AIP Conference Proceedings 2023, 020226 (2018); https://doi.org/10.1063/1.5064223 2023, 020226
© 2018 Author(s).
Result comparison between categorical and numerical predictor variables on CART method in predicting factors related to
diabetic retinopathy in patients with type 2 diabetes mellitus
Cite as: AIP Conference Proceedings 2023, 020226 (2018); https://doi.org/10.1063/1.5064223 Published Online: 23 October 2018
S. F. Hariany, T. Siswantining, A. Bustamam, et al.
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Result Comparison Between Categorical and Numerical Predictor Variables on CART Method in Predicting Factors Related to Diabetic Retinopathy in
Patients with Type 2 Diabetes Mellitus
S. F. Hariany
1, T. Siswantining
1,a), A. Bustamam
1, and B. Budiman
21Department of Mathematics, Faculty of Mathematics and Natural Sciences (FMIPA), Universitas Indonesia, Depok 16424, Indonesia
2Endocrine Metabolic Division, Department of Internal Medicine, Faculty of Medicine, Universitas Indonesia, Salemba Campus, Jakarta 10430, Indonesia
a) Corresponding author: [email protected]
Abstract. CART (Classification and Regression Tree) is a classification nonparametric method that employs learning sample to construct decision tree. Type 2 Diabetes mellitus is classified under diabetes mellitus group that could result in complication, both macrovascular and microvascular. Diabetic Retinopathy is a part of microvascular complication of diabetes mellitus that is considered as the most frequent cause of blindness in adult. Predicting factors related to diabetic retinopathy is important to be done to decrease the prevalence of diabetic retinopathy. The aim of this research is to determine the factor related to diabetic retinopathy in patients with type 2 diabetes mellitus using CART method. CART method is applied in two types of independent variable data (numeric and category). The research uses 174 patients with type 2 diabetes mellitus in Cipto Mangunkusumo Hospital Jakarta as its sample. From the result of analyzing numeric data, the factor related with diabetic retinopathy is microalbuminuria, blood creatinine, gylocohemoglobin, and triglyceride. Meanwhile, from categorical data, factors that has correlation with diabetic retinopathy is microalbuminuria, 2 hour post prandial glucose, the history of diabetes mellitