Comparison of various approaches to combine logistic regression with genetic algorithms in survival prediction of hepatocellular carcinoma

Abstract

Hepatocellular carcinoma (HCC) is the most common liver cancer in adults. Lots of different factors make it hard to diagnose in humans. In this paper, a novel diagnostics approach based on machine learning techniques is presented. Logistic regression is one of the most classic machine learning models used to solve the problem of binary classification. In typical implementations, logistic regression coefficients are optimized using iterative methods. Additionally, parameters such as solver, C-a regular-ization parameter or the number of iterations of the algorithm operation should be selected. In our research, we propose a combination of logistic regression with genetic algorithms. We present three experiments showing the fusion of those methods. In the first experiment, we genetically select the logistic regression parameters, while the second experiment extends this approach by including a genetic selection of features. The third experiment presents a novel approach to train the logistic regression model-the genetic selection of coefficients (weights). Our models are tested for the survival prediction of hepatocellular carcinoma based on patient data collected at. The model we proposed achieved a classification accuracy of 94.55% and an f1-score of 93.56%. Our algorithm shows that machine learning techniques optimized by the proposed concept can bring a new and accurate approach in HCC diagnosis with high accuracy.

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Computers in Biology and Medicine 134 (2021) 104431
Available online 11 May 2021
0010-4825/© 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Comparison of various approaches to combine logistic regression with
genetic algorithms in survival prediction of hepatocellular carcinoma
Wojciech Ksią˙
zek
a
, Michał Gandor
a
, Paweł Pławiak
a
,
b
,
*
a
Department of Computer Science, Faculty of Computer Science and Telecommunications, Cracow University of Technology, Krakow, Poland
b
Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Gliwice, Poland
ARTICLE INFO
Keywords:
Logistic regression
Machine learning
Hepatocellular carcinoma
Genetic algorithms
ABSTRACT
Hepatocellular carcinoma (HCC) is the most common liver cancer in adults. Many different factors make it
difcult to diagnose in humans.. In this paper, a novel diagnostics approach based on machine learning tech-
niques is presented. Logistic regression is one of the most classic machine learning models used to solve the
problem of binary classication. In typical implementations, logistic regression coefcients are optimized using
iterative methods. Additionally, parameters such as solver, C - a regularization parameter or the number of it-
erations of the algorithm operation should be selected. In our research, we propose a combination of logistic
regression with genetic algorithms. We present three experiments showing the fusion of those methods. In the
rst experiment, we genetically select the logistic regression parameters, while the second experiment extends
this approach by including a genetic selection of features. The third experiment presents a novel approach to
train the logistic regression model - the genetic selection of coefcients (weights). Our models are tested for the
survival prediction of hepatocellular carcinoma based on patient data collected at Coimbra’s Hospital and
Universitary Center (CHUC), Portugal. The model we proposed achieved a classication accuracy of 94.55% and
an f1-score of 93.56%. Our algorithm shows that machine learning techniques optimized by the proposed
concept can bring a new and accurate approach in HCC diagnosis with high accuracy.
1. Introduction
In recent years, we are witnessing the constant growth of the amount
of data we store. This creates new challenges which besides big data
storage, also includes its interpretation. Machine learning algorithms
make it possible to interpet the data in a specic manner that humans
cannot handle. These algorithms are characterized by their efciency,
exibility and ability to generalize the data they process. That is one of
the reasons why ML enabled the engineers to full the demands of to-
day’s world including the analysis of credit scoring, advertisements and
much faster treatment of complicated illnesses. Machine learning algo-
rithms are successfully used in ECG interpretations including abnormal
heart rate diagnoses [18], arrhythmia detection [38] or assessing of
electrocardiogram visual interpretation strategies [34]. In medicine ML
is also used to diagnose coronary artery diseases [1,2,30,49], breast
cancers [3], wart diseases [4], heartbeat classications [24] and Alz-
heimer’s disease [6]. On the other hand, ML can also be used in other
elds like credit scoring [36], approximating of phenol concentration
[39], modelling of the results of tympanoplasty in chronic suppurative
otitis media patients [45], chemical analysis [46], assessing of dots and
globules in dermoscopic colour images [23]. In this paper, we also use
genetic algorithms to accelerate the computation and get more precise
results [37].
Hepatocellular carcinoma (HCC) is one of the leading causes of death
associated with cancer-related deaths worldwide [11]. One of the most
promising prevention approaches is an early diagnosis [16], but the
number of different factors causing cancer makes it hard to distinguish it
from other diseases, especially at an early stage. We believe that ma-
chine learning methods can be widely used for various types of problems
making the analysis faster and less error prone.
There are two main reasons that drove us to apply machine learning
in the HCC problem. First, HCC is the leading type of liver cancer
worldwide. There are many factors that can indicate the presence of
cancer. Accurate and early diagnosis can prevent many deaths and
improve life quality. The second reason is that using genetic algorithms,
the accuracy of the prediction models can be improved compared to
* Corresponding author. Department of Computer Science, Faculty of Computer Science and Telecommunications, Cracow University of Technology, Krakow,
Poland.
E-mail addresses: plawiak@pk.edu.pl, plawiak@iitis.pl (P. Pławiak).
Contents lists available at ScienceDirect
Computers in Biology and Medicine
journal homepage: www.elsevier.com/locate/compbiomed
https://doi.org/10.1016/j.compbiomed.2021.104431
Received 13 January 2021; Received in revised form 14 April 2021; Accepted 21 April 2021

Computers in Biology and Medicine 134 (2021) 104431
2
solutions already present in literature.
The main goal of this study is to design a novel logistic regression
learning algorithm using genetic algorithms. The algorithm imple-
mented is based on 49 different features, which are considered to be key
factors causing HCC. It allows for faster diagnosis taking into consider-
ation all of the provided indicators simultaneously.
The main contributions to our work are: (1) investigation and pre-
processing of the HCC dataset, (2) examination of the standard logistic
regression learning, (3) applying GA to the logistic regression learning,
(4) comparison of the results.
