=Paper=
{{Paper
|id=Vol-2753/paper50
|storemode=property
|title=The Problem of Analysing the Relationships between Individual Characteristics of Individuals with COVID`19
|pdfUrl=https://ceur-ws.org/Vol-2753/paper32.pdf
|volume=Vol-2753
|authors=Nataliia Melnykova,Natalya Shakhovska,Volodymyr Melnykov,Mykola Logoyda,Yulia Peleshchak
|dblpUrl=https://dblp.org/rec/conf/iddm/MelnykovaSMLP20
}}
==The Problem of Analysing the Relationships between Individual Characteristics of Individuals with COVID`19==
https://ceur-ws.org/Vol-2753/paper32.pdf
The Problem of Analysing the Relationships between Individual
Characteristics of Individuals with COVID`19
Nataliia Melnykova,a, Natalya Shakhovska,a, Volodymyr Melnykov,b, Mykola Logoyda,a and
Yulia Peleshchak,a
a
Lviv Polytechnic National University, S. Bandery Str., 12, Lviv, 79013, Ukraine
b
Danylo Halytsky Lviv National Medical University, 69 Pekarska str., Lviv, 79010, Ukraine
Abstract
The paper proposes the development of an approach to modelling the nature of individual
morbidity based on the Big Data approach. Analysis of large amounts of data requires the
definition of groups of attributes that form functional dependencies. However, in real datasets
obtained from different sources, important relationships are defined only for a subset of
attribute group values. There are relationships, for example, between previously transmitted
diseases and the nature of the disease now - such a relationship is established between subsets
of values of different tuples and cannot be found existing methods of searching for hidden data.
The authors will call such dependences partial functional dependencies. Accordingly, the level
of support for such dependencies is low, which does not allow to use them for further data
analysis. At the same time, partial functional dependencies are modified associative rules, but
they are executed only for a part of the data and depend on the time factor. The method of
finding such dependencies will be based on the modification of the method of associative rules,
which allows to reduce the time complexity and to use parallel and distributed mode for
calculation.
Keywords 1
Big Data, associative rules, dependency analysis, Covid`19
1. Introduction
It is a well-known fact that artificial intelligence really gives us many opportunities to understand
and solve many complex problems in the practical and scientific space. The use of artificial intelligence
can be useful primarily in systems that are designed to detect, track and predict disease outbreaks. The
better we can track the spread of the virus, the more effective and faster we can fight it.
By analysing press reports, social networking platforms, and government documents, artificial
intelligence can learn to detect outbreaks faster. It even turns out that such systems already exist and
work, for example, the Canadian system for launching BlueDot [1]. The company's software is designed
to protect against the risk of pandemic outbreaks and protects lives by reducing the impact of infectious
diseases that threaten human health. The developers claim that their software allows you to convey all
the information about the threat of the COVID`19 epidemic within a few hours to the Centres for
Disease Control and Prevention or the World Health Organization. The app also helps detect potentially
infected people.
The Chinese surveillance system used SenseTime's face recognition technology and software to
identify people who may have a fever. The Chinese government has also developed a monitoring system
called the Health Code, which uses a variety of data to identify and assess each person's risk based on
their behaviour, namely travel history, time spent in hotspots, and potential contact with those who
IDDM’2020: 3rd International Conference on Informatics & Data-Driven Medicine, November 19–21, 2020, Växjö, Sweden
EMAIL melnykovanatalia@gmail.com (A. 1); natalya233@gmail.com (A. 2); v.melnikov2013@gmail.com (B. 3); logoyda47@ukr.net (A.
4); yulia.peleshchak@gmail.com (A. 5)
ORCID: 0000-0002-2114-3436 (A. 1); 0000-0002-6875-8534 (A. 2); 0000-0002-7008-4014 (B. 3) 0000-0001-6476-7305 (A. 4); 0000-0003-
1057-6743 (A. 6)
©️ 2020 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
carries the virus. Citizens are assigned a colour code (red, yellow or green), which they can access
through the popular WeChat or Alipay applications for verification [2]. Also, to investigate this
problem, the researchers used a convolutional neural network model to detect patients with COVID-19
using CXR images. They used pre-trained ImageNet and trained the model based on open source X-ray
imaging Chest (CXR) [3]. Other researchers have used of the LSTM model to predict country-specific
risk of COVID-19 virus infection, based on country-specific trends and meteorological data, to predict
the likely spread of COVID-19 disease [4].
