Decision support systems (DSS) allow us to help the doctor in making diagnoses to the patient, also medical DSS help to assess the need for a particular examination of the patient. In this article methods of medical data classification are considered, these methods are the part of the medical DSS. The paper includes investigation of data classification methods as hierarchical cluster analysis, k-means analysis and discriminant analysis. The selected methods are implemented using the example of cardiological data. A hypothesis is put forward that it is possible to determine the presence or absence of tuberculosis in a person from cardiological data by using data classification methods. Such indicators as sensitivity and specificity evaluate the effectiveness of the methods. In addition, ROC and AUC are presented. Thus, the DSS will be able to determine a certain degree of probability to assume the presence of tuberculosis in a person. The doctor will decide on the need for additional examinations depending on the values obtained,
Currently, the creation of decision support systems (DSS) is relevant, and this
direction is also developing in the field of medicine. DSS allow us to help the doctor
in making diagnoses to the patient. In addition, with the help of these systems, it is
possible to determine the need for various examinations for the patient [
The paper discusses methods of data analysis that will be implemented in the medical DSS in order to help doctors. The paper implements such methods as hierarchical cluster analysis, k-means analysis and discriminant analysis.
The parameters of electrocardiogram (ECG) were used as experimental data. This data is depersonalized.
With implementing the methods of medical DSS a hypothesis is put forward about the possibility of predicting the presence or absence of tuberculosis by ECG parameters. The sample contains a nominal variable (tb), which reflects the presence of diagnosed tuberculosis in a person (tb = 1) or its absence (tb = 0). The experimental data collected ECGs recorded in people with a confirmed form of tuberculosis in the second stage of the disease.
Currently ETU “LETI” under the leadership of Professor Kalinichenko A. N. is
doing the similar studies. However, investigations of ETU “LETI” have a direction
different from this work. They research the detection of signs of cardiac disease in
ECG using machine learning [
The sample used in the study is divided into training and test samples, where the mathematical model is created on the training one, and the quality of the obtained model is evaluated on the test one. As a result, a model and an accuracy value of the correct prediction of belonging to the group are obtained for each of the considered methods.
An approach with training of DSS methods based on medical data will make it possible to make an early diagnosis of the patient's health condition. This means that it is possible to assume with a certain degree of probability that a person has signs of tuberculosis or not according to the recorded ECG. If possible signs of the disease are detected, this patient should be sent to get a more detailed examination together with a pulmonologist.
The purpose of this work is to implement classification methods to the medical SPR for early diagnosis to determine the presence or absence of tuberculosis signs. In accordance with this goal, the following tasks were identified: to compile descriptive statistics of the initial experimental data, to investigate and apply methods for classification on experimental data, and to formulate a conclusion.
The performance of the methods is evaluated using sensitivity and specificity
indicators. Sensitivity is the percentage of correctly classified "ill" people, and
specificity is the percentage of correctly classified "healthy" people [
General information of the person and parameters of his cardicycle were taken to study the methods of data classification and subsequent verification of the proposed hypothesis about the possibility of determining the presence or absence of tuberculosis in a person from cardiological data.
A cardiocycle (or cardiac cycle) is a period of blood circulation generated by the
cyclic activity of the heart. The measurement unit for this periodicity is one cardiac
cycle. The length of the cardiocycle is the period of cardiac contractions [
The main elements for the ECG analysis are the start and end time of the elements of the cardiocycle, as well as the PQ interval, the QRS complex, the ST segment, the QT interval and the P wave stands out especially among the elements of the cardiocycle.
The data is presented in the form of a table, where each row corresponds to one ECG. Also in the same row in columns contains non-personally-identifying information about the person. Below is a table with parameters for analysis and explanations to them (Table 1).
The total sample consists of 5928 registered ECGs. Below is a table with general information about people from the data sample (Table 2).
The distribution of the number of people according to their age classification is also presented (Fig. 2). In the sample by age, there is a bias towards people over 18 years old. This is explained by the fact that ECG registration of persons under 18 years old is possible in the presence of a parent and with his permission, so there were few persons of younger groups in the collected data.