This study introduces a novel method of determining logistics
regression coefcients. The computation is done using genetic algo-
rithms through data classication provided in the Hepatocellular Car-
cinoma dataset [42]. The aim of the experiment is to efciently train the
logistic regression model and classify the data into two classes present in
the dataset - die or live. The experiment includes a deep analysis of
preprocessing paths, including missing values replacement and scaling
methods which are implemented within the experiment. Various ap-
proaches to combine logistic regressions are presented in this study.
The paper is organized as follows: after the introduction of the
examined problem, we deeply describe the methods used in section 2.
Later on, we give a brief introduction of logistic regression as the main
algorithm used in the analysis 3. The next section 4 is fully aimed at
describing the performed experiments, including genetic algorithms
applied in different paths we took. The two last sections include detailed
results - comparison 5 and discussion 6.
1.1. HCC dataset
The dataset was collected at Coimbra’s Hospital and University
Centre (CHUC), Portugal. It contains data on 165 patients described by
49 features [41]. There are 23 quantitative variables and 26 qualitative
variables. Lots of missing values are present (10.22%). Moreover, only
eight patients have complete information in all elds (4.85%). The
dataset has unbalanced classes (63 vs 102).
Using the random forest algorithm (with 1000 estimators), we ana-
lysed the signicance of the data set features [28]. According to the
algorithms, the most important features are the following: International
Table 1
Details of HCC dataset [41].
# Feature Range Type Missing Mean Std
1 Gender 0, 1 binary 0
2 Symptoms 0, 1 binary 18
3 Alcohol 0, 1 binary 0
4 Hepatitis B Surface Antigen 0, 1 binary 17
5 Hepatitis B e Antigen 0, 1 binary 39
6 Hepatitis B Core Antibody 0, 1 binary 24
7 Hepatitis C Virus Antibody 0, 1 binary 9
8 Cirrhosis 0, 1 binary 0
9 Endemic Countries 0, 1 binary 39
10 Smoking 0, 1 binary 41
11 Diabetes 0, 1 binary 3
12 Obesity 0, 1 binary 10
13 Hemochromatosis 0, 1 binary 23
14 Arterial Hypertension 0, 1 binary 3
15 Chronic Renal Insufciency 0, 1 binary 2
16 Human Immunodeciency Virus 0, 1 binary 14
17 Nonalcoholic Steatohepatitis 0, 1 binary 22
18 Esophageal Varices 0, 1 binary 52
19 Splenomegaly 0, 1 binary 15
20 Portal Hypertension 0, 1 binary 11
21 Portal Vein Thrombosis 0, 1 binary 3
22 Liver Metastasis 0, 1 binary 4
23 Radiological Hallmark 0, 1 binary 2
24 Age at diagnosis 20–93 scale 0 64.7 13.37
25 Grams of Alcohol per day 0–500 scale 48 71.01 76.28
26 Packs of cigarets per year 0–510 scale 53 20.46 51.57
27 Performance Status 0, 1, 2, 3, 4 ordinal 0 1.02 1.18
28 Encefalopathy degree 0, 1, 2, 3 ordinal 1 1.16 0.43
29 Ascites degree 0, 1, 2, 3 ordinal 2 1.44 0.69
30 International Normalised Ratio 0.84–4.82 scale 4 1.42 0.48
31 Alpha-Fetoprotein (ng/mL) 1.2–1810348 scale 8 19299.95 149098.34
32 Haemoglobin (g/dL) 5–18.7 scale 3 12.88 2.15
33 Mean Corpuscular Volume () 69.5–119.6 scale 3 95.12 8.41
34 Leukocytes(G/L) 2.2–13000 scale 3 1473.96 2909.11
35 Platelets (G/L) 1.71–459000 scale 3 113206.44 107118.63
36 Albumin (mg/dL) 1.9–4.9 scale 6 3.45 0.69
37 Total Bilirubin(mg/dL) 0.3–40.5 scale 5 3.09 5.50
38 Alanine transaminase (U/L) 11–420 scale 4 67.09 57.54
39 Aspartate transaminase (U/L) 17–553 scale 3 96.38 87.48
40 Gamma glutamyl transferase (U/L) 23–1575 scale 3 268.03 258.75
41 Alkaline phosphatase (U/L) 1.28–980 scale 3 212.21 167.94
42 Total Proteins (g/dL) 3.9–102 scale 11 8.96 11.73
43 Creatinine (mg/dL) 0.2–7.6 scale 7 1.13 0.96
44 Number of Nodules 0–5 scale 2 2.74 1.80
45 Major dimension of nodule (cm) 1.5–22 scale 20 6.85 5.10
46 Direct Bilirubin (mg/dL) 0.1–29.3 scale 44 1.93 4.21
47 Iron (mcg/dL) 0–224 scale 79 85.60 55.70
48 Oxygen Saturation (%) 0–126 scale 80 37.03 28.99
49 Ferritin (ng/mL) 0–2230 scale 80 439.00 457.11
50 Class 0, 1 binary 0
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Normalised Ratio(0.079), Gamma glutamyl transferase (U/L)(0.075),
Alpha-Fetoprotein (ng/mL)(0.056), Oxygen Saturation (%)(0.056),
Platelets (G/L)(0.044). The signicance values for all features are
available in the supplementary materials.
Table 1 provides details about the characteristics in the data set and
information about missing values.
1.2. Goals
The main goals of this study are as follows:
•introduction of a new logistic regression model training method,
instead of iteratively reweighted least squares, genetic algorithms
are used;
•fusion of genetic algorithms for both training the logistic regression
model and feature selection;
•verication of solutions implemented and comparison against stan-
dard learning methods.
1.3. Related works
Many machine learning models have been prepared to detect of liver
cancer, especially hepatocellular carcinoma, in recent years. Santos
et al. [41] proposed a new cluster-based oversampling approach for HCC
detection based on the K-means clustering and SMOTE algorithm to
build a representative data set. In this study, logistic regression and
neural networks were also used. The best model achieved a classication
efciency: 75.19%. Sawhney et al. [44] proposed a method based on the
rey algorithm and random forest to detect several types of cancer. In
the case of hepatocellular carcinoma, the proposed model had an ac-
curacy of 83.5%. Ksiazek et al. [26] designed a machine learning model
based on the support vector machine and genetic algorithms. Genetic
algorithms were used to optimize both the classier’s parameters and
feature selection. The proposed model obtained a high classication
accuracy of 88.49%. Nayak et al. [31] prepared a classication model
enabling the detection of hepatocellular carcinoma based on CT images.