Artificial intelligence experts have used machine learning techniques to process online activity,
news, health organizations' reports and media activities to predict the spread of the outbreak in China.
As well as the application of the Bayesian approach to predict the number of deaths in the future, using
empirical data [5].
An important role is played by the problem of analysing the relationships between the individual
characteristics of the patient and the characteristics of dynamics of changes in his condition during
treatment and recovery.
The course of diseases, that caused by infections and viruses (even with known treatment prevention
schemes) is influenced by various factors, namely [6,9]:
• variability of strains,
• nature of interaction,
• features of the distribution area: climatic conditions, development of infrastructure and
connections, quality of medical care, chronic diseases inherent in this area, political situation, etc.
2. The main material
The peculiarity of medical data is their hierarchy and networking. Network data include
information on comorbidities, allergic reactions, etc. These are the direct or indirect factor,
which determines the nature of disease of the individual. Therefore, to find the hidden
dependencies of the data and to determine the nature of the disease of the individual, it is
necessary to find not only linear dependencies in the data.
The task of finding dependencies in the data requires the analysis of dependencies between
dozens of parameters of the studied process and hundreds of possible sources of influence on
this process. Dependencies are nondeterministic, and therefore modelling requires the use of
statistical methods for analysing random processes. Often much of the information is hidden
from observation or is not monitored. This introduces many difficulties in the process of
analysing the collected information.
The modelling process requires data that can be obtained from known statistics, namely:
– the population of the districts of the region;
– the population density;
– the social distance between people;
– the disease duration;
– the probability of disease in human contact; mortality rate;
– the availability of crowded places (supermarkets, churches, pharmacies, markets,
construction sites, gyms);
– the percentage of people who carry the disease asymptomatically;
– the presence of the procedure of isolation of sick people;
– the ability to move a person from the area to the regional centre and back;
– the incubation period
– and others.
The above factors can negatively affect the conduct, interpretation and generalization of
research results, as well as the understanding and interpretation of the phenomenon under
study. For stability of result, it is necessary to use ensembles of models, which are easy to
parallelize.
The analysis of large amounts of data requires the definition of groups of attributes that form
functional dependencies. However, in real data sets obtained from different sources, important
relationships are defined only for a subset of attribute group values. For example, between
previously transferred disease and the nature of the disease now - such a relationship is
established between subsets of values of different tuples and cannot be found by existing
hidden methods. We can call such dependences partial functional dependencies. Accordingly,
the level of support for such dependencies is low, which does not allow to use them for further
data analysis. At the same time, partial functional dependencies are modified associative rules,
but they are executed only for a part of the data and depend on the time factor. The method of
finding such dependencies will be based on the modification of associative rules. This reduces
time complexity and uses parallel and distributed mode for calculation.
As part of the study of the problem is necessary to:
– propose the development of already special methods of forming a training set of data and
preprocessing of attributes, taking into account the specifics of the content of medical data
and environmental data.
– develop an ensemble of data imputation models on the basis of basic models of various
nature as a part of specialized information technology of recovery of the missed data for
the automated processing of information.
– simulate different scenarios of influence by the state at the next stage of forecasting the
dynamics of infection.
2.1. The formal model of the individual
Therefore, for a formal representation of the individual's condition, the task of which is to find a
personalized assessment and find solutions to improve it, it is necessary to build a formal model of the
object, as a model of production expert system, which is usually used to solve this class of problems.
The knowledge base in accordance with the structural scheme of the system of personalized
assessment is the selection of a set of rules R [7,12,14]:
𝑅 = {𝑅1 , … , 𝑅𝑗 }, (1)
where the production of type
𝑅𝑗 = 𝑝𝑑𝑗1 ⋀𝑝𝑑𝑗2 ⋀ … ⋀𝑝𝑑𝑗𝑛 → 𝑘𝑚 (2)
Thus, the production R is a ratio, the elements of which are indicators of the characteristics of the
state of the individual and the assessment of the state of the individual.
𝑅: 𝑃𝐷 → 𝑉𝑆
𝑅 ⊂ 𝑃𝐷 × 𝑉𝑆 = {(𝑎, 𝑣): 𝑎 ∈ 𝑃𝐷 & 𝑣 ∈ 𝑉𝑆} (3)
where
𝑃𝐷 = 𝑃𝐷(𝑎𝑛 ),
𝑝𝑑𝑛 ∈ {𝐴𝑡 ∪ 𝐴𝑡 },
So
𝑃𝐷 = {{𝐴𝑖𝑛 } ∪ {𝐴𝑡 }}, (4)
PD – is a set whose elements are the parameters of the state of the individual, namely the elements
of sets of time-independent characteristics (𝐴𝑖𝑛 ) and time-dependent parameters of the object (𝐴𝑡 ).
An example of rules is the search for optimal conditions and strategic decisions for the treatment of
the individual based on selected characteristics and parameters.
The composition of many informative factors depends on the specific task. In the general case, the
dependencies can be divided into linear and nonlinear. In addition, if for linear dependencies
informative factors are determined by known methods of correlation and analysis of variance, then for
nonlinear dependencies such procedures are often empirical. In our case, the dependencies are predicted
as linear [8,10,11].
Among the parameters of the individual to determine the presence of the disease, the data are divided
into time-dependent and independent. The parameters must be prepared before the analysis, namely it
is necessary to determine the priority data that will affect the results. The importance of finding
relationships between data optimizes the process of determining an individual's resistance to COVID`19
[21].
General Diseces Specifics Laboratory results
The area of the
Identification Was ill of Covid`19 Allergy
inflammatory center
Age Was ill of influenza Edema Temperature
Gender Was ill tuberculosis Thrombosis Heart rate
Weight Diagnose Saturation
Blood group Comorbidities IgM level
Vaccination of
Smoke IgG level
influenza
Vaccination of
Region
tuberculosis
Figure 1: Parameters of the individual to determine the presence of the disease.
2.2. The use of associative rules for study dependencies
The basic concepts in the theory of associative rules are subject set and transaction. A thematic set
is a non-empty set of elements that can be part of a transaction:
I i1 ,i2 ,,ik ,,in ,
(5)
where ik - are the elements included in the subject sets, k = 1..n, n - is the number of elements of the set
I.
The database has a certain set of transactions:
T t1 ,t2 ,,ti ,,tm ,
(6)
where ti - is the corresponding transaction, m - is the total number of transactions.
The concepts of set and associative rule are closely related to another characteristic of an associative
rule - trust, which is calculated as the ratio of a set that has both a condition and a consequence (in other
words, support for an associative rule) to support a set that has only a condition.
Conf X Y = Supp X Y Supp X =
(7)
X t Y t T X t T
X t Y t X t ,
MinSupp and MinConf minimum support and validity thresholds are used to determine the
significance of the rules, which are usually determined by experts based on their own experience:
Supp X Y MinSupp
(8)
Conf X Y MinConf
(9)
Methods for finding associative rules find all associations that meet the constraints of support and
confidence. However, this leads to the need to review a large number of associative rules, which it is
desirable to reduce in such a way as to analyse only the most important of them.
Among the main algorithms for generating associative rules are AIS, SETM, Apriori, AprioriTid,
AprioriHybrid [8]. The efficiency and feasibility of using each of them is determined by the structure
and scope of the data set for which the search for associative rules, as the basis of these methods lies in
the different principles of generation and selection of subject sets – candidates [13,15].
The disadvantages of the above algorithms are solved by the Apriori algorithm that proposed by R.
Agraval and R. Srikant. Unlike AIS and SETM, it eliminates the generation and counting of excessive
numbers of candidates through the using of the antimonotonic properties and can significantly reduce
the set of frequent sets of items and thus reduce the search space for associative rules. The property of
diversity states that if the set Z is not common, then adding a new object Y to the set Z does not change
its frequency (respectively, if Z is not a frequent set, then ZY is not frequent either). Modifications of
the classic Apriori algorithm are AprioriTid and AprioriHybrid [16,19,20].
