American Journal of Business Management, Economics and Banking 
ISSN (E): 2832-8078                               Volume 13, | June, 2023                                

 

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USING ARTIFICIAL NEURAL NETWORKS AND MULTIPLE 

LOGISTIC REGRESSION ANALYSIS TO STUDY SOME FACTORS 

RESULTING LEUKEMIA 
Hayder Sami Alwan 

College of Administration and Economics / University of Maysan-Iraq 

haydersami.a87@uomisan.edu.iq 

 

A B S T R A C T K E Y W O R D S 

This study investigated some factors which lead to leukemia using, 

artificial neural networks (ANN) and multiple logistic regression analysis. 

The study also compared between these methods determine which method 

is better. The study included 150 observations and four variables: Chronic 

myeloid leukemia (CML) as a response variable, patient weight, blood 

platelets (PLT), and the bone marrow edema (EME) as explanatory 

variables. The model's goodness of fit was measured using the maximum 

likelihood ratio test, which followed a chi-square distribution. Results 

showed that the relationship between the explanatory variables and 

response variables is significant, indicating the importance of the 

explanatory variables in the model. The logistic regression model 

(LRM)'s parameters were estimated using the maximum likelihood ratio, 

and the neural network method was also used to analyze the data. The 

neural network method achieved a much higher accuracy rate than the 

multiple logistic regression method, with a difference of 20%, indicating 

the superiority of the neural network method over the multiple logistic 

regression method. 

Analysis, artificial 

neural networks, cancer, 

factors,  Leukemia,  

multiple logistic 

regression, Wald , MLE.  

 

Introduction: 

In recent years, there has been an increase in the use of modern statistical methods and applications for 

analyzing classified data, particularly in fields such as medical, agricultural, and social research (Al-

Obeidi, 2013). This study discusses the use of two different statistical methods in analysis: artificial 

neural networks, which are an important product of artificial intelligence and simulate natural 

intelligence, specifically human intelligence. These two methods are known for their ability to interpret 

incomplete or noisy data, handle new types of problems, process data in parallel, and high flexibility 

compared to traditional mathematical methods. Additionally, neural networks have surpassed the 

limitations of traditional solutions because all cells within the network process a huge amount of data 

quickly at the same time (Davalo & Naim, 1991). Logistic regression analysis (LRA), the second 

method, is an important statistical method that deals with analyzing classified data, especially in cases 



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where the response variable is nominal or ordinal and consists of two levels (two classifications) or 

more (Al-Afifi, 2010; Maiprasert & Kitbumrungrat, 2012). The analysis using logistic regression does 

not assume any conditions regarding the distribution of explanatory variables, making it relatively better 

and more robust than many other methods. It is characterized by flexibility and simplicity, as well as 

giving a clear and meaningful interpretation and implications for describing the relationship between 

the response variable and explanatory variables. 

 

Research Objective 

The current research aims is to study some factors which lead to leukemia using a multiple logistic 

regression (MLR) model and an intelligent method represented by artificial neural networks (ANN), 

and to compare between them.  

 

Research Problem 

Regression models in general, and binary and multiple response logistic regression models in particular, 

are characterized by their high ability to model causal relationships between explanatory variables on 

the one hand and the dependent variable on the other hand. However, they suffer from some 

assumptions that, if not met, will lead to misleading results. Therefore, more flexible methods with 

fewer assumptions compared to traditional regression models are used to avoid such problems. 

 

Literature Review 

Artificial neural networks (ANN) 

The relationship between statistics and ANN has received significant and increasing attention from 

researchers and practitioners in both fields in recent years. Many ideas related to ANN are based on the 

fundamentals of statistics, and many statistical methods and techniques can be programmed using 

neural networks and building algorithms for them. The reason for this is due to the great similarity and 

congruence between the methods used in both fields (Jarrah, 2003). The general principle of building 

ANN is to develop a system for information processing to reach the closest point to human efficiency  

(Omar, 1999). Therefore, an ANN is a computer system for information processing, consisting of a very 

large number of interconnected processing elements with a dynamic nature. Its main function is the 

parallel division of network calculations. The neural network consists of a number of interconnected 

and homogeneous processing units, each of which is a computational tool that can model its behavior 

with simple mathematical equations (Rao & Raao, 1993).  Neural networks are named after their 

resemblance to the internal communication systems of biological neurons, as these units are inspired 

by the study of biological neural systems , Figure 1 (Newbold, 1974).  

 
Figure 1. System of artificial neural networks 

 



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1- Components of an artificial neuron  

Zurada (1997) listed the following components: 

1. Synapses: The neuron receives input signals from other connected cells through input channels, 

and these incoming signals are called inputs and are denoted by (xi, i = 1, 2, 3, 4, ..., n). 

2. Summation function: The function of this function is to unify the input signals into one signal. 

3. Activation function: This function aims to propagate the input value according to the type of 

function used according to the scale of the output value limits . 

4. Axon path's: The function of this channel is to send the output signal to other neurons, and it is 

considered an input signal to those cells, and the output signal is called outputs. 

 

1. 2 Types of artificial neural networks 

1-2-1 Feedforward neural networks  

These networks allow information to flow in only one direction, meaning that the data spreads from 

the back to the front (i.e., from the input layer to the output layer) because their structure lacks 

closed loops of connections between the layers (Stergiou & Siganos, 2006).  

1-2-2 Backpropagation neural networks (NNN) 

Backpropagation networks allow information to flow in both directions, and they are complex and 

powerful. They are dynamic networks that continuously change their stability until reaching a point 

of equilibrium, and they remain there until the input changes and a new equilibrium needs to be 

found (Stergiou & Siganos, 2006). BNN is based on the concept of training the network using the 

mean square error, by finding the minimum value of the total error square for the output values 

computed by the network. The weights between the layers are updated until the optimal weights 

that provide the best fit for the model are achieved (Al-Nasser &  Al-Obaidi, 2003). The key to an 

ANN model is the structure of the information processing system that connects and organizes a 

large number of internally connected processing elements (neurons) that work together to solve 

specific problems. Signals pass between nodes (neurons) through connecting lines, and each line is 

associated with a certain weight. The incoming signals to the node (neuron) are multiplied by these 

weights, and the weighted inputs are summed up in the nodes or neurons. Then, the outputs of each 

node are processed by a non-linear function with a specific threshold called the activation function 

(Stergiou & Siganos, 2006).  

 

1-3 Activation function 

It is also known as conversion functions because it converts input values by mixing them with weights 

from one mathematical formula to another. It also has several forms, including linear and nonlinear, 

and is characterized by its ability to determine the type of relationship between inputs and outputs and 

forms of activation functions (Wasserman, 1989; Zurada, 1960).  

 

1- Linear activation function 

a=f(n)=n…….(1) 

The derivative of this function is in this form 

f ̅(n)=1………(2) 

 

 



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2- Logistics activation function 

This function is often used at the hidden layer of neural networks since the input values are basically 

real values (-∞, +∞) while the output values of the function for each node of the network are (0,1) and 

are according to the following formula: 

  f(n)=(1 + e
−n

Q )−1……..(3) 

This function can be derivated in this form 

f̅(n)=(f(n)(1-f(n)/Q……..(4) 

 

3-The step activation function  

This function is used in classification models, and its outputs depend entirely on the inputs. The output 

of the function equals (1) if the input is greater than or equal to (0), otherwise, the output equals (0). 

This function differs from the previous two functions in that it has no derivative. It can be expressed 

as: 

a=f(n)=n…….(5) 

a={0,n<0
1,n≥0

 

4-Threshold activation function  

The threshold activation function is similar to the step function, as it has no derivative. The output 

values equal (+1) if the inputs are greater than or equal to (0), and (-1) if the inputs are less than (0). It 

can be expressed as:  

a=f(n)……(6) 

a={−1,n<0
1,n≥0

 

 

5- Bipolar Sigmoid activation function 

This function is commonly used in feature estimation. The input values range from (-∞ to +∞), while 

the output values range from (-1 to +1). It can be expressed as: 

f(n)=tanh(n/Q)=1-2/(1+e^(2n))......(7) 

The derivative of the function is given by:f(̅n )=
1−[f(n)]2

Q
 …….(8) 

 

1-4 Backpropagation Algorithm python 

The backward backpropagation  is one of the most important supervised training algorithms for neural 

networks. Its name comes from the fact that the error is propagated backward through the network from 

layer to layer. This algorithm relies on choosing a suitable error function, which is determined by the 

actual and desired output values, as well as the network's features such as weights and thresholds 

(Arabic Encyclopedia for Computer and the Internet, 2004) 

Al-Sheikhly (2003) states that training an ANN using backpropagation involves three stages, as 

follows: 

1. Forward propagation of error. 

2. Backward propagation of error. 

3. Weight tuning.  

 

 



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During the forward propagation stage, the input signal is transmitted to each node in the hidden layer, 

and the activation value for each node in the hidden layer is calculated based on this signal. Then, these 

nodes send their signals to each node in the output layer, and the activation value for each node in the 

output layer is calculated to form the network's response to the given input sample. During the training 

stage, each node in the output layer compares its calculated activation with the actual output value to 

determine the error value for that node. Based on this error value, the error correction factor δk is 

calculated. The error correction factor δk is used to distribute the error among the nodes in the output 

layer and is then sent back to each node in the previous layer. This factor is also used to update the 

weights in the output and hidden layers. Similarly, the error correction factor δj is calculated for each 

node in the hidden layer, and this factor is used to update the weights in the hidden and output layers. 

After determining all the error correction factors δ, the weights for all layers are adjusted 

simultaneously. 

The algorithm or methodology for this network can be summarized in the following steps: 

1. Generate initial weight values from a statistical distribution. 

2. Each node in the input layer receives input signals and sends them to all nodes in the hidden 

layer. 

3. Each node in the hidden layer aggregates weighted input signals according to the equation:  

hj = 2 / (1 + exp (-  xiwij)) – 1 ……… (9) 

 

4. Applying the activation function to estimate the outputs of the hidden layer, and sending the 

activation values to all nodes in the output layer. 

5. Each node in the output layer aggregates weighted input signals according to the equation: 

 

)10(…………1 –)) ikwih 
j

= 2 / (1 + exp ( ky 

6. Calculating the error for each output node by finding the difference between the activation value 

y_k and the target value t_k, as follows: 

)11(  ……… ky – k= t kE 

The output of the neural network is compared with the real values to estimate the error according to 

the equation: 

 

)12( ……..) . f(v) ky-k= (t k 

Where f(v) represents the logistic or tansig function when the output node is nonlinear and equals 1 

when the function is linear. Then, calculate the change in weight wjk using the following equation: 

wjk =  . k . hj ........ (13) 

7. Each node in the hidden layer aggregates weighted error signals from the output layer according to 

the equation: 

)14( ………. jkwk 
j

=  j 

Then this value is multiplied by the activation function to calculate j
, after which the change in the 

magnitude of the error vij is calculated and according to the equation: 

vjj =  . j . xi ……… (15) 

8. Update the weights of each node in the output layer, according to the equation: 



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)16(  …….. jkw(old) +  jk(new) = w jkw 

Then the weights for each node is updated in the hidden layer, according to the equation: 

)17( ………ijv(old) +  ij(new) = v ijv 

9. The network continues to update the weights "i.e. the process of learning and training" until the 

optimal weights are obtained. Thus, the desired outputs are obtained, i.e. reaching the best fit for 

the model under study . 

Where: 

  xi: represents the network inputs, w: represents the weights between levels.  

 

2. Logistic Regression 

Logistic regression is used to find the best fit model that describes the relationship between a response 

variable (dependent) and one or more explanatory variables (independent). Many natural phenomena 

exhibit non-linear behavior, and to analyze such phenomena, non-linear models are used. However, due 

to the difficulty in using these models, linear regression models are often used for this purpose. Logistic 

regression models are one such statistical model used to describe and analyze such phenomena. The 

logistic model is used to describe the relationship between a response variable (y) and one independent 

variable (x) or several independent variables (x1, ..., xn) (Al-Afifi, 2010; Ghanem & Al-Jaouni, 2011; 

Johnson, 1998). When there is a binary response variable and one independent variable, the general 

formula for the logistic model is: 

𝑝(𝑥) =
1

1+𝑒−𝛼−𝛽𝑥𝑖
  …….(18) 

Since: i=1,2,3,4,……,n,  

Β and α: are the two parameters of the model to be estimated. 

