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2020 International Conference on Computer, Control, Electrical, and Electronics Engineering (ICCCEEE)
Comparison between Neural Networks and Binary logistic Regression for Classification
Observation (Case Study: risk factors for cardiovascular disease)
Eyas Gaffar Abdelraheem Osman2 Associated professor, Shaqra
University, Saudi Arabia
eyas-gaffar@su. edu. sa
Ebtehag Mustafa Mohammed 1 Faculty o f economic and rural development, University o f Gezira, PhD
Wad Medani, Sudan ebtehagmustafa22 @gmail. com
Abstract— the distinction between the artificial neural network method and the logistic regression method was discussed in this study as one of the methods suggested to be used in dual-data response. That is for preference between the two used methods, we used the proportion of misclassified observations, model accuracy and the area under the curved ROC as a criterion to compare between the two methods. Accordingly, This hospital-based case-control study involved 750 cardiovascular disease cases and 50 controls all recruited from Madani Heart Centre in Sudan, in 2019, The study aimed at knowing the most important risk factors for cardiovascular disease, and comparison between the Binary Logistic model and the Neural Networks models, also recognition of the best statistical approaches between the two methodologies for processing such data. To process the data, the study used the (SPSS) version 25.The main results that the study reached that the two used methods are similar regarding the significance of both the effect and the importance of the independent variables considered in the analysis, but the method of artificial neural networks gained a better classification proportion than the Binary Logistic Regression model .The most important recommendations of the study that making use of the statistical methods and generalizing the application of both Neural Networks and Logistic model in all fields of knowledge.
Keywords— Artificial Neural Network, logistic regression, cardiovascular disease, dual-data response.
I. In t r o d u c t i o n
Cardiovascular diseases (CVDs) are one o f the leading causes o f death all over the world, and by 2030, more than 23 million people are expected to die from CVD according to
the World Health Organization [1]. It has a serious socio- economic effect on individuals, families, and societies as far as o f healthcare costs, work absenteeism, and national productivity. Four risk factors (tobacco use, inordinate liquor utilization, less than stellar eating routine and absence of actual work) are related with four illness bunch (cardiovascular infection, malignant growth, ongoing aspiratory sickness and diabetes [2]. Six of the best ten driving reasons for death in 2012 were Non-Communicable Diseases (NCDs), including the best three diseases (ischemic coronary illness, stroke and ongoing obstructive pneumonic infection) [3].
Machine learning algorithms:
A. Artificial Neural Network ANNs are computing systems ambiguously excited by the
biological neural networks that compound animal brains' [4]. A neural network is made up of neurons which are simple and interconnected processors. The neurons are connected with one another by weighted connections over which signs can pass. The cycle comprises o f data assortment, examination and handling, network structure configuration, number of hidden layers and units, initializing, training the
network, network simulation, weights/bias adjustments, and testing the network. Artificial neural networks are utilized in various fields to manage enormous arrangements of information, frequently giving valuable investigations that permit to forecast and recognition o f new information. Artificial neural networks figure underlying information through a cycle of learning and preparing. Information regularly utilized by these designs has nonlinear connections among data sources and yields. They are utilized in applications, for example, discourse acknowledgement, imaging, control, assessment, enhancement, and host of different things. They are additionally applied in certifiable applications in the territories of account, clinical, business, mining, etc. [5]. The figure below shows the architecture of ANN which used in this study.
978-1-7281-9111-9/20/$31.00 ©2020 IEEE
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B. . Logistic regression : Logistic Regression sometimes called the logistic model or logit model, analyses the
relationship between multiple independent variables and
a categorical dependent variable, it is a method for
fitting a regression curve, y =f(x) when y consists o f
binary-coded (0, 1- -failure, success) data. When the
response is binary (dichotomous) variable and x is
numerical, logistic regression fits a logistic curve to the
relation betwixt these variables. The logistic curve is an
S-shaped or sigmoid curve, often used to model
population growth [6]. A logistic curve starts with slow,
linear growth, followed by exponential growth, which
then slows again to a stable rate.