All
The following table includes the main values of the number of ECGs for different groups (Table 3). l l
A
It should be noted that not all parameters of the cardiocycle were calculated for all ECGs, so observations with partially uncalculated parameters were automatically discarded methods implementation. 2.2
This section describes methods of data analysis and provides brief information on
them [
Cluster analysis is used to separate the original data into groups (clusters) that are
amenable to interpretation so that the elements of one group were similar in the
parameters, while elements from different groups should differ from each other [
Hierarchical cluster analysis is used for relatively small numbers of observations. During the analysis, initially each observation is located in its own cluster, then neighboring clusters are combined in pairs until there are only two clusters left.
K-means analysis allows you to divide an arbitrary data set into a given number of
groups so that the objects of the same cluster are close enough to each other, and the
objects of different groups do not intersect [
First, the center of the class is determined, then all objects within the specified threshold value from the center are grouped.
Discriminant analysis is a method of statistical analysis that allows you to divide
data into disjoint groups. This method allows us to identify the variables that affect
the separation, as well as their weight coefficients [
IBM SPSS Statistics 23 software was used in order to implement selected methods.
IBM SPSS Statistics is a statistical analysis platform with a set of functions [
The use of the hierarchical cluster analysis method did not lead to significant results. The number of observations in 5928 recorded ECGs was too large as a sample for this method.
Further, the number of observations in the sample was reduced to 50% of randomly selected observations. As an assumption, a range was set for the number of classes: there should be 2-3 clusters. This was done because a huge number of clusters are obtained on this sample without this restriction. The values in two or three clusters were chosen based on the following: we need to get two clusters with measurements of people without tuberculosis and with tuberculosis. The possible number of three clusters is taken to compare the results.
The model was built, its variables were saved with the indication of belonging to the cluster. A conjugacy table was constructed for two variables containing information about the distribution of all variables into 2 and 3 clusters in order to evaluate the performance of this method (Figure 4).
According to the table almost all observations fell into the first cluster, it also observed when the data divided into two clusters and into three clusters. It is also seen that the second and third clusters in both divisions are very small relative to the first cluster. If we compare the decision to divide into two clusters or three, we can conclude that the two-cluster solution is the most stable.
Further, for the sake of clarity of the obtained solution an analysis of the averages was carried out, the part of the resulting picture is presented below (Fig. 5).
The target variable – the variable of the presence or absence of tuberculosis in this dimension (tb). During the application of hierarchical clustering it was found that the average values of clusters are 0.24 and 0.73, where 0 is “healthy” and 1 is “sick”. You can also pay attention to other parameters, for example, taller people fell into the “healthy” cluster, and almost all smokers fell into the “sick” cluster. It is worth noting the average weight of the subjects in the second cluster – 138 kg, which is quite a lot.
When analyzing this model in detail we conclude that hierarchical clustering is not suitable for working with this sample of medical data.
When implementing the k-means method two clusters are initially set: people without a diagnosis of tuberculosis and people with diagnosed tuberculosis (parameter tb=0 and tb=1, respectively). There are many observations in the medical dataset, so 10 iterations were set for the method to work.
The centers of the two clusters obtained are presented below (Fig. 6).
We also obtained an estimate based on Fischer statistics on the significance of the parameter in the differentiation of clusters (Fig. 7).The figure below reveals an example that shows that the target variable tb is significant, as is weight, height, and smoking. The most significant parameters among the parameters of the cardiocycle are the R wave, S wave and the QRS complex.
In addition, the k-means method obtained results is similar to the hierarchical clustering method: outputs data on the number of observations in clusters are 2331 observations in the first cluster and 30 observations in the second cluster. The obtained values coincided with the values for the number of observations when dividing into two clusters during hierarchical clustering. These calculations were obtained by randomly selecting 50 % of all observations.
When using the k-means method with the same parameters on a full sample the following division was obtained by the number of observations in clusters: 4707 and 56 observations, respectively. Thus, the result was obtained that one cluster is dominated by data when clustering into two groups.
Two additional parameters were created using of the k-means clustering method: indicating the number of the membership cluster and the distance to its center.
Next a graphical illustration of the results of this method was constructed: the grouping variable is the cluster number, the differentiating variable is the distance to the cluster center. The figure below, as well as the line on the cluster, shows the median value (Fig. 8).
