Fuzzy Decision Support System

Fuzzy Decision Support System for Coronary Artery Disease Diagnosis Based on Rough Set Theory

Abstract

The objective of this research is to develop an evidence based fuzzy decision support system for the diagnosis of coronary artery disease. The development of decision support system is implemented based on three processing stages: rule generation, rule selection and rule fuzzification. Rough Set Theory (RST) is used to generate the classification rules from training data set. The training data is obtained from University California Irvine (UCI) heart disease data sets. Rule selection is conducted by transforming the rules into decision table based on testing data set and then RST attribute reduction is applied to select the most important rules. The selected rules are transformed to fuzzy rules based on discretization cuts of numerical input attributes and simple triangular and trapezoidal membership functions. A weighing of fuzzy rules is also applied based on rules support on the training data. The system is validated using UCI heart disease data sets collected from U.S., Switzerland and Hungary, data from Ipoh Specialist Hospital Malaysia and verified by three cardiologists. The results show that the system is able to give the approximate possibility of coronary artery blocking without the help of coronary angiography and considered efficient and useful.

1. Introduction

Artificial Intelligence (AI), including artificial neural networks (ANN), fuzzy logic, evolutionary computing, machine learning and expert systems has been widely accepted as a tool for intelligent decision support system. In recent year, there are wide applications of AI in medical decision support systems for diagnosis, prognosis and treatment of patients. One of the first killer diseases in developed country is coronary artery disease as well as in developing country.1, 2 Thus, research on the AI application on the diagnosis of coronary artery disease is very important to support the physician to give the better and accurate diagnosis.

Coronary Artery Disease (CAD) is the development of plaque inside the wall of coronary arteries. The development of plaque will narrow or block the coronary arteries and make the wall of arteries less elastic. This plaque will make the blood difficult to flow freely. The CAD is considered presence when the narrowing of at least one of the coronary arteries is more than 50%. Coronary angiogram or cardiac catheterization is considered as “gold standard” method to diagnose the presence of CAD. This method has high accuracy but it is invasive, risky, expensive and not possible as a diagnosis for large population. Many research works were conducted to diagnose the CAD using less expensive and non-invasive methods such as electrocardiogram (ECG) based analysis, heart sound analysis, medical image analysis and others. 2-5

AI and knowledge discovery from data (KDD) methods have also been used as a decision support tool to diagnose CAD. The AI and KDD methods use heterogeneous data from the patients such as physical and historical data, exercise test, and diagnostic test to develop a computer system that can classify and diagnose the presence of CAD.

There are several research works on coronary artery disease diagnosis. A Multilayer perceptron based medical decision support system was developed to diagnose five types of heart diseases (hypertension, coronary heart disease, rheumatic valvular heart disease, chronic cor pulmonale and congenital heart disease) simultaneously.6 However, artificial neural network itself cannot explain its knowledge, even though the system has high accuracy. Bayesian network model of heart disease is proposed.7 The system could predict the probabilities of heart diseases and dependency among attributes related to heart diseases. A set of machine learning methods was evaluated on the atherosclerotic coronary heart disease.8 The objective is not to compare different machine learning results but to explore the possibilities of both machine learning and medical expertise improving the quality of regular medical practice. Prognosis of cardiac events (cardiac death or non-fatal myocardial infarction) was proposed.9 Diagnosis of ischemic heart disease using various machine learning techniques was developed.10 Data consists of 4000 patients is used. Extension of multi layer perceptron for coronary heart disease diagnosis by making it interpretable was introduced.11 Fuzzy discrimination analysis for diagnosis of valvular heart disease was also proposed.12 Most of these research works use large number of patients. A combination of data mining technique, namely C4.5 and fuzzy modelling was used to diagnose CAD.13, 14 This work emphasized on fuzzy modelling of C4.5 generated rules. This system used 19 attributes of 199 objects to predict the presence of 50% or more narrowing in at least one of coronary artery vessels. There are research works that concentrate on the risk prediction of CAD using risk factor categories.15-18 The works using large amount of data and performed in long term study. The objectives are not the diagnosis but risk prediction of CAD during certain years based of Framingham score with modification such as QRISK1 and QRISK2.

In this work, a decision support system for the diagnosis of CAD is proposed. The system uses Rough Set Theory (RST) technique to discover the knowledge from CAD data sets.19 The discovered knowledge is in the form of decision rules. A RST based rule selection is also proposed. Finally, a fuzzy modelling based on the selected discovered rules is presented to estimate the percentage possibility of blocking without the help of doctor and coronary angiography.

The CAD data sets are taken from University of California, Irvine (UCI) Data Mining Repository.20 Finally, the system is validated using all UCI CAD data sets, Ipoh Specialist Hospital Malaysia and verified by three cardiologists.