C. Decision Tree: Decision (Regression) Tree is a tree-like structure that classifies instances by sorting them based
on the estimations o f the variables. Every hub in a
choice tree addresses a variable in a guide to be ordered,
and each branch addresses a worth that the hub can
expect. Occurrences are ordered beginning at the root
hub and arranged dependent on the values of the
variables. The variable that best divides the dataset
would be the root node of the tree. Internal nodes (or
split nodes) are the decision-making part that makes a
decision, based on multiple algorithms, and to visit
subsequent nodes. The split process is terminated when a
user-defined criterion is reached. The paths from root
nodes to the leaf nodes represent classification rules.
D. Random Forest: Random Forest is an ensemble model constating o f multiple regression trees like in a forest.
Random forest combines several regression trees,
prepares every one on a marginally unique arrangement
of the dataset examples, parting hubs in each tree
thinking about a predetermined number o f the factors.
The last forecasts o f the arbitrary backwoods are made
by averaging the expectations o f every individual tree,
which enhances the prediction accuracy for unseen data
E. k-Nearest Neighbor: k-Nearest Neighbour (kNN) is one of the most basic and non-parametric algorithms, it does
not make any assumptions about the distribution o f the
underlying data. The algorithm is relies on the principle
of Euclidean distance which is the cases inside a dataset
for the most part exist in closeness to different examples
that have comparative properties. In the event that the
cases are labelled with a grouping name, at that point ,
the estimation o f the mark o f an unclassified occasion
can be dictated by noticing the class of its closest
neighbours [7].
II. MATERIALS AND METHODS
This study endeavoured to: determine the most important variables that determine the risk factors for cardiovascular diseases, comparison of the two models o f artificial neural networks and the binary logistic regression in differentiating between a group of patients and those without the disease. Identify the best statistical method among the two mentioned methods for classifying study data and for processing such data.
This hospital-based case-control study relied on
observations o f 800 patients involved 750 CVD cases and
50 controls all recruited from Madani Heart Centre in
Sudan, in 2019 and there were selected randomly, all of
them aged 15 years and above. All subjects were
interviewed face-to-face to fill in a questionnaire that
covered many CVD-related variables (containing modifiable
and non-modifiable risk factors for CVDs, Non-modifiable
risk factors such as age and sex, and modifiable such as
state, residence, obesity).
Data was collected with consideration of ethical aspects, as
approval was obtained from the Medani Heart Centre and
the University o f Gezira.
After collecting the data, the data has been coded and
organized and has been examined using SPSS version 25 for
windows, to achieve the desired objectives of this study,
data were investigated utilizing the method of the binary
logistic model and the method of multilayer perception
network which are feed forward neural networks and The technique which used in training here is supervised
learning with Back propagation (BP) algorithm. To equate the results o f the binary logistic model and network model
the proportion o f misclassified observations was used for
each model separately.
Related Works: -Aravind Akella and Vibhor Kaushik in their study, applied
six different machine learning (ML) algorithms to predict
the presence o f cardiovascular diseases amongst patients
listed in an openly available dataset, all six ML algorithms
accomplished correctnesses more noteworthy than 80%, with the "Neural Network" calculation accomplishing
exactness more prominent than 93%. The review
accomplished with the "Neural Network" model is likewise
the most noteworthy o f the six models (0.93). Also, five of
the six calculations brought about fundamentally the same
as AUC-ROC bends. The AUC-ROC bend compared to the
"Neural Network" calculation is somewhat more extreme
suggesting higher "genuine positive rate" accomplished with
this model. In this research, they demonstrated that ML
algorithms can be applied with high accuracy and recall to
detect the presence o f CAD using a publicly available
dataset.
-The research o f Simon Nusinovici et al, 2020 expected to
evaluate the exhibition of (ML) calculations and to contrast
them and strategic relapse for the expectation o f danger of
cardiovascular infections (CVDs), ongoing kidney sickness
(CKD), diabetes (DM), and hypertension (HTN) and in an
imminent companion study utilizing straightforward clinical
indicators. The aftereffects of the examination demonstrated
that Logistic relapse, angle boosting machine, and neural
organization were deliberately positioned among the best
models, Additionally the examination reasons that Logistic
relapse yields as great execution as ML models to anticipate
the danger of major ongoing illnesses with the low
occurrence and basic clinical indicators. The study Suggest
that traditional regression models should continue to have a
key role in disease hazard expectation and further studies
are needed to confirm this result for different settings and
study characteristics [8].
- Aiguo Wang et al, 2014 results demonstrate that
integration of logistic regression and artificial neural
networks provides an effective method in the determination
o f risk factors and the forecasting o f hypertension, as well as
a general approach for the prediction of other chronic
diseases [9].