He proposed to use SVM with the RBF kernel. The best result was 86.9%.
Brehar et al. [13] designed a classication model for HCC detection
based on ultrasound images. The model was prepared with the use of
AdaBoost and achieved a classication accuracy of 72%. A combination
of the support vector machine together with the Lasso method was
proposed by Aonpong et al. [9]. The research was conducted on a data
set of 331 patients from Sir Run Run Shaw Hospital, Zhejiang University,
China. The proposed model achieved a classication accuracy of
89.18%. Research using decision trees as well as linear regression and
boosting was conducted by Hashem et al. [19]. Their work was based on
a data set of over 4000 patients obtained from the Egyptian National
Committee for the Control of Viral Hepatitis and the multidisciplinary
HCC clinic at Cairo University’s Kasr Al-Aini Hospital. The best proposed
model was characterised by a very high classication accuracy: 95.6%.
A new method for HCC detection was proposed by Tuncer et al. [47]. It is
based on a neighbourhood component analysis and a relief based
method. Using FGSVM, a very high accuracy was obtained: 92.12%. Sato
et al. [43] conducted hepatocellular cancer detection studies in two
groups (539 and 1043 patients). They used the following classiers:
logistic regression, support vector machine, gradient boosting, random
forest, neural network and deep learning. The best result was obtained
with the use of the boosting gradient - 87.34%. In order to detect this
disease, research was also carried out using gene expression proles data
sets. Zhang et al. [48] conducted their experiments with the support
vector machine and achieved very high results. Ali et al. [7] proposed
the LDA-GA-SVM method combining the LDA method for dimensional
reduction, genetic algorithms and a support vector machine. The pro-
posed classier achieved an accuracy of 90.30%. A model with exactly
the same accuracy was proposed by Ksia ˙
zek et al. [27]. A model of
ensemble learning based on stacking learning was designed, consisting
of 7 classiers and a meta-classier. Genetic algorithms were also used
to optimize parameters and select features of individual classiers.
Hattab et al. [20] proposed a new approach using the k-means algo-
rithm, SMOOTE method and SVM. Their model achieved a classication
efciency of 84.90%. Al-Islam et al. also used the SMOOTE technique.
Combining it with the XGBoost algorithm, they achieved a high detec-
tion efciency of hepatocellular carcinoma equal to 87%. For the
detection of liver disease, Abdar et al. [5] proposed a regression tree
(Cart) with a boosting technique, as well as a multi-layer perceptron
neural network (MLPNN). It also implemented a combination of the two
MLPNNB-C5.0 methods as well as the MLPNNB-CHAID algorithm. Deep
learning methods described in detail in the works were also used to
detect liver cancer: [12,14,15].
2. Methods
This section presents all the steps taken to achieve the introduced
results. Firstly, we discuss the scaling methods, later on lling in missing
values. In the end, genetic algorithms are introduced, which are being
used to calculate logistic regression coefcients as well as to select the
best set of features.
2.1. Preprocessing
Since machine learning algorithms demand the data to be complete,
there are a few preprocessing scenarios tested. A vast amount of missing
values present in the processed dataset (Table 1), require additional
investigation to prepare the data for further analysis. Furthermore, the
data have a large numerical spread. To scale data, the standardisation
method was applied. It must be noted that in machine learning pre-
processing plays a crucial role in optimizing the classier’s performance
and accuracy. Without using proper preprocessing the output model can
be easily over-tted and have a poor generalisation ability. Pre-
processing also impacts the classier’s training and prediction perfor-
mance. It is crucial when fusing it with genetic algorithms since lot of
different classiers with different parameters and features must be
trained in order to achieve the best results.
2.1.1. Scaling
•standardisation was calculated for each feature separately, using a
standard formula:
scaled value =
x−u
s(1)
where:
– x - a sample
– u - mean of training samples for a single feature
– s - a standard deviation of training samples for a single feature
Preprocessing is applied to both ordinal (including binary) and nu-
merical values.
2.1.2. Missing values
The amount of missing values in each feature is presented in Table 1.
Corresponding to the referenced table the count of missing samples
varies between 0 and 80 for a single feature. Moreover, a different type
of data is to be noticed (binary, ordinal, scale) which forces usage of
different preprocessing scenarios. Two methods of lling the missing
values were tested:
•Samples of the binary and ordinal type were replaced using mode,
samples of scale type were replaced using mean for each feature
separately.
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•Additionally, a more advanced method of lling in the missing
values was tested: the k-nearest neighbours algorithm. The experi-
ment was carried out for 3 and 5 neighbours using the Euclidean
metric [32].
2.2. Cross-validation
For all the presented experiments, the stratied ve-fold CV is used.
Each fold has randomly selected train and test sets with the original
proportions between classes preserved. Preserving the number of in-
stances from all the classes in each set is crucial in unbalanced data sets
processing. Cross-validation helps the model to over-t.
2.3. Genetic algorithms
Genetic algorithms are algorithms based on the fundamental laws of
evolution [21,29,40]. Each individual in a population is a potential so-
lution to the problem. The algorithm is iterative - during the subsequent
epochs, individuals are selected, crossed and mutated. After each iter-
ation, new individuals are created as a result of crossover and mutation.
The next generation is created, which is later on assessed again using the
same adaptation function. The algorithm ends when the specied ac-
curacy is reached or after a given number of epochs. Genetic algorithms
have also found application in machine learning problems. They were
used to optimize parameters and select features in hepatocellular car-
cinoma detection [26,27], ECG signal [35,38], credit scoring [37] or the
detection of heart diseases [2,8,10]. The single individual in the popu-
lation is, in this case, a single set of parameters for the machine learning
model. Additionally, this individual can be expanded with the set of
features from the data set. It is assessed through classic machine learning
metrics such as accuracy, or the f1-score presented in section 2.4. Other
metrics as specicity, sensitivity or AUC can also be applied. We decided
to use the f1-score and accuracy because they are the most frequently
used in the literature and therefore, we can compare our results to the
results of other authors.