β>0 

P(x): the probability of the response 

xi: the explanatory variable 

Where:  

  −∞ <xi< ∞  &   −∞ ≤ 𝑎 ≤ ∞ 

The above formula is known as the logistical response function and is characterized by the fact that P 

(x) is defined between (1,0) and that the two parameters (Β, α) are unrestricted. However, in the case 

of each of the nominally dependent variables that have multiple responses consisting of two levels or 

two classifications or more and there are several independent variables. Therefore we have the multiple 

logistic model; it is formulated as: 

𝑝(𝑥) =
1

1+𝑒−𝑍    …….(19) 

Where,                              Z=a+B1X1+B2X2+………+BpXp………(20) 

There are two types of LRM, the first model is the two-response LRM and this model is used in the 

case if the response variable consists of two levels (two classifications) only. The second model is the 

multiple-response LRM and is used in the case if the response variable consists of three levels and 

more. 

 

1-Two-response logistic regression model 

The LRM is based on a basic assumption, which is that the dependent variable (y), the response variable 

that we are interested in studying, is a binary variable and follows the Bernoulli distribution, and takes 



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the value (1) with a probability of (π) and the value (0) with a probability of (1-π), that is, the occurrence 

of the response and not occurring (Al-Afifi, 2010; Timm, 2002).  

 

2. Multiple response logistic regression model 

The multiple-response LRM is considered one of the important statistical models in analyzing classified 

data, and it is generally used when the response variable belongs to variables of nominal or ordinal type 

consisting of two levels or two classifications or more. Likewise, the multiple-response LRM is a 

development and expansion of the two-response LRM, and it depends mainly on the multinomial 

distribution (Al-Afifi, 2010; Maiprasert & Kitbumrungrat, 2012).  

 

2-1 Logistic model assumptions  

Zelen (1983) stated that there are many hypotheses for the logistics model, the most important of 

which is: 

1. If the value of the dependent variable is confined or restricted to the period [1,0] 

2. The values of the dependent variable are either (0) or (1) and the remainders are generally large and 

the value of (R2) is small. 

3. The logistic model does not assume a specific distribution of the dependent variable, but it is 

assumed that its distribution is within the distributions of the exponential family (i.e., binomial 

distribution). 

4. To ensure a sufficient number of items for the response variable, the sample sizes must be large in 

the logistic regression. 

5. The logistic model does not assume a certain distribution of the explanatory variables, and there 

should not be a high correlation between the explanatory variables, because this causes problems in 

estimation. 

6.  There shouldn't be a linear relationship between the independent variable and the dependent 

variable, but it assumes linearity between the independent variables and the logarithm of probability 

(Cook et al., 2001).    

  

2-2 Model estimation  

2-2-1 Maximum likelihood estimation  

The parameters of the multiple-response LRM will be estimated in the manner of greatest possibility 

(Agresti, 1990; Al-Bayati, 2005; Al-Razami, 2000) which can be described as follows: 

The probability density function for a polynomial distribution is as follows : 

𝑃𝑟(𝑌𝑖1 = 𝑦𝑖1,   .  .  .  .  . , 𝑌𝑖𝑗 = 𝑦𝑖𝐽) =  (
𝑛𝑖

𝑦𝑖𝑗 ,……,𝑦𝑖𝐽
) 𝜋𝑖1

𝑦𝑖1  .  .  . 𝜋
𝑖𝐽

𝑦𝑖𝐽 …….(21) 

Hence,  

iJi y

iJ

y

i  ....1

1 represents the percentage of response groups in the community. 

 
ijyn

i

J

j

j xL 
= =

=
1 1

)()(  ……..(22) 

Calculating the logarithm of the possible function, we get: 

𝐿𝑁 𝐿(𝛽) = ∑ ∑ 𝑦𝑖𝑗  𝑙𝑜𝑔 𝜋𝑗(𝑥)𝑗𝑖……..(23) 



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Substituting πj (x) into equation (23), we get: 

𝐿𝑁 𝐿 (𝛽) = ∑ ∑ 𝑦𝑖𝑗  𝑙𝑜𝑔
𝑒

𝛼𝑗+𝛽𝑗
′  𝑥

1+∑ 𝑒
𝛼𝑗+𝛽𝑗

′  𝑥𝐽
𝑗=1

 𝑗𝑖…….(24) 

= ∑ ∑ 𝑦𝑖𝑗(𝛼𝑗 + 𝛽𝑗
′  𝑥  )𝑗𝑖 − ∑ ∑ 𝑦𝑖𝑗 𝐿𝑜𝑔(1 + ∑ 𝑒𝛼𝑗+𝛽𝑗

′  𝑥𝐽
𝑗=1𝑗𝑖 )…….(25) 

By deriving the maximum possibility function with respect to the parameter vector (β) 

∂LnL(β)

∂(β)
=

∑ ∑ yij((αj+βj
′  x )ji

∂(β)
−  

∑ ∑ yij Log(1+∑ e
αj+βj

′  xJ
j=1 )ji

∂(β)
………(26) 

When equating the derivative to zero (
∂LnL(β)

∂(β)
= 0),  we get natural equations, and the roots of these 

equations represent the values of the estimated parameters resulting from the process of maximization 

and because the equations are non-linear, we resort to using one of the iterative methods (Newton 

Raphson), which produces appropriate estimates according to the following formula: 

B(t + 1) = B(t) + {X ́ v(t)X}
−1

X́r(t)…….(27) 

  

Where, 

t :  represents the number of cascades 

r : represents the remainder vector with dimension [N(g-1),1] 

v: is Diag(v1 … … vn)and each vi is a square array written in the following form: 

vi = ni  {Ps (Xi)(δst − Pt(Xi))}St……(28) 

And that δstis the Kronecker delta and is defined by the following: 

δst=[
 1           S = t    
0           S ≠ t   

] 

Accordingly, we can start from initial values by equating the feature vector to zero, and in the binary 

case, the graph or the usual least squares method can be used, or the estimates of the linear 

discrimination function can be used as initial values in estimating the features, as their use will reduce 

the number of successive cycles, and when obtaining the required convergence between sessions, these 

optimal estimates are required. 

 

2-3 Tests 

2-3-1 Wald           

One of the important tests used to test the significance of the effect of the independent variable on the 

dependent variable in non-linear models is the Wald test. This test corresponds to the t-test used in 

linear models (Garson, 2013). The formula for the Wald test is as follows: 

 

2)
ˆ

ˆ
(









=





Se
wT         ……..(29) 

 

In statistical analysis, (
̂

) represents the parameter estimate and ( 






 ̂Se ) represents the standard 

error of the parameter. The test value is compared to χ2 a chi-squared distribution with one degree of 



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freedom. However, the accuracy of this test is questionable in small samples because the standard error 

may be large. Menard (Zelen, 1983) pointed out that large logit coefficients lead to large standard errors, 

which can reduce the accuracy of the Wald statistic and lead to type II errors. This is one of the 

drawbacks of the Wald statistic, as very large effects can lead to large standard errors. In most cases, 

the results of this test are very similar to the results of the odds ratio test (i.e., they rarely differ). 

Therefore, it is best to use the odds ratio test to test for the significance of variables with and without 

parameters. Additionally, logistic regression analysis is sensitive to violations of assumptions about 

large sample sizes. For these reasons, the odds ratio test is generally preferred (Cook et al., 2001).  

 

2-3-2   Likelihood ratio test     

If we want to test two models, the first () includes all the variables, and the second (LM2) includes a 

part of those variables, then in this case we use the Likelihood-Ratio test to show which of the two 

models has better significance than the other( Dessens & Janson, 2005). 

The formula for the probability test is: 

)30) ......(2log LM – 12 (log LM-) = 2/ LM 12 log (LM-D =      

whereas :- 

LM1: represents the possibility function under the null hypothesis. lm1 

 LM2: represents the possibility function under the alternative hypothesis.LM2 

The D value is close to the distribution of and compared with the tabular value of the distribution with 

a degree of freedom that represents the difference between the parameters of the two models.  

 

2-4 Model quality   

The quality of relevance means how appropriate the statistical model is to the data of the study 

sample. The quality of relevance measures measure the closeness between the observed and expected 

values of the model. Here are some important tests for relevance quality. 