Using the method of a priori implement the search for associative rules. Since the size of modern
databases can reach quite large volumes (gigabytes and terabytes), the search for associative rules
requires efficient algorithms that are scalable and allow you to find a solution to this problem in a
reasonable time [17,18].
Algorithms for recognizing patterns with learning assume the presence of a retrospective, which
allows you to build statistical models of dependencies x → y, where y ∈ Y, Y user actions (answers) are
observed or a random variable is modelled x ∈ X, X - a set of variables (predictors) that are supposed to
explain the variability of the variable y. Most models with a teacher are designed in such a way that
they can be written as
y f x, ,
(10)
where f - a mathematical function selected from some arbitrary family, β - the vector of parameters
of this function, ε - errors that usually generate unbiased, uncorrelated random processes.
When building a model at fixed sample values, y minimizes the residuals of some function Q (y, β).
As a result, found β̂. This is a vector with optimal estimates of the model parameters. By changing the
shape of the functions f and Q, you can get different models, of which the most efficient model is
preferred. This model provides unbiased, accurate, and reliable y predictions.
2.3. The proposed method
Based on the data analysis, information was collected about patients taking into account the
parameters of the individual to determine the presence of diseases that are characterized as a priority.
Dataset is collected using google form https://docs.google.com/forms/d/1o8CMGVZv6BDkw-
QIYg2F8VQzqcXxqklomRwXCLOZIcY, is funded by Central European Initiative and is verified by
Lviv regional centre Covid`19 resistance. This dataset consists of the following characteristics:
– Age (categorical): 0-15, 16-22, 23-40, 41-65,>66
– Gender (categorical): male, female
– Region (string): Lviv (Ukraine), Chernivtsi (Ukraine), Belarus, Germany, Other
– Do you smoke (Boolean): yes, no
– Have you had COVID`19 (categorical): yes, no, maybe
– IgM level (numerical): [0..0.9) (negative), [0.9..1.1) (indefinite), >=1.1 (positive)
– IgG level (numerical): [0..0.9) (negative), [0.9..1.1) (indefinite), >=1.1 (positive)
– Blood group (numerical)
– Do you vaccinated influenza? (categorical): yes, no, maybe
– Do you vaccinated tuberculosis? (categorical): yes, no, maybe
– Have you had influenza this year? (categorical): yes, no, maybe
– Have you had tuberculosis this year? (categorical): yes, no, maybe
Taken into account 480 responses are presented in dataset.
Sample for training, consisting of states of 30 individuals. For data analysis, it was proposed:
• grouping of data by patient ID,
• separation of factors by patient ID,
• division into factors according to the patient's condition,
• separation of factors according to the treatment scheme.
A three-step algorithm was used to recognize the patterns:
• creating a cluster of patients - to find the behavior of the condition,
• template construction - to find the sequence of state changes,
• next run ConditionType - to predict the next condition of the patient.
The cluster of the studied objects was created by means of R, factoextra packages (Fig. 2 shows the
results of hierarchical clustering):
Figure 2: Dendrogoram of hierarchical clustering
In this work we use k-means and k-medoid separation algorithms. First, we found the optimal
number of clusters using the Elbow method and gap statistics. Gap statistics can be applied to any
clustering method. It compares the total variation of the internal cluster for different values of k with
their expected values at the null benchmark distribution data (ie distribution without explicit clustering).
The reference data set is generated by Monte Carlo simulation of the sampling process [22]. (Fig. 3):
Figure 3: The optimal number of clusters
The x-axis ranges from zero trees to the maximum number of trees in which any variable was used
for splitting which is in this case equal to 500 and is reached by all variables plotted. Therefore, the
maximum depth in created trees is for vaccinated influenza. The first level in the biggest part of “poor
classifiers” is presented by IgG.