The proper conguration of the genetic algorithm is signicant.
Depending on the problem to be solved, it can be very different. Table 2
shows the setup used in our experiments. The particular values have
been selected based on trial and error but also based on our experience.
The high mutation probability ensures high variance in the whole
population. An elitist strategy ensures that the best individual is auto-
matically moved to the next epoch without crossover and mutation. It is
crucial in keeping the constant convergence of the genetic algorithm.
The best potential solution can be easily lost due to the high probability
of mutation and crossover. In order to compare the results achieved by
the genetic algorithm, a reference experiment was carried out using the
PSO algorithm [25]. We set the number of iterations and individuals to
2000 for PSO. Additionally, we have congured omega =0.2, phip =
0.2, phig =0.2.
2.4. Metrics
For the purpose of evaluating the model’s performance, standard
metrics were chosen: Accuracy (ACC) and F-measure (f1-score), Sensi-
tivity, Specicity, Brier Score. All metrics were calculated based on the
confusion matrix generated for each experiment separately [27]. Those
metrics are used to show the nal results of the classication.
3. Logistic regression
Logistic Regression is a mathematical model which enables the
probability estimation of belonging to a certain class. In this paper, the
LR model is used for binary classication, but in other cases, it can easily
be extended for multi-label classication.
To calculate regression coefcients, usually, iterative methods are
used such as iteratively reweighted least squares (IRLS) or the Newton-
Raphson method. In this study, those common methods are replaced
with genetic algorithms.
The logistic regression model implementation used in this study
comes from the Sklearn library [33]. It allows for easy control of a few
parameters, such as:
•Penalty - adds bias to the model when it is suffering from high
variance,
•C - the higher values generalize the model, whereas the smaller
values constrain it more,
•Max iteration - the maximum number of iterations done in order to
converge the model,
•dual - an objective function type,
•t_intercept - increase or decrease the impact of an intercepted value,
•solver - a type of an algorithm solver,
•l1_ratio - controls the penalty impact.
All those parameters are tuned using genetic algorithms. The details
are presented in section 4.
4. Experiments
As part of this research, experiments were conducted on a data set
collected at Coimbra’s Hospital and University Center (CHUC), Portugal.
The data set is described in detail in section: 1.1. In the rst stage of the
experiment, the missing values were completed. For quantitative attri-
butes, an average is used, and for qualitative attributes, a mode value.
The entire experiment was performed using 5-fold cross-validation. The
accuracy and f1-score were selected as the basic metrics. The research
was divided into 3 stages:
•Genetic optimization of parameters
•Genetic optimization of parameters and selection of features
•Genetic weight optimization
These experiments are described in detail in the sections: 4.1, 4.2 and
4.3. Fig. 1 shows the experiment schematics. The three experiments
mentioned will be described in detail later in this chapter.
4.1. Genetic parameters optimization
In the rst experiment, genetic algorithms were used to optimize the
parameters of the logistic regression model.
Table 3 shows the parameters of the logistic regression model
available to tune. These parameters include C, Max iteration, Penalty,
Dual, Fit intercept, solver, and L1 ratio. Each individual in the genetic
population consists of a chromosome containing the parameters
mentioned above. The values are randomly generated within the spec-
ied ranges to create the initial population.
Fig. 2 shows the structure of the chromosome for an exemplary
Table 2
Genetic algorithm parameters [27].
Parameter Value
Crossover algorithm Two points crossover or arithmetic crossover
Selection algorithm Tournament selection (with three individuals participating in
each tournament)
Mutation algorithm Own implementation of a single point mutation in each
experiment
Probability of
crossover
0.7
Probability of
mutation
0.7
Population size 2000
Number of iteration 2000
Elitist strategy The best individual goes to the next iteration
Fitness function Accuracy or F1-score
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individual. It consists of 7 genes.
4.2. Genetic parameters optimization and feature selection
The second experiment extends the rst one with the use of genetic
algorithms to select the features. It is widely known that many machine
learning algorithms perform better on fewer features. However, it is not
a simple task to choose the optimal set of features. In this experiment,
this selection will be made by evolutionary algorithms.
Table 4 presents in detail the parameters of the implemented model.
As in the rst experiment, these are logistic regression parameters, as
well as 49 parameters, each corresponding to one feature available in
Fig. 1. Experiment schema.
Table 3
Logistic regression parameters.
Parameter Value
C [1–100]
Max iteration [1–2000]
Penalty [L1, L2, Elasticnet, none]
Dual True or False
Fit intercept True or False
Solver [newton-cg, lbfgs, liblinear, sag, saga]
L1 ratio [0–1]
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Computers in Biology and Medicine 134 (2021) 104431
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the dataset. If the value of the parameter equals 1, the analogical feature
is used to train the classier when it is 0.
Fig. 3 shows the structure of the chromosome used in experiment
number 2. The structure of a chromosome consists of logistic regression
parameters and features from the data set. In total, the chromosome
consists of 56 genes. Therefore, the optimization problem becomes
much more complex compared to the one introduced in section 4.1.
4.3. Genetic weights optimization
The last experiment presents a novel approach to calculate the lo-
gistic regression coefcients. The weights optimization was performed
using genetic algorithms, contrary to the most common method like
IRLS (gradient algorithms). This approach provided the highest
accuracy.
Table 5 shows the detailed parameters of the model in the experi-
ment on optimizing logistic regression weights. In this case, this algo-
rithm’s classic parameters, such as max iteration, C or solver, are not
optimized - because the goal of the experiment is to use genetic algo-
rithms to select an appropriate set of weights. In the standard approach,
it is done by algorithms that are implemented in the Sklearn library. The
amount of weights is equal to the number of features in dataset 49.
Fig. 4 shows the structure of the chromosome used in experiment 3.
This chromosome consists only of logistic regression weights. There are
49 values present in the chromosome, each in the range [-3, 3]. This
constructs a much more complex optimization problem which has to be
solved.
5. Results
In this section, the results obtained with the models proposed in
sections 4.1, 4.2 and 4.3 will be presented.