 

2-4-1 Chi square test χ2    

It is one of the important tests used to fit or define the quality of the model, and it shows how the model 

describes the response variable, which is equal to the sum of squares. The differences between the 

observed and expected values divided by the expected values, and estimating the suitability of the model 

includes the convergence of the expected values from the observed values, as in the following formula 

(Cowan, 1994): 

.............(31)         
=

−

ected

ectedobserved

exp

)exp(2
2


 

Where (observed) means the observed values and (expected) means the expected values, and compares 

the value of the test statistic with the χ2 distribution with a degree of freedom equal to the number of 

classes minus the number of parameters in the logistic model. 

d.f = n – p  ….(32 

whereas:- 

p: represents the number of parameters,  

n: represents the number of items  

 



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2-4-2 Hosmer–Lemeshow 

This test is widely used in estimating the quality of fit of the model and allows any number of 

independent variables, which may be continuous or discrete, and this test is somewhat similar to the χ2 

test for the quality of fit. This test is as in the χ2 method for the quality of fit and approaches the χ2 

distribution with a degree of freedom equal to the number of classes minus the number of parameters 

in the logistic regression model. With a small sample size, this test is weak and this test requires a 

sample size of more than 400 observations (Cowan, 1994), and it is possible using equation (31).  

  Where the (observed) means the observed values and (expected) means the expected values 

 

2-5 The coefficient of determination R2   

R2 does not explain the quality of fit of the model as in linear regression, but it is an indicator of the 

importance of explanatory variables to predict the response variable and then measure the effect size 

(Agresti, 2002). 

We can mention the Cox & Snell R2 formula as follows: 

 (33)       .....

N

BL

BL

scR

/2

)(ˆ

)
0

(ˆ

12

































−=

 

The Nagelkerke R2 formula can be explained by the following formula : 

(34)     .....


















−
=

NBL

csR
NR

/2)}
)0(

(ˆ{1

2
2

 

The L(β(0)) represents the possibility function of the model under the null hypothesis, and L(β) 

represents the possibility function of the model under the alternative hypothesis. The large sample size 

gives power to the test analysis of the logistic model, as the larger the sample size, the greater the test 

power of the model 

 

Results 

This section includes an applied study of the multiple LRM using the maximum likelihood method, as 

well as an analysis of ANN for data on CML obtained from a master's thesis by the researcher (Mirdas, 

2023).  The data represent 150 observations and four variables, which are as follows: 

• Type of CML infection: as a response variable with three categories (Chronic phase CP, 

Accelerated phase AP, and Blast phase BP), represented by the code (1) for CP patients, (2) for 

AP patients, and (3) for BP patients. 

• Patient weight: The first explanatory variable. 

• Blood platelets (PLT): The second explanatory variable. 

• Number of cancer cells in bone marrow (BME): The third explanatory variable. 

 

Statistical data analysis using multiple logistic regression 

Model fitness quality  



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To measure the goodness of fit of the model, in the case of the multiple LRM, the likelihood ratio test 

is used, which follows a chi-square distribution. The outputs of the SPSS program are as follows: 

Table 1 Goodness of fit of the multiple LRM 

Sig. df Chi-Square -2 Log Likelihood Model 

0.000 6 42.240 
323.294 Fixed 

281.054 Final model 

 

According to the values of Sig in Table 1, the relationship between the explanatory variables and the 

response variable is significant. This means that there is a difference in the model when the explanatory 

variables are present compared to when they are absent. Other tests also support this conclusion, as 

shown in Table 2: 

 

Table 2 Goodness of fit of the multiple LRM using non-parametric tests 

Sig. df Chi-Square Model 

0.573 290 284.938 Pearson 

0.658 290 279.667 Deviance 

 

It can be observed  from Table 2 that the Sig values for both tests are greater than the significance 

level (0.05), indicating the importance of the explanatory variables in the model. 

 

Parameters estimation of the multiple LRM 

The parameters of the multiple LRM were estimated using the maximum likelihood method. Table 3 

summarizes the estimates of these parameters, along with their standard errors, Wald statistics, and 

accompanying Sig values: 

 

Table 3. Estimates of parameters of the multiple LRM 

Sig. df Wald Std. Error B CML (1) 

0.950 1 0.004 2.450 0.155 Fix CML=1.00 

0.829 1 0.047 0.034 -0.007 Weight 

0.090 1 2.867 0.004 0.007 PLT 

0.000 1 14.954 6.054 -23.410 BME 

0.028 1 4.843 2.341 5.151 Fix CML=2.00 

0.040 1 4.222 0.034 -0.069 Weight 

0.754 1 0.098 0.004 -0.001 PLT 

0.061 1 3.506 3.025 -5.665 BME 

 

It can be observed that the effect of the constant term and the explanatory variables on the response 

variable varies from category to category. For example, the effect of the constant term on the logit of 

the Chronic phase is 0.155, while it is 5.151 for the AP. Additionally, the weight variable has a negative 

 
1 The value (3) was used as a reference category. 



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effect on the logit of the Chronic phase with a regression coefficient of -0.007, and -0.069 for the 

Accelerated phase of the illness.  