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According to K. Uma Maheswari and J. Jasm ine, 2017, the
upside o f logistic regression is the interpretability o f model
indicators and usability. The benefit of the neural network is
it requires less formal factual preparing to create and can
verifiably identify complex non-linear relationships among
dependent and independent factors. The joining o f logistic
regression and neural network gives the novel methodology
in predicting a person's heart disease. The future work can
be reached out fo r longitudinal investigations of the sick
persons and to enhance the preciseness in Predicting heart
disease [10].
III. RESULTS
A. Results o f binary logestic model After collecting the data, the data has been coded and
organized and has been analyzed using the Statistical
Package for Social Science (SPSS), We used binary logistic
regression, To assay the multiplicative effect o f Pathological
and socio-economic and demographic variables as
explanatory on cardiovascular disease status as a dependent
variable. Patients were separated into two categories: (1)
patients who have heart disease are labelled 1. (2) Patients
who have not have heart disease are labelled 0. A number of
steps were utilized to estimate logistic regression. First, we
evaluated the generic model. Second, determine the
significance o f each explanatory variable .third, the
reckoning o f predictive accuracy.
Table (1) below shows the Omnibus Test of Model
Coefficients used to check that the new model (with
explanatory variables included) is an improvement over the
baseline model (does not include explanatory variables). It
utilizes Chi-square tests to check whether there is a
significant difference between the Log-likelihoods of the
baseline and the new model. The statistics for the Step,
Model and Block are the same because we have not used
stepwise logistic regression or blocking. The table shows
that Chi-Square has 9 degrees o f freedom, a value of
224.829 and probability o f p = .000, which reflect the
precision of the model improvement when we add
explanatory variables respectively, as the overall chi-
squared test hypotheses are : H0: Bt=0 , Hi : Bt^0 (Minimum of one coefficient) so H0is rejected since p-value = 0.000.
TABLE 1. Omnibus Tests o f Model Coefficients
Chi-square f S ig Step 1 Step 224.829 9 0.000
Block 224.829 9 0.000
Model 224.829 9 0.000
The model statistics in the table (2) below provides the -2
Log-likelihood (-2LL), Cox & Snell R Square and
Nagelkerke R Square values for the full model. The -2 LL
value for the model (149.237) which tell us that there was
huge a diminishing in the - 2LL, for example that the new
model (with informative variable) has a fundamentally
preferable fit over the model with just constant. Cox and
Snell's R -Square attempt to imitate R- squared based on
likelihood and (usually less than 1). Here it is indicating that
(2.45%) o f the variety in the dependent variable is clarified
by the logistic model. Nagelkerke R Square is a more
reliable measure of a relationship. It is indicating that
(6.55%) o f the variety in the dependent variable is clarified
by the logistic model
TABLE 2_______ Logistic Regression’s Model Summary step -2loglikelihood Cox&snell R square
Nagelkerke R square
1 149.237 .245 .655
Table (3) below shows the Hosmer and Lemeshow test. H -
L test of the model fit which proposes that the model is a
solid match to the data.From the table Chi-square has 8
degrees o f freedom, a value of 6.871 and probability of P =
.0.551 which is more than 0.05 suggesting that the model
was best to the data.
TABLE .3 Hosmer and Lemeshow Test step Chi-square d f Sig.
1 6.871 8 .551
Table (4) below shows that the cases where the observations
of the dependent variable (heart disease status) were 1 or 0
respectively have been correctly predicted.
TABLE .4 Classification Table O b s e r v e d P r e d i c t e d
N o n - h e a r t p a t i e n t
H e a r t p a t i e n t
P e r c e n t a g e c o r r e c t
P a th o l o g ic a l
c a s e
N o n - h e a r t
p a t ie n t
26 2 4 5 6 .0
H e a r t p a t ie n t 9 741 9 8 .5
O v e r a ll
P e r c e n t a g e
9 5 .9
From the table, the columns are the two predicted
estimations of the dependent, while the rows are the two
observed (actual) values of the dependent. In a perfect
model, all cases will be on the diagonal and the overall per
cent correct will be (100%).
