     0.0024                 0.8718                    0.0604                        0.0653
 3            0              0           0                  1                     0.0011                 0.0471                    0.1133                        0.8385
 4            0              0           0                  1                     0.0002                 0.0113                    0.1042                        0.8843
 5            0              0           1                  0                     0.0068                 0.1163                    0.8384                        0.0387
 6            0              0           1                  0                     0.0008                 0.0004                    0.9615                        0.0373
 7            0              0           1                  0                        0.0                 0.0147                    0.9170                        0.0683
 8            0              0           1                  0                     0.0015                 0.0340                    0.9496                        0.0149
 9            0              0           1                  0                        0.0                 0.0778                    0.9032                        0.0189
 10           0              0           1                  0                        0.0                 0.0035                    0.9513                        0.0452
 11           0              0           1                  0                     0.0031                 0.0023                    0.9743                        0.0203
 12           0              1           0                  0                     0.0003                 0.8380                    0.1061                        0.0556
 13           0              1           0                  0                     0.0006                 0.9466                    0.0042                        0.0486
 14           0              1           0                  0                     0.0004                 0.8859                    0.0223                        0.0915
 15           0              0           0                  1                     0.0137                 0.1030                    0.0455                        0.8378
 16           1              0           0                  0                     0.8815                 0.0375                    0.0329                        0.0480
 17           0              0           1                  0                        0.0                 0.1084                    0.8901                        0.0015
 …            …              …           …                  …                          …                      …                         …                             …
Table 6
Model prediction results for the test dataset
                     initial                                                       predict




                                                                                                              INTERMITTENT
                                                  INTERMITTENT




                                                                              PERSISTENT
                                                                              MODERATE
           PERSISTENT




                                                                 PERSISTENT




                                                                                              PERSISTENT
                        MODERATE
                        PERSISTENT


                                     PERSISTENT
             SEVERE




                                                                   SEVERE




                                                                                                 MILD
                                        MILD
 N#



 1            0           0             0          1             0.0040       0.0012         0.8675        0.1273
 2            0           0             0          1             0.0001       0.0030         0.9824        0.0145
 3            0           1             0          0                0.0       0.7886         0.2009        0.0105
 4            0           0             1          0             0.0002       0.9660         0.0131        0.0208
 5            0           0             0          1             0.0200       0.3471         0.2856        0.3474
 6            0           0             0          1             0.0473       0.1614         0.3864        0.4049
 7            0           0             0          1             0.0089       0.3165         0.0480        0.6265
 8            0           0             0          1             0.2180       0.0613         0.3427        0.3781
 9            0           0             0          1             0.0016       0.0445         0.0721        0.8818

     The accuracy of predicting the severity class of bronchial asthma using the developed model was
determined as follows: for each class corresponding to the severity class, the prediction probability is
calculated based on the Softmax function; the column with the maximum probability value for the
training dataset is determined; the severity class for the resulting column is considered as the prediction
result. The severity class of the disease course for each patient is determined according to the given
value provided in the training dataset. This result is expected, which is explained by the low value of
MSE corresponding to the training dataset. Table 6 gives the quantitative values of predicting of the
bronchial asthma course for the test dataset. The bronchial asthma course severity was correctly
predicted for 70% of the patients from the test dataset. This is an encouraging result compared to studies
based on a linear regression model. To conduct the study, software libraries in Python were used for
data processing and analysis: Pandas (version 2.0.0), Pytorch (version 2.0.0).

5. Conclusion
In this paper, a neural network based model for predicting the severity of the course of bronchial asthma
in children has been reviewed. 142 factors that could be responsible for the occurrence of bronchial
asthma disease were analysed. The training sample is divided into two parts, for training the neural
network and testing the training results, in the proportion of 80/20. The model architecture is represented
by a multilayer perceptron. The dependence of MSE value for training and test data set at different
values of nodes in hidden layers has been analysed. A comparative analysis of MSE values for the model
using linear regression equation for prediction and neural network based models is presented.
     The developed model for predicting the severity of bronchial asthma, the foundation of which is a
neural network, allowed to correctly determine the severity class of the disease for 70% of patients from
the test dataset. For the remaining 30%, the model predicted the result as a neighbouring severity class.
The result of further research is to investigate the dependence of the number of regressors of the model
on the accuracy of the results of predicting the severity class of bronchial asthma. A critical issue for
future research is to identify factors that can identify disease severity based on the results of clinical
blood and urine tests. This will reduce the cost of conducting examinations, which require significant
financial costs and conducting research in clinics with access to specialized and expensive equipment.


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