2. Materials and Methods

2.1. Data

Coronary artery disease data sets from UCI database repository attract many researchers to build decision systems.21-28 The UCI-CAD data sets contain 920 patients that are collected from Cleveland Clinic Foundation U.S. (303 patients); Hungarian Institute of Cardiology, Budapest, Hungary (294 patients); Veterans Administration Medical Center, Long Beach, California, U.S. (123 patients) and University Hospital, Zurich, Switzerland (200 patients). The results of CAD disease are obtained by coronary angiography. There are 14 attributes of CAD data, which are proved to be complete data set. These attributes can be seen in Table 1.

Most researchers use Cleveland data set that consists of 303 patients because it contains only six patients having missing values on thallium scintigraphic defects or number of vessels colored by fluoroscopy. The number of disease prevalence is 139 out of 303 patients (45.87%). Hungarian data set has the disease prevalence of 106 out of 294 patients (36.05%). Long Beach data set has the disease prevalence of 149 out of 200 patients (74.5%). Switzerland data set has the disease prevalence of 115 out of 123 patients (93.5%). These three data sets have many missing values not just in thallium scintigraphic defects and number of vessels colored by fluoroscopy, but also in the slope of the peak exercise ST segment and serum cholesterol. A few missing values are also found in other attributes of these three data sets. There are two reported works that use Hungarian, Long Beach and Switzerland data sets which contain many missing values to develop CAD diagnosis system which are proposed by Detrano, et al 21 and Pedreira, et al 28. However, Detrano, et al, have the complete version of data sets while Pedreira, et al, eliminates the objects that contain missing data. The three data sets that contain missing values are too valuable to ignore during the development of data driven decision support system. In this work, 661 selected objects from Hungarian and Long Beach data sets, which are incomplete, are used. The missing values are imputed using ANNRST imputation.29-31 These imputed data sets then are used as the training data of RST based rule generation. The data from Ipoh Specialist Hospital, Malaysia, consist of 22 patients having the same attributes as UCI-CAD. All values in thal attribute are missing. This data set will be used as validation data.

2.2. Rule Generation

RST is used to discover the knowledge from the training data set. RST rule discovery is based on a decision table such as Table 2. A decision table is defined as:

(1)

is called decision. In this work, D is attribute num (the presence of CAD). C is set of conditions, which are attributes age, sex, …, ca and thal or written as {age, sex, …, ca, thal}. For and x represents the object, indiscernibility relation is defined as:

(2)

The indiscernibility relation (2) will induce a partition of U into sets using only condition in A. Each object in the set cannot be discerned from other object in same set. The sets of classified objects are called equivalence classes denoted as. Set approximation is used when a decision concept such as d cannot be defined in a crisp manner. For, the approximations of using only information in A are a lower-approximation and an upper-approximation that are defined as:

(3)

(4)

The set that contains objects that cannot be classified as definitely inside X or outside X is called boundary region of X:

(5)

D is decision and as conditions, A-positive region of D is defined as:

(6)

represents the partition of U according to decision D.

The condition attributes of decision system DS may be redundant so they can be reduced. The reduction of DS will result in reducts. A reduct is a minimal set of attributes such that . A reduct is combination of conditions that can discern between objects as well as all conditions. Reducts can be computed using discernibility matrix and discernibility function. 32 For Table 2, assuming all the missing values are removed and discretized using equal frequency binning,32 one of the shortest reducts is {age, thalach, ca}.

Sometimes reducts computed based on objects relative discernibility are more interesting than full discernibility reduct, especially for decision rule generation. Once all of the relative reducts are determined, a set of decision rules can be generated from those reducts. Various algorithms are available to generate rules from those reducts. RST can handle the discrete values only. Thus, discretization of numerical attributes must be done. Boolean reasoning algorithm is used to discretize the numerical attributes. 32 Number of “cuts” is generated during the discretization process.

Consider as decision table. defines a series , where and . Hence, the decision rules can be generated in the form of . C can be the condition attributes of reduced form of decision table (reduct or relative reduct). Using first object relative reduct, referring to the first, second, eighth and fourteenth objects and ignoring objects that contain missing values, rule “if age = 3 then num = 0” can be generated. This work uses relative reduct as a base to generate decision rules. The definition of rule support is described as how many objects match the corresponding rule. In aforementioned generated rule, the support is four because it has four objects that match the rule. Support can be used as rule filtering criterion when there are too many rules generated.