Also, According to the above table, overall (95.9%) were
correctly classified (741+26)/800=0.959).while 33 cases
were classified incorrectly
Logistic regression parameterization: TABLE .5_____ Variables in the Equation
Variables B S.E Wald d f Sig. Exp (B)
Renal disease 1.971 .818 5.806 1 .016 7.177
Using oil cooking 8.06 .468 2.973 1 .085 .446
No of meals that has been eaten with oil per day
.021 .019 1.144 1 .285 1.021
passive smoking .676 .668 1024 1 .311 14.77
Drinking alcoholic 2.692 1.14
9
5.494 1 .019 14.77
Operating heart injury
.500 .582 .739 1 .390 1.65
Level of education .115 .169 .459 1 .498 .892
Smoking .140 .017 65.05
5
1 .00 6.69
Constant 4.55 3.34 9
1.849 1 .174 .011
The parameter estimate coefficient B in the table (5)
summarizes the effect o f each predictor. the ratio of the
coefficient to its standard error squared equals the wald
statistic, the standard explaining of the logistic regression is
that for a unit change in the predictor variable, the logistic
regression of outcome relative is relied upon to change by
its particular coefficient estimate which is log-odds units,
given that different factors in the model are held steady.
From the table, the Wald statistics to every independent
variable confirms the significant Confirms a significant
impact on the status of cardiovascular diseases. The result of
regression for renal disease, there is Strong significant with
large impact (Wald = 5.806, df=1 p=.016), “Sig.” is a p-
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Network Informationvalue of significance test of beta. Usually, the coefficients
which p-values are below 0,05 are considered to be
significant. Based on our output, 3 explanatory variables are
significant. The main source leading to CVDs is drinking
alcohol with (14.8) times odds compared to other CVDs
factors, followed by renal diseases with (7.17 ) times odds,
likewise smoking with ( 6.7 ) times odds.
The equation of the line found here is :
Ln [ B (* ) 1= 4.55+ 1.971 x, + 2.692x2+.140xx3 i - b \ x ) 1 2 3
Where: x 1 represents (renal disease), x 2 represents drinking
alcoholic and x3represents smoking
“S.E”-s are standard errors related to the coefficients. The
standard error is used to test whether the parameter is
significantly different from 0 or not. Standard errors are also
utilizing in the calculation of the Wald statistic.
If we look again at the previous table, the sign of a
parameter of the educational level takes a negative value,
this means that the more a person receives a higher
education, the less likely they are to have cardiovascular
disease.
Roc curve:
Table (6) below shows that. The magnitude of detoured is
0.984 (0.976, 0.991). Also, this region is significantly
different from 0.5 since the p-value is 0.000 meaning that
the logistic regression classifies the group significantly
better than by chance.
TABLE .6____ ̂Curve Region T est result Predicted probability Asymptotic 95% variables
Asymptotic sig confidence level
Area std. Error
0.984 1 0.004 0.000 0.976 0.991
R O C C u r v e
Fig. 2 Roc curve
B. Results o f (ANN) s: There are many steps that were followed here in designing a
neural network (1): collecting data,(2)preprocessing data,
(3) building the network, (4): training, and (5) test the
model rendering .
Table (7) displays information about networks like hidden layer and output layer, activation function and error function
applied. The table shows that there are 9 factors and the Number of units in the input layer is 44. The numbers of units in the layer of output are 2 representing two categories of our variable- heart patients and non-heart patients. The architecture has included one hidden layer with 7 units, the function of activation is Softmax which also known as the logistic function or sigmoid
TABLE.7
factors 1 Renal disease 2 Using oil cooking
3 Number of meals that have been eaten with oil per day
4 Passive smoking
5 Drinking alcoholic
6 Operated heart injury
7 Level of education
8 Smoking
9 Symptoms
Hidden layers Number of units 44
Number of hidden layers
1
Number of units in hidden layers
7
Output layer Activation
function Softmax
Error function Cross-entropy
Information presented in Table 8 is a summary of the model. It shows Cross entropy error, per cent of incorrect predictions in training, testing. Cross entropy error in training is 0.043 while Cross entropy error in the testing sample is 0.027.
TABLE .8 (ANN)’s Model Summary
training Cross Entry error .043
Percent in correction
prediction 0.0%
Stopping rule used Ceiling number of epochs (663)exceeded
Training time 0:00:02.27
testing Cross Entropy error .027
Percent incorrect prediction 0.0%
It is clear from the previous table that the wrong classification in the training sample was 0.0% and the
misclassification in the test sample was 0.0% too and this indicates that the network has been excellently trained in categorizing new samples.