The models were implemented using Python (version 3.8) with li-
braries: Sklearn [33], Pandas, PySwarm and Deap [17].
The calculations were performed on a machine with the following
specications:
•Processor: Intel(R) Xeon(R) CPU E5-2670 v3 @ 2.30 Ghz 2.30 Ghz
(two processors)
•RAM: 512 GB
•Operating system: Windows Server 2019 (64-bits)
Due to the high amount of epochs used to optimize the model, the
computation times on the specied machine took around 2 h to com-
plete for a single experiment. The calculations were performed using all
available cores. That made it possible to speed up the calculations
compared to common one-core solutions.
For each-cross validation fold the presented results are calculated on
different test sets for each fold, which is not used during the classiers
training. At each cross-validation iteration, 132 samples formed the
training set, and the remaining 33 built the test set. 12 samples from
class 0 and 21 samples from class 1 formed a test set, where 51 samples
from class 0 and 81 from class 1 formed a training set.
5.1. Genetic parameter optimization
In this experiment, the model detailed in section 4.1 was extended to
optimize logistic regression parameters genetically. The results for two
different target functions of the genetic algorithm: accuracy and f1-
score, are presented below.
5.1.1. Model with accuracy optimization
The model prepared in this experiment achieved a classication ac-
curacy of 78.79%. It was a model that used the liblinear gradient algo-
rithm to solve the problem of selecting logistic regression weights. The
best result was achieved after 25 iterations. The model using the training
set achieved an accuracy equal to: 90.15%.
The detailed parameters of the model are presented in Table 6. The
experiment was performed using 5-fold cross-validation.
Fig. 2. Example chromosome in experiment 1.
Table 4
Model parameters in experiment 2.
Parameter Value
C [1–100]
Max iteration [1–2000]
Penalty [L1, L2, Elasticnet, none]
Dual True or False
Fit intercept True or False
Solver [newton-cg, lbfgs, liblinear, sag, saga]
L1 ratio [0–1]
Feature 1 0-feature rejected, 1 – feature accepted
Feature 2 [0–1]
Feature … [0–1]
Feature 49 [0–1]
Fig. 3. Example chromosome in experiment 2.
Table 5
Model parameters in experiment 3.
Parameter Value
Weight 1 [-3,3]
Weight 2 [-3,3]
Weight … [-3,3]
Weight 49 [-3,3]
Intercept [-3,3]
Fig. 4. Example chromosome in experiment 3.
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Computers in Biology and Medicine 134 (2021) 104431
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Table 7 shows the detailed classication results for the proposed
model. In this experiment, the k-nearest neighbours algorithm (3
neighbours) was chosen to ll in the missing values. The average clas-
sication accuracy in individual folds is 78.79%.
Fig. 5 shows the ROC curve for the proposed model. For both class 1
and class 2, the area under the curve is 0.79.
5.1.2. Model with f1-score optimization
In this part of the experiment, the model proposed in section 4.1 was
re-used. This time the matching function in the genetic algorithm has
been changed. The f1-score was used instead of the accuracy measure-
ment. In this part of the experiment, the missing values were completed
using the k-nearest neighbours algorithm with 5 neighbours. The ob-
tained results are similar to those in section 5.1.1. The best result ob-
tained by the model was the f1-score equal to 78.71%. In order to verify
the model overtting, it was tested on the training set. The achieved f1-
score was 89.88%.
This time the best model was obtained with the use of the solver
’liblinear’. The algorithm took 9 iterations to achieve convergence.
Detailed parameters of the presented model are available in Table 8.
Table 9 shows the detailed results of the model under the individual
cross-validation folders.
Fig. 6 shows the ROC curve for the model used in this experiment.
The AUC area under the ROC curve is 0.81.
5.2. Genetic parameters optimization and feature selection
This experiment is a continuation of the experiment described in
section 4.1. Here it is additionally extended with a genetic selection of
features. A detailed description of this experiment is presented in section
4.2. As in the previous experiment, the model was optimized once with
the use of accuracy as a tness function - section 5.2.1, and then the f1-
score - section 5.2.2.
5.2.1. Model with accuracy optimization
In this section, the results will be presented for the accuracy as the
tness function. This time the optimization problem is more complex -
apart from the selection of the logistic regression parameters, it was also
necessary to choose the best set of features. In this experiment, the knn
algorithm was again used to ll in the missing values with the number of
neighbours set to 3. This task was solved - the proposed model achieved
a classication accuracy of 89.7%. However, the accuracy achieved on
the training set is 89.09%.
Table 10 shows the parameters and a set of features for a given
model. This time, the ’liblinear’ algorithm was used as a solver, which
achieved convergence already in epoch 111. Additionally, the set of
features has been reduced from 49 to 25.
Table 11 shows the detailed results of the experiment performed. The
classication accuracy of over 90% can be seen in as many as 3 folds out
of 5. Additionally, the set of features necessary to build an effective
model has been signicantly reduced.
Fig. 7 shows the ROC curve for the proposed model. Much higher
AUC value is to be noticed compared to the models from section 4.1. This
time it is 0.88.
5.2.2. Model with f1-score optimization
In this model, the F1-score measure was used as the tness function.
The knn algorithm for missing values has been congured with a
number of neighbours of 5. The result obtained was very similar to the
result from section 5.2.1. The model obtained an f1-score: of 88.31%.
The f1-score value on the training set was: 86.33%.
Table 12 shows the best set of parameters for this model. The algo-
rithm converged in 181 iterations with the ’lbfgs’ algorithm. As in the
case of the model in section 5.1.1, 23 features were used to achieve the
best result.
Table 13 shows the detailed results of the experiment performed.
Table 6
Model parameters in experiment 1 with accuracy
as a tness function.
Parameter Value
C 4.0753
Max iteration 25
Penalty l2
Dual True
Fit intercept True
Solver liblinear
Table 7
Detailed results for the model with an optimized accuracy in experiment 1.