2.3. Rule Selection

There are many studies that proposed various rule filtering methods.33-39 In this work, we propose modified RST based rule importance measure to select the rules by converting the rules to decision tables.34 Filtering method based on rule support is applied to select the rules to reduce the amount of rules before applying rule importance measure to select the most important rules. The modification is proposed by applied this method to decision system and converting rules to decision tables based on testing data, which is complete CAD data set instead of training data, which is incomplete CAD data set for rule importance measurement. Consider as a set of rules generated from training decision tables. If there are i objects on testing decision table, a new decision table can be formed. The value of attribute of object is 1 if can be applied on both its antecedents and consequence. The value is 0 if the rule cannot be applied. The value equals decision value for column j+1. With a = 1,…,j and b = 1,…,i. The new decision table then can be reduced using RST reduct concept explained in subsection 2.2. The attribute of the shortest reduct are chosen as the selected rules based on their importance. For illustration, consider Table 3 as an example of rule set generated by RST with their support.

Using support filtering with stopping criteria based on accuracy and coverage, the number of rule will be reduced. If there are l number of removed rule, the number of rules become j = k – l. The j number of rules then applied to the testing data set which is the complete CAD data set to create new decision tables with rules as the attributes as shown in Table 4.

Table 3 Example of k rules with their support

Reduct computation is applied to the Table 4 using ROSETTA based on Johnson's algorithm. 32, 40 The attributes of the reduct is then the selected rules.

Table 4 Decision table with rules as attributes

2.4. Fuzzy Modelling

The selected generated RST rules are crisp. To develop fuzzy model of decision support system, three steps must be performed. These steps are fuzzification, inference and defuzzification. Fuzzification must be applied to convert the crisp rules into fuzzy rules.41 The fuzzy membership functions are in the form of triangular and trapezoidal shapes. Fuzzification of a numerical-valued variable is done by using combination of intuition, experience and analysis of the set of rules and conditions associated with the input data variables. There are no fixed procedures for the fuzzification process.

Triangular membership function of attributes A is described in the form:

(7)

Trapezoidal membership function of attributes A is described in the form:

(8)

Values of a, m, n and b are determined based on discretization results. As an example, the numerical attribute age is discretized using Boolean reasoning into three discrete values which are [*, σ1), [σ1, σ2) and [σ2, *) that mean “less than σ1”, “greater or equal than σ1 and less than σ2 “ and “ equal or more than σ2 “ respectively. Therefore, the “cuts” are σ1 and σ2. All numerical value of conditions are fuzzified based on the value of these discretization “cuts”. Two trapezoidal and single triangular membership functions of attribute age, which are LOW, MEDIUM and HIGH, can be generated as shown in

For the attribute that has only two values, the membership function can be made as shown in 2. In this case, c is determined intuitively. As an example, the numerical attribute thalach is discretized using Boolean reasoning into three discrete values which are [*, σ) and [σ, *) that mean “less than σ” and “ equal or more than σ “ respectively. Therefore, the “cuts” are σ. Two trapezoidal and single triangular membership functions of attribute age, which are LOW and HIGH, can be generated. The nominal attributes can have the fuzzy membership function. Crisp value is the fuzzy value with the degree of membership function is one with no overlapping between the membership functions.

For simplification, no optimization is applied to the fuzzy membership functions. Fuzzy weighing method is proposed based on selected RST rules support of training data. If the nth crisp rule has support sp(n) then the corresponding fuzzy rule weight is:

(9)

and i is the total number of rules.

Consider Table 5 for an illustration of fuzzification of crisp rules for medical data. The rules are crisp.

Table 5 Example of crisp rules

After fuzzification, the fuzzy rules generated are shown in Table 6.

Table 6 Example of fuzzy rules

The Mamdani inference engine is used for the inference process.42 Centroid defuzzification is chosen to get the numerical output of CAD diagnosis. For AND operator and implication, min function is used. Centroid defuzzification is defined as:

(10)

An example of Mamdani fuzzy inference process for the medical data set using only two rules is shown in 3

3. Results

There are 358 objects (patients) in the training set. Using ROSETTA software 32, RST rule generation results in 3881 rules. RST based rule selection method is able to select only 27 rules as shown in Table 7. These rules are fuzzified using the proposed method described in section 2.4. Based on these fuzzified rules, Fuzzy Decision Support System (FDSS) to diagnose CAD is developed.

To test the performance of fuzzy decision support system, all four data sets from UCI-CAD is used which are Cleveland, Hungarian, Long Beach and Switzerland. All of the data sets contain missing values. Cleveland has only six objects that have missing values. Switzerland is the largest number of missing values. For comparison, multi layer perceptron ANN, k-Nearest Neighbour (k-NN), C4.5 and Repeated Incremental Pruning to Produce Error Reduction (RIPPER) methods are implemented using WEKA software 43 to diagnose the CAD on the four UCI-CAD data sets and Ipoh Specialist Hospital data set . The result can be seen in Table 8, 9 and 10.