 

The results of the classification are exhibited in Table 4 as follows: 

Table 4. Confusion matrix for the multiple LRM 
Correct rating 

ratio 

Predictor 

Classification 
Total Blast phase Accelerated phase Chronic phase 

80.6% 62 1 11 50 Chronic phase 

Observation 39.6% 48 7 19 22 Accelerated phase 

32.5% 40 13 5 22 
Blast phase 

54.7% 150 21 35 94 Total  

Table 4 shows that the correct classification rate (CCR) for the CP is 80.6%, but it is lower for both the 

PB and BP. The overall CCR is only 54.7%, which is relatively low. 

 

Statistical data analysis of using ANN 

The results of the ANN were obtained from the SPSS program after applying it to the study data. The 

network for the study model is shown in Figure 1.  

 

 
Figure 1. Artificial neural networks 

The estimated parameters were as following: 

Table 5. Estimated parameters 

Predictor 

Predicted 

Hidden Layer 1 Output Layer 

H(1:1) H(1:2) H(1:3) CML=1 CML=2 CML=3 

Input Layer 

(Bias) 0.062 -0.772 1.069       

Weight -0.655 1.823 -0.914       

PLT 1.428 1.84 0.543       

BME -1.889 2.864 3.01       

Hidden Layer 

1 

(Bias)       -0.551 -0.469 1.204 

H(1:1)       2.318 -0.402 -1.773 

H(1:2)       2.053 -2.714 0.982 

H(1:3)       -1.422 2.045 -1.309 



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This method achieved a much higher correct classification rate than the multiple LRM, as shown in 

Table 6 below: 

 

Table 6. Confusion matrix for the artificial neural network 

Correct 

rating ratio 

Predictor 

Classification Total Blast 

phase 

Accelerated phase Chronic 

phase 

91.9% 62 2 3 57 Chronic phase 

Observation 62.5% 48 3 30 15 Accelerated phase 

65.0% 40 26 4 10 Blast phase 

75.3% 150 31 37 82 Total  

 

It can be seen from Table 6 that the CCR for the Chronic phase is 91.9%, which is higher than the CCR 

in the multiple logistic regression model (80.6%). The correct classification rate for the Accelerated 

phase is 62.5%, which is higher than in the LRM (39.6%), and the CCR for the Blast phase is 65%, 

which is higher than in the LRM (32.5%). Therefore, the overall CCR for the ANN method is 75.3%, 

which is higher than the overall CCR in the multiple LRM (54.7%). 

 

Conclusions 

From the results, we conclude that the correct classification rate (CCR) when modeling using the 

multiple logistic regression method is approximately 55%, while CCR when using the artificial neural 

network method was approximately 75%. This indicates a superiority of the artificial neural network 

(ANN) method by about 20%. 

 

Recommendations 

1. Adopting the use of ANN models in studies and research due to their high accuracy, low error rates, 

and adaptability in dealing with data as they are considered adaptive methods. 

2. It is important to measure the quality of fit of the model in the case of MLR to determine the 

significance of the relationship between response and explanatory variables before starting the 

analysis process. 

3. Developing the healthcare sector by the relevant authorities and create a plan to increase health 

awareness through educating and encouraging citizens to have regular check-ups for early detection 

of blood cancer diseases. 

4. It is necessary to record complete information and data for each patient in their own medical records 

to benefit from them as data is the basis for conducting research and studies. 

  

References  

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Appendix  

Leukemia patient data 

No. CML Weight PLT (BME) No. CML Weight PLT (BME) 

1 1 53 147 0.03 76 1 66 331 0.03 

2 1 60 139 0.01 77 1 68 213 0.02 

3 2 52 311 0.09 78 3 63 194 0.24 

4 1 51 130 0.04 79 2 61 217 0.18 

5 1 61 186 0.03 80 1 63 251 0.02 

6 2 63 194 0.18 81 1 63 217 0.03 

7 3 70 315 0.24 82 1 66 321 0.04 

8 1 57 215 0.03 83 3 51 312 0.23 

9 1 55 197 0.04 84 1 67 215 0.01 

10 2 57 311 0.14 85 1 71 314 0.01 

11 1 63 219 0.03 86 1 61 215 0.01 

12 1 67 312 0.04 87 1 53 313 0.02 

13 1 71 221 0.02 88 2 62 211 0.09 

14 3 59 332 0.25 89 1 63 281 0.04 

15 1 61 212 0.03 90 1 67 223 0.04 

16 1 66 211 0.04 91 1 71 277 0.03 

17 1 70 311 0.02 92 1 61 217 0.04 

18 1 68 286 0.01 93 2 59 319 0.14 

19 1 65 147 0.02 94 1 52 271 0.03 

20 2 61 137 0.17 95 1 51 233 0.04 

21 3 67 360 0.25 96 3 53 247 0.23 

22 1 60 294 0.03 97 1 71 313 0.01 

23 1 70 148 0.01 98 1 68 306 0.03 

24 1 65 393 0.04 99 1 65 217 0.02 

25 3 70 325 0.23 100 2 53 333 0.18 

26 2 75 312 0.18 101 1 71 193 0.01 

27 2 63 330 0.09 102 1 66 268 0.04 

28 1 65 314 0.01 103 1 75 256 0.03 

29 1 60 299 0.03 104 3 53 321 0.24 

30 1 61 260 0.01 105 1 72 222 0.04 

31 1 52 321 0.02 106 1 59 187 0.03 

32 1 50 360 0.03 107 1 73 212 0.01 

33 1 61 315 0.04 108 1 68 325 0.02 

34 1 66 217 0.01 109 1 63 198 0.03 



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35 1 52 314 0.02 110 1 59 219 0.04 

36 1 60 187 0.03 111 2 52 227 0.12 

37 2 61 220 0.11 112 1 57 300 0.04 

38 1 58 265 0.01 113 1 50 311 0.01 

39 1 66 255 0.01 114 1 49 343 0.03 

40 1 52 255 0.01 115 3 51 288 0.23 

41 3 62 315 0.22 116 1 63 216 0.03 

42 1 51 180 0.01 117 1 67 325 0.01 

43 1 61 257 0.02 118 1 73 213 0.03 

44 1 65 251 0.03 119 1 64 313 0.02 

45 2 70 341 0.13 120 2 51 279 0.15 

46 1 60 266 0.02 121 1 67 317 0.04 

47 1 67 317 0.02 122 1 66 316 0.01 

48 3 59 218 0.24 123 1 72 213 0.02 

49 1 71 219 0.01 124 2 52 331 0.17 

50 1 62 307 0.01 125 1 62 227 0.03 

51 1 52 222 0.03 126 1 48 232 0.02 

52 1 55 237 0.04 127 1 49 331 0.03 

53 1 58 315 0.01 128 1 69 234 0.04 

54 1 51 357 0.02 129 2 51 331 0.16 

55 1 71 313 0.01 130 1 67 239 0.04 

56 1 65 310 0.02 131 1 62 277 0.02 

57 1 70 218 0.01 132 3 51 312 0.24 

58 1 60 317 0.01 133 1 62 212 0.04 

59 2 52 218 0.07 134 1 67 214 0.01 

60 1 55 218 0.01 135 1 71 341 0.02 

61 1 72 211 0.02 136 1 62 279 0.03 

62 3 58 351 0.23 137 2 53 377 0.16 

63 1 51 217 0.02 138 1 62 288 0.02 

64 1 71 315 0.01 139 1 61 361 0.03 

65 2 61 217 0.11 140 1 72 241 0.04 

66 1 68 317 0.03 141 1 67 342 0.01 

67 1 73 217 0.01 142 1 57 271 0.03 

68 1 61 219 0.03 143 3 49 197 0.03 

69 1 61 317 0.04 144 1 71 313 0.03 

70 1 62 211 0.01 145 2 48 201 0.04 

71 1 71 306 0.03 146 1 67 319 0.02 

72 1 61 211 0.01 147 1 56 287 0.01 

73 1 65 312 0.03 148 1 64 267 0.03 

74 1 62 213 0.03 149 1 72 312 0.01 

75 2 61 222 0.13 150 1 67 2.79 0.03