Classier Fold TP TN FP FN Sen Spec Brier Acc
Logistic regression 1 6 20 6 1 0.5 0.9524 0.2092 0.7879
2 9 19 3 2 0.75 0.9048 0.1309 0.8789
3 11 14 2 6 0.8462 0.7 0.2396 0.7576
4 12 15 1 5 0.9231 0.75 0.2116 0.8182
5 7 17 6 3 0.5385 0.85 0.2367 0.7273
Total 0.7115 0.8314 0.2056 0.7879
Fig. 5. The ROC curve in experiment 1 for the model with accuracy.
Table 8
Model parameters in experiment 1 with an f1-score
as a tness function.
Parameter Value
C 1.8815
Max iteration 9
Penalty ’l1′
Dual False
Fit intercept False
Solver ’liblinear’
L1 ratio 0.8959
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Computers in Biology and Medicine 134 (2021) 104431
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Again, high F1-scores in individual folds are to be noticed, which
translates into a high nal, average result.
Fig. 8 shows the ROC curve for the proposed model. The area under
the curve is identical to the model with accuracy and amounts to 0.86.
5.3. Genetic weights optimization
The last part of the experiment shows the results for the model
proposed in section 4.3. This is a novel approach to nd weights of the
logistic regression model. Evolutionary computations were used instead
of usual weight optimization with gradient methods. This allowed for
Table 9
Detailed results for the model with an optimized f1-score in experiment 1.
Classier Fold TP TN FP FN Sen Spec Brier F1-score
Logistic regression 1 9 19 3 2 0.75 0.9048 0.154 0.8332
2 10 19 2 2 0.8333 0.9048 0.1067 0.869
3 11 13 2 7 0.8462 0.65 0.2227 0.7263
4 13 11 0 9 1.0 0.55 0.2489 0.7263
5 10 16 3 4 0.7692 0.8 0.195 0.7806
Total 0.8397 0.7619 0.1855 0.7871
Fig. 6. The ROC curve in experiment 1 for the model with f1-score.
Table 10
Model parameters in experiment 2 with accuracy as a tness function.
Parameter Value
C 13.6838
Max iteration 111
Penalty ’l2′
Dual False
Fit intercept False
Solver ’liblinear’
Selected
features:
Gender, Symptoms, Hepatitis B e Antigen: HBeAg, Hepatitis B Core
Antibody: HBcAb, Hepatitis C Virus Antibody: HCVAb, Endemic
Countries, Diabetes, Arterial Hypertension: AHT, Human
Immunodeciency Virus: HIV, Nonalcoholic Steatohepatitis:
NASH, Age at diagnosis, Grams of Alcohol per day: Grams/day,
Encefalopathy degree, International Normalised Ratio: INR,
Leukocytes(G/L), Platelets (G/L), Total Bilirubin(mg/dL): Total
Bil, Alanine transaminase (U/L): ALT, Aspartate transaminase (U/
L): AST, Alkaline phosphatase (U/L): ALP, Total Proteins (g/dL):
TP, Creatinine (mg/dL), Major dimension of nodule (cm), Iron
(mcg/dL), Ferritin (ng/mL)
Table 11
Detailed results for the model with optimized accuracy in experiment 2.
Classier Fold TP TN FP FN Sen Spec Brier Acc
Logistic regression with genetic parameteroptimization and genetic feature selection 2 12 21 0 0 1 1 0.0448 1
3 12 19 1 1 0.95 0.9231 0.1205 0.9394
4 11 16 2 4 0.8 0.8462 0.1745 0.8182
5 10 17 3 3 0.85 0.7692 0.1785 0.8182
Total 0.901 0.891 0.1287 0.897
Fig. 7. The ROC curve in experiment 2 for the model with accuracy.
Table 12
Model parameters in experiment 2 with an f1-score as a tness function.
Parameter Value
C 91.7618
Max iteration 181
Penalty ’None’
Dual False
Fit intercept True
Solver ’lbfgs’
Selected
features:
Gender, Hepatitis B Surface Antigen: HBsAg, Hepatitis B e Antigen:
HBeAg, Hepatitis C Virus Antibody: HCVAb, Diabetes, Arterial
Hypertension: AHT, Chronic Renal Insufciency: CRI, Portal
Hypertension, Liver Metastasis, Radiological Hallmark, Age at
diagnosis, Ascites degree, International Normalised Ratio: INR,
Platelets (G/L), Total Bilirubin(mg/dL): Total Bil, Alanine
transaminase (U/L): ALT, Aspartate transaminase (U/L): AST,
Gamma glutamyl transferase (U/L): GGT, Total Proteins (g/dL):
TP, Creatinine (mg/dL), Major dimension of nodule (cm), Iron
(mcg/dL), Ferritin (ng/mL)
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Computers in Biology and Medicine 134 (2021) 104431
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obtaining new, high results. As in the previous experiments, this section
will present the results for optimizing the two tness functions.
5.3.1. Model with accuracy optimization
This subsection describes the results for the model optimized for
accuracy. In this experiment, we optimize the logistic regression weights
using all the features from the data set. The missing values were lled in
using the k-nearest neighbours algorithm, where k =3. The best result is
higher than the results from previous experiments. The accuracy ach-
ieved is 94.55%. The same accuracy was achieved on the training set.
Table 14 shows the detailed calculation results for the model with
weight optimization. Very high scores can be observed in each cross-
validation fold, above 90%.
Table 15 shows the weight and intercept values used in the logistic
regression model within the experiment.
Fig. 9 shows the ROC curve for the implemented model. The AUC
value is very high: 0.92. The AUC is much greater than in previous
experiments.
5.3.2. Model with f1-score optimization
An analogous experiment of weight optimization with the use of
genetic algorithms was performed for the f1-score. Again, very high
results were achieved. The f1-score was 93.56%. A similar F1-score
value was achieved on the training set: 93.65%.
Table 16 shows the exact results of the experiment performed. High
f1-scores can be observed in each cross-validation fold.
Table 17 shows the weight and intercept values used in the logistic
regression model within the experiment.
Fig. 10 shows the ROC curve for the optimized model. Again, a much
higher AUC value can be observed than in the previous experiments for
the f1-score. This value is 0.93.