Table 7 Selected Rules

Table 8 Accuracy of different diagnosis methods on UCI-CAD data sets and Ipoh data set

Table 8 shows that FDSS has the best accuracy in Ipoh data set. FDSS and RIPPER have the best accuracy in Cleveland data set. MLP-ANN has the best accuracy in Switzerland data set. k-NN has the best accuracy in Hungarian and Long Beach data sets. The average shows that FDSS has better accuracy than the others. k-NN got its high accuracy on Hungarian and Long Beach which the training data mostly are taken from these data sets. k-NN is distance based classifier which will have very high accuracy if it is applied on the training data set.. FDSS has better accuracy than k-NN in Cleveland and Switzerland data sets. The knowledge of FDSS is transparent where k-NN's knowledge is less transparent. The result of FDSS is also numerical value which represents the percentage of coronary artery blocking where k-NN is categorical which can only have yes or no.

Table 9 Sensitivity of different diagnosis methods on UCI-CAD data sets and Ipoh data set

Table 9 shows that k-NN has better average of sensitivity than FDSS. FDSS has the best sensitivity on Ipoh data set but has the worse sensitivity on Switzerland data set. But if specificity is considered as in Table 10, FDSS has the best of specificity on Switzerland data set.

Table 10 Specificity of different diagnosis methods on UCI-CAD data sets and Ipoh data set

The average specificity of FDSS is below MLP-ANN and k-NN classifiers. From the results, it can be considered that FDSS is comparable with the other classifiers. However FDSS has advantage of transparent knowledge, handling continuous values directly and numerical output that represent the approximate blockage of coronary arteries. FDSS has good diagnosis accuracies for all data sets, which are between 0.7 and 0.84 and the average is 0.79. The sensitivities of FDSS are between 0.7 and 1 and the average is 0.81. The specificities of FDSS are between 0.49 and 0.91 and the average is 0.66. FDSS can be considered robust and has the best diagnosis performance compared to the others.

Comparison with three cardiologists on 30 arbitrarily selected patients from Cleveland shows that FDSS is better as shown in Table 11.

Table 11 Diagnosis performances of FDSS on Cleveland data set

For data set having many missing values, the comparison between FDSS and cardiologists is performed by using Long Beach data set. The result is shown in Table 12.

Table 12 Diagnosis performances of FDSS on Long Beach data set

The ability of FDSS estimating the possibility of CAD in numerical value or percentage is demonstrated in 4. There is only one cardiologist able to provide the results as percentage possibility of blockage of the coronary artery. The other cardiologists only provide the results of “yes” or “no”. It is found in the graph that the possibility estimation of CAD is similar with the cardiologist's estimation, even FDSS has better accuracy.

4. Discussion

The proposed FDSS is able to diagnose the presence of CAD with possibility level. The proposed method is proven able to extract the knowledge directly from raw medical data without the help of medical doctor or cardiologists. The resulting knowledge is in the form of small number rules, which is easy to understand by human. The proposed fuzzy modelling is able to fuzzify the extracted crisp rules, which are used to develop the fuzzy inference system. The comparison of FDSS with other artificial intelligence techniques such as ANN, k-NN, C4.5 and RIPPER shows that FDSS is generally better than other methods and robust for all UCI-CAD and Ipoh Specialist Hospital data sets. FDSS is verified by three cardiologists and provides good results. The result of FDSS possibility estimation of CAD is similar to the estimation of the cardiologist.

With these findings, cardiologist can make better diagnosis based on historical data, risk factors and non-invasive tests and decide whether coronary angiography should be performed or not. The result of FDSS in the form of possibility level is very helpful to cardiologist to determine the further step of CAD diagnosis, because the possibility level represents the severity of CAD. Screening of large number of patients suffered from CAD will be available with the help of FDSS fast diagnosis. Since it does not need full complete input data, FDSS can be used in the place where there is no advanced test equipment available. For junior medical doctor, this FDSS will be helpful for the education of CAD diagnosis, because FDSS provides explainable result and understandable reasoning in the form of decision rules.

However, the ability of FDSS is still can be improved. Due to the limited data for the training purpose of FDSS, the more number of CAD data can be used to increase the generalization ability of FDSS. The new type of input data also can be included such as body mass index, smoking habit, HDL, triglyceride, family history, diastolic blood pressure and other necessary data. The optimization method can be applied to determine the optimum membership function of fuzzy inference system to provide the better diagnosis accuracy.

5. Conclusion

The development of FDSS for CAD diagnosis has been demonstrated in this paper. The system, which is based on evidence from UCI-CAD data sets, is successfully able to diagnose the presence of CAD with the level of possibility. The comparison with other computer based methods and the verification of three cardiologists show the good performance of FDSS. The limitation and the completeness of CAD data is still the problem in this study. Further work is necessary by considering more number of data and more input attributes for the process of FDSS development. The proposed FDSS is useful to help cardiologist for the better diagnosis and to decide whether coronary angiography should be performed or not. FDSS is helpful for the training and education of junior medical doctor.

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