For further explore variable importance measures we pass our forest to measure_importance
function and get the following data frame.
variable mean_min_depth no_of_nodes mse_increase node_purity_increase no_of_trees times_a_root
1 Age 1.511688 3023 0.050938625 11.558790 499 112
2 Blood_group 1.820000 3387 0.013201974 9.690663 500 53
3 Gender 1.723688 1484 0.052533296 6.322656 499 111
4 Had_influenz 1.727688 2225 0.034935393 7.862122 499 92
5 Smoke 2.030000 1507 0.005027793 4.138718 500 79
6 Vaccinated_influenza 2.372752 1896 -0.008977258 3.495168 496 25
7 Vaccinated_tuberculosis 2.164000 2348 0.015751848 5.870700 500 28
We can see that all depicted measures are highly correlated.
After selecting a set of most important variables, we can investigate interactions with respect to
them, i.e. splits appearing in maximal subtrees with respect to one of the variables selected. To extract
the names of 5 most important variables according to both the mean minimal depth and number of trees
in which a variable appeared, we have the following result:
[1] "Age" "IgG" "Blood_group" "had_influenz" "IgM"
Naive Bayes shows the density for each features in the dataset (Fig. 4). The accuracy of Naive Bayes
is much less than random forest and is equal to 67%.
Naive Bayes Plot Naive Bayes Plot
0.30
0.30
0 0
1 1
Density
Density
2 2
0.15
0.15
0.00
0.00
0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0
had_influenz had_influenz
Naive Bayes Plot Naive Bayes Plot
0.30
0 0
0.20
1 1
Density
Density
2
0.15
2
0.10
0.00
0.00
0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0
vaccinated_influenza smoke
Naive Bayes Plot Naive Bayes Plot
0 1 2 0 1 2
1
1
var
var
2
2
3
4
grouping
grouping
Figure 4: Naive Bayes plot of density
Random forest shows the better results. 500 trees are built.
OOB estimate of error rate: 16.61%
Confusion matrix:
0 1 2 class.error
0 153 9 17 0.14525139
1 8 88 12 0.18518518
2 1 3 20 0.16666666
The biggest error is for class 1 (COVID’19 - yes). It can be explained by differences in IgG and IgM
representation (data scatter is between 0.00 and 18.00) in different countries.
The minimal depth values for all trees in a random forest is given on Fig. 5.
Figure 5: Distribution of minimal depth of developed trees
Building a template
There are objective and subjective measures of compliance with the associative rule [7]. The tasks
are the above support and confidence. Subjective measures of significance are the elevator and levers.
The rise is determined by the ratio of the preservation of the associative rule to the state of product
support and the effect separately:
Supp X Y
Lift X Y (11)
Supp X * Supp Y
Lift is a so-called generalized measure of connection between two subject sets.
Its meaning can be interpreted as follows:
if Lift X Y 1,
then Supp X Y Supp X * Supp Y , (12)
that is, the state and the consequence do not depend on each other;
if Lift X Y 1,
then Supp X Y Supp X * Supp Y , (13)
that is, the effect is positively dependent on the condition;
if Lift X Y 1,
then Supp X Y Supp X * Supp Y , (14)
that is, the effect is negatively dependent on the condition.
An algorithm for extracting associative rules is proposed. For the relationship with the scheme
R Ai ,dom Ai , i 1,m, (15)
allows you to find statistically significant rules that reflect the dependence of the attribute Am on the
attributes A1 , A2 , , Am1 , , ie the dependence of the species. A1 , A2 , , Am1 Am
The Kullbach-Leibler information index is used as a measure of statistical significance. The
algorithm allows you to search only for dependencies defined by a common set of input data; in
addition, it has a high computational complexity if there are many classification rules.
3. Conclusion
An approach to modelling the nature of individual morbidity based on the Big Data approach is
proposed. Analysis of large amounts of data requires the definition of groups of attributes that form
functional dependencies.
Explained on real data sets obtained from different sources, important relationships are defined only
for a subset of the values of the attribute group.
Dependencies with partial functional dependencies have a low level of support, which does not allow
their use for further data analysis, and partial functional dependencies are modified associative rules,
but they are executed only for part of the data and depend on the time factor.
A method of finding dependences is proposed, which is based on the modification of the method of
associative rules, which allows to reduce the complexity of time and use parallel and distributed mode
for calculation.
4. Funding
Funding of article by grant contribution of the Central European Initiative in according project STOP
COVID`19, Ref. No. 305.2825-20, CEI.
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