TABLE .9 Classification Rresult
Sample
Observed
Predicted
Percent Correct
Training
Non- heart patient
Heart patient
non- heart patient 36 0 100.0%
heart patient 0 512 100.0%
Overall Percent 6.6% 93.4% 100.0%
Testing
non- heart patient 14 0 100.0%
heart patient 0 236 100.0%
Overall Percent 5.6% 94.4% 100.0%
Per cent of incorrect predictions are taken from the classification table. As we can see in T able 9, the overall per cent of correct predictions is 100%. The per cent of incorrect predictions is 0% that is calculated as (100% - 100%). It means to say that a total of correct prediction and total of incorrect predictions makes 100 %. To understand this table, we shall first see in rows. In training, there are 36 non-heart patients. All of them are correctly predicted as a non-heart patient that is why; the overall per cent of correct predictions is 100%. In the next row, there are a total of 512 heart patients, 512 of them correctly predicted as heart
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patients. Therefore the per cent of correct predictions is 100%. In the last row o f the training section, overall per cent (6.6 % + 93.4 = 100%) represents the total number o f case analyzed in each category.
Table (10) below shows that the area under the curve is 1.0
Table. 10 Area under the ROC Curve for the Neural Network Model
Area
Pathological case Non- heart patient 1.0 Heart patient 1.0
Table (11) shows the normalized importance of each predictor variable. As the table depicts; the normalized importance o f smoking is the highest then drinking alcoholic then the renal disease.
TABLE . 11 Independent Variables Important
V ariable Importance Normalized importance
renal disease .073 11.8% using oil .019 3.1%
The number o f foods
consumed with oil
.067 10.8%
passive smoking .020 3.3% drinking alcoholic .076 12.2% operated heart injury .045 7.3% level of education .050 8.1% Symptoms .031 5.0% Smoking .618 100.0%
The following table shows the results and similarities and differences between the two models. logistic results indicated that the main elements of the risk of cardiovascular disease are drinking alcoholic followed by experiencing renal infections and afterward smoking, then, the neural network demonstrated that the main factor of the danger elements of cardiovascular sickness is smoking followed by drinking alcoholic and then renal disease.
TABLE . 12 Comparison between The Two Models
Item Model Neural network Logistic regression
Assumptions and conditions o f the dependent variable
Binary nominal variable
Binary nominal variable
Assumptions and conditions o f the independent variables
None A mixture of quantitative and qualitative variables
The important of independent
variable for classification
Smoking is followed by drinking alcoholic and then renal disease
Drinking alcoholic is followed by renal
disease and then smoking
Area under the roc curve 1.0 .98
Correct prediction ratio 100% 95.9
Estimated final form coefficients
Shows the relative
importance of independent variables in an
automatic way
Indicates signals of the coefficient that reflect
the relationship between the dependent variable and the
independent variables
Re c o m m e n d a t i o n s
• Developing a database for gathering statistical data in the ministry o f health to obtain a real, realistic and extremely accurate data so that the results are good and satisfactory that helps us in developing that field to reach the desired goal.
• Making use o f the statistical methods in all fields of knowledge, and generalizing the application of both Neural Networks and Logistic model in all fields of knowledge.
• Attention should be paid to all factors that increase the risk of CVD, whether pathological or behavioral factors or others.
CONCLUSION
The study aimed at knowing extreme influential risk factors for cardiovascular disease, and comparison between the Binary Logistic model and the Neural Networks models, besides the recognition of the best statistical approaches between the two approaches fo r processing such data. The most important recommendations of the study that making use of the statistical methods in all fields of knowledge, and generalizing the application of both Neural Networks and Logistic model in all fields o f knowledge.
R e f e r e n c e s
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[2] Lozano, R., Naghavi, M., Foreman, K., Lim, S., et al, Global and regional mortality from235 causes o f death for 20 age groups in 1990 and 2010: a systematic analysis for theGlobal Burden o f Disease Study 2010. The Lancet. [Online] 380 (9859), 2095-2128.Available from: doi:10.1016/S0140-6736(12)61728-0 ,2012 .
[3] Luke, A. , Are we facing a noncommunicable disease pandemic? - ScienceDirect.[Online]. 2017. Available from: https://www.sciencedirect.com/science/article/pii/S221 0600616301009 [Accessed: 25April 2018].
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