5.4. The impact of lling the missing values technique
One of the most important obstacles to be solved before starting the
design of a machine learning model is lling the missing values in the
dataset. The easiest techniques require lling them using mode or mean
values. Results for the experiment with the use of mode and mean are
available in supplementary materials. However, the use of more
advanced techniques such as the k-nearest neighbours algorithm can
signicantly improve the results. In our case, thanks to the mentioned
algorithm, it was possible to improve the nal results in 5 out of 6
conducted experiments.
Table 18 shows that the use of the nearest neighbours algorithm
signicantly improved the results achieved. Especially signicant
improvement is to be noticed in the rst experiment - genetic selection
of parameters.
5.5. Comparison of genetic algorithms with PSO
The experiment compared two very popular biology-inspired
methods for solving the optimization problem: evolutionary algo-
rithms and PSO.
By analyzing Table 19, one can observe that the genetic algorithms
achieved better results. It is especially visible in the case of the last
experiment - weight optimization. That problem was particularly dif-
cult to optimize, because 66 parameters had to be selected (having
values on a continuous scale) in the range [-3.3]. In the case of experi-
ments 1 and 2, which were simpler in terms of optimization, the results
achieved by PSO were less divergent compared to the results obtained
with the use of evolutionary calculations. A detailed analysis of the re-
sults obtained from genetic algorithms and PSO is provided in the sup-
plementary materials.
6. Discussion
In this article, we focused on different approaches to fuse genetic
algorithms with a logistic regression model. A proper preprocessing
demanded by the investigated dataset is designed. It includes lling in
Table 13
Detailed results for the model with an optimized f1-score in experiment 2.
Classier Fold TP TN FP FN Sen Spec Brier F1-score
Logistic regression with genetic parameter optimization and genetic feature selection 1 11 20 1 1 0.9524 0.9167 0.1238 0.9345
2 11 21 1 0 1.0 0.9167 0.0619 0.9666
3 10 17 3 3 0.85 0.7692 0.1813 0.8096
4 11 18 2 2 0.9 0.8462 0.1383 0.8731
5 9 17 4 3 0.85 0.6923 0.1822 0.7746
Total 0.9105 0.8282 0.1375 0.8717
Fig. 8. The ROC curve in experiment 2 for the model with an f1-score.
Table 14
Detailed results for the model with optimized accuracy in experiment 3.
Classier Fold TP TN FP FN Sen Spec Brier Acc
Logistic regression with genetic weights optimization 1 10 20 2 1 0.9524 0.8333 0.1005 0.9091
2 12 21 0 0 1.0 1.0 0.0303 1.0
3 12 18 1 2 0.9 0.9231 0.097 0.9091
4 13 18 0 2 0.9 1.0 0.0862 0.9394
5 12 20 1 0 1.0 0.9231 0.0541 0.9697
Total 0.9505 0.9359 0.0736 0.95
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Computers in Biology and Medicine 134 (2021) 104431
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missing values and data scaling. We conducted three different experi-
ments showing how those algorithms can be combined. A general
overview of the experiment is presented in Fig. 1. The experiments were
carried out on the dataset collected in Coimbra’s Hospital and University
Center (CHUC), Portugal. A detailed description of the data set is pro-
vided in section 1.1.
In the rst experiment, we optimized the logistic regression param-
eters using evolutionary calculations. This experiment is detailed in
section 4.1. The results for this experiment are described in detail in
section 5.1, which is divided into two sections, 5.1.1 and 5.1.2 -
depending on the optimized objective function (accuracy or f1-score).
The model from the rst experiment achieved a classication accuracy
Table 15
Logistic regression coefcients for each feature with intercept for an ACC measure.
weights −0.4843 −1.7421 −0.4282 0.9403 0.0129 −0.6173 −1.9304
0.3465 1.1663 1.8194 −1.3592 0.2901 −0.5994 0.8925
0.5636 −1.4497 −1.1905 0.4035 −1.6433 0.9284 −1.774
−0.7573 0.7663 −2.7800 −0.7964 −1.5463 −1.6388 −1.802
0.3005 −1.2226 1.7008 −0.6957 0.4234 −1.0089 1.7387
0.7882 −1.335 1.3087 −1.7784 −0.6852 −1.9369 −0.1891
−1.5178 1.0284 −0.6915 −1.7842 1.9373 1.7000 −1.2787
intercept 0.8192
Fig. 9. The ROC curve in experiment 3 for the model with accuracy.
Table 16
Detailed results for the model with an optimized f1-score in experiment 3.
Classier Fold TP TN FP FN Sen Spec Brier F1-score
Logistic regression with genetic weights optimization 1 9 19 3 2 0.9048 0.75 0.1652 0.8332
2 12 21 0 0 1.0 1.0 0.0173 1.0
3 13 13 0 2 0.9 1.0 0.0951 0.938
4 13 19 0 1 0.95 1.0 0.062 0.9687
5 13 18 0 2 0.9 1.0 0.105 0.938
Total 0.931 0.95 0.0889 0.95
Table 17
Logistic regression coefcients for each feature with intercept for the f1-score measurement.
weights 0.7485 −1.9286 1.0083 1.3137 1.1659 −1.5984 −1.909
−1.3562 1.3241 0.5996 −2.3965 1.0252 −0.1267 2.8711
−1.9769 −1.5686 0.5767 0.1817 −0.7776 1.0228 −0.6392
0.4413 1.4618 −1.8221 −1.3657 −1.1935 −1.7647 −0.728
0.2569 −1.4082 0.3251 1.0778 1.0223 −0.7939 0.9067
1.9502 −0.4915 1.791 −1.9927 −0.7666 −0.8295 0.1534
1.2789 −0.0325 −1.1064 −1.9777 1.4487 −0.0712 −1.8004
intercept 1.7241
Fig. 10. The ROC curve in experiment 3 for the model with an f1-score.
Table 18
Comparison of results for different approaches to ll in missing values.
Experiment Missing value
algorithm
Accuracy
[%]
F1-score
[%]
Genetic parameter optimization Mean and mode 76.36 75.14
KNN 78.79 78.71
Genetic parameters and feature
selection
Mean and mode 89.09 88.31
KNN 89.7 87.17
Genetic weights optimization Mean and mode 93.94 91.83
KNN 94.55 93.56
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Computers in Biology and Medicine 134 (2021) 104431
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of 78.79% (detailed results are presented in Table 7) and an f1-score of
78.71% (detailed results are available in Table 9). Tables 6 and 8 present
the parameters of the best models after the optimization process. Figs. 5
and 6 show the ROC curves obtained in this experiment. The areas under
these curves are 0.77 and 0.79 and 0.81, respectively. Experiment 2 is an
extension of experiment 1 with a genetic selection of features. The se-
lection of appropriate attributes signicantly improves the classication
results in most machine learning models. This experiment is detailed in
section 4.2. Section 5.2 presents the results of this experiment. As in the
case of the rst experiment, the model was optimized twice - rstly,
when the target function was accuracy (section 5.2.1), secondly, for the
F1-score function (section 5.2.2). Genetic selection made it possible to
signicantly improve the results for both the model with optimized
accuracy (Table 11) and the f1-score (Table 13). The best accuracy
achieved was 89.7%, while the f1-score’s result was 87.17%. The pa-
rameters for these models are presented in Tables 10 and 12. ROC curves
were also prepared for this experiment - they are presented in Figs. 7 and
8. The AUC area under those curves was 0.88 and 0.86. The last
experiment is a new approach to t logistic regression model. In this
approach, the classic gradient learning method was replaced with ge-
netic algorithms - the logistic regression weights were selected through
evolutionary computations. This experiment is detailed in section 4.3.
As done for previous experiments, the results are presented in section
5.3 (divided into two tness functions: accuracy - section 5.3.1 and f1-
score - section 5.3.2). Thanks to this innovative approach, very high
results were achieved. The accuracy of the classication was: 94.55%,
and the f1-score was 93.56%. Detailed results for this experiment are
shown in Tables 14 and 16. The ROC curves (Figs. 9 and 10) were again
prepared - with values of AUC 0.92 and 0.93, respectively.
A summary of the obtained results is shown in Fig. 11. We observed
that with subsequent experiments, the obtained results were rising. The
best result was achieved by using the novel approach with a genetic
optimization of weights. This shows another application of evolutionary
computing in optimization problems - applied to weights optimization.
In the literature, a few papers described the detection of hepatocel-
lular carcinoma in the CHUC dataset. The collected results are presented
in Table 20. Various methods to solve the problem of hepatocellular
carcinoma detection can be noticed in the scientic papers. Paper [41]
based on the use of neural networks obtained results at the level of 70%.
The use of genetic algorithms to optimize models [7,26,27] allowed for a
signicant improvement in the results achieved - the best accuracy of
such models is 90.30%. In Ref. [47] the authors proposed a completely
new approach built on the NCA and the relief-based method. The clas-
sication accuracy obtained in this paper equals to 92.12%. The papers
[20,22] use the SMOOTE algorithm with various classiers. This made it
possible to obtain models with an accuracy of over 80%. Our research is
signicantly different from the rest. Even though a very popular logistic
regression algorithm was used, it has been linked to genetic algorithms
in three different ways. Testing various fusion scenarios of these two
algorithms allowed us to obtain very high results, achieving the best
result in all of the literature - a classication accuracy equal to 94.55%,
and at the same time a high value of f1-score 93.56%. The main ad-
vantages of the proposed model are:
•three approaches to fuse logistic regression with evolutionary
computation,
•comparison of genetic algorithms with the PSO algorithm,
•assessment of the algorithm’s impact to ll in missing values,
•proposing a novel method to select model weights using genetic al-
gorithms instead of gradient algorithms,
•achieving high results - accuracy: 94.55% and F1-score: 93.56%.
The main disadvantages of the solution are:
•the model requires testing on a larger data set,
•in the case of larger data sets, the weight optimization process can be
much more time consuming.
•perhaps other biology-inspired algorithms would have achieved
better results
As part of our further work, we plan to use genetic algorithms to
optimize the weights of the neural network and use deep learning to
solve problems in the survival prediction of hepatocellular cancer.
7. Conclusion
This work focused on training the logistic regression classier. The
three possibilities to fuse logistic regression with genetic algorithms in
the survival prediction problem of hepatocellular carcinoma are tested.
In the rst experiment, the model parameters were optimized. In the
Table 19
Comparison of the results achieved from using GA and PSO.
Experiment Optimization Accuracy
[%]
F1-score
[%]
Genetic parameter optimization GA 78.79 78.71
PSO 77.57 78.07
Genetic parameters optimization and
feature selection
GA 89.7 87.17
PSO 86.66 85.98
Genetic weights optimization GA 94.55 93.56
PSO 89.09 87.05
Fig. 11. Summary of the obtained results.
Table 20
Comparison of the results obtained in the HCC detection problem on the CHUC
dataset.
Study Method Accuracy F1-score
Santos et al. NN +augmented set approach 0.7519 +-
0.0105
0.6650 +-
0.0182
Sawhney
et al.
BFA +RF 0.835 N. A
Ksiazek
et al.
SVC with new 2-level genetic
optimizer approach
0.8849 0.8762
Ali et al. LDA–GA–SVM (with linear and
RBF kernel)
0.9030 N. A
Ksia˙
zek
et al.
StackingGA 0.9030 0.8857
Hattab et al. K-Means +SMOOTE +SVM 0.8490 N. A
Al-Islam
et al.
SMOOTE +XgBoost 0.87 N. A
Tuncer et al. reliefF +LDA
NCA +FGSVM
0.8303
0.9212
0.8202
0.9161
This study GA-LR 0.9455 0.9356
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Computers in Biology and Medicine 134 (2021) 104431
12
second, a genetic selection of features was added, while the third
experiment is a new approach to logistic regression model training -
genetic selection of weights. Subsequent experiments allowed obtaining
better and better results. The best results achieved had an accuracy of
94.55% and an f1-score of 93.56%. This shows how modifying a typical
logistic regression allows for achieving signicantly better results. In the
future, we plan to work on the detection of hepatocellular carcinoma on
larger data sets using the ensemble method and deep learning (espe-
cially neural networks) combining these methods with the genetic
algorithms.
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi.
org/10.1016/j.compbiomed.2021.104431.
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