Based on the results of the analysis it can be concluded that the parameters of the R wave were the most significant parameters in clustering by this method. Below is the spread of the R wave indicator depending on the presence or absence of tuberculosis (Fig. 9).
The figure shows that the variations of this indicator differ depending on the presence or absence of tuberculosis, but visually almost half of the values of the indicator are the same both in the presence of tuberculosis and in its absence. According to the results of the clustering analysis the k-means indicator is the most significant when divided into groups. This leads to the conclusion that the model is not sufficiently accurate using the k-means method.
Then the discriminant method was implemented and investigated. The sample was
first divided into training and test samples: 60% and 40%, respectively [
A table "Group statistics" was obtained with an indication of the average values of each parameter, its standard deviation by group. The inequality of the mean and standard deviation does not prove that these variables are distinctive features of the selected clusters.
The figure below shows the calculated values of the variables. Parameters whose values in the table are greater than 0.05 can be excluded later for analysis purposes.
From the figure below it can be seen that there are parameters that are insignificant when divided into groups, for example, p_da, t_da and others. Thus, they can be excluded when composing the equation (Fig. 10).
The coefficients of the canonical discriminant function were also obtained to create the equation (Fig. 11).
The accuracy of the division into clusters is determined by the distance between the average values of the discriminant function in the studied clusters. The greater the distance, the better the groups are separated. The values of the centroids of the groups are as follows: -0.376 and 1.242.
You can determine the quality of the model based on the results of the classification at the following table (Table 4).
In the training sample the sensitivity is 71.4% and the specificity is 82.4%. In the test sample the sensitivity is 71.5% and the specificity is 83.1%. This shows good accuracy of this model.
In addition, a ROC curve was constructed, the area under the curve of which was 0.853 (Fig. 12).
Using the table with the coordinates of the curve points the threshold value for the final discriminant equation 0.4511434 was selected. At this threshold the sensitivity is 76.4% and the specificity is 76.5%.
The threshold value was selected from the points of the coordinate ROC. The sensitivity and specificity values were selected so that the sum of sensitivity and specificity was the maximum. Three methods were implemented: hierarchical cluster analysis, k-means analysis, and discriminant analysis.
Analysis of the hierarchical cluster method showed that this method is not suitable for analyzing large datasets. Even with the usage of reduction in the number of observations in the sample it was not possible to obtain acceptable results.
Analysis of the k-means method showed that this method can be used for classification problems into two clusters "sick" and "healthy", but the accuracy of this method did not show high results. The parameters that were identified by the method as the most significant have not significant differences in the spread between "healthy" and "sick". For more accurate operation of this method it is necessary to filter out the least significant parameters and continue a more detailed study.
The discriminant method analysis allowed us to obtain a discriminant equation with sensitivity and specificity values of 76.4% and 76.5% respectively. Based on the selected sensitivity and specificity values, a threshold was selected for working with the discriminant equation.
In order to implement the best method in terms of sensitivity and specificity in medical DSS it should be tested on a larger sample size. Also for better accuracy in predicting the probability of a person having second-stage tuberculosis, crossvalidation should be performed. 5
In this paper several classification methods for working in the medical DSS were investigated. The idea of creating a medical DSS is as follows: according to the ECG parameters the trained methods determine the degree of probability of the presence of tuberculosis of the second type in the examined person, whose open symptoms are practically not observed. Thus, the system will help in the early stages of the disease to determine the presence of it on the ECG.
Medical data were used as experimental data in order to train DSS methods. Medical data includes parameters calculated from an electrocardiogram, as well as general impersonal parameters about its owner (height, weight, age, etc.). The experimental sample consisted of more than five thousand electrocardiograms. Also a hypothesis was put forward and tested about the possibility of determining the presence or absence of signs of tuberculosis in a person by the parameters of an electrocardiogram. This hypothesis was confirmed.
Three methods were implemented: hierarchical cluster analysis, k-means analysis, and discriminant analysis. The program for statistical data processing IBM SPSS Statistics was used to carry out the work.
Of the methods considered in this paper the most suitable for the classification problem with a nominal target variable on the example of the study of medical experimental data was the method of discriminant analysis. This method is similar to regression analysis, which will be studied further, as well as other classification methods that are not included in this work. In the future the model should be refined to obtain a higher accuracy of the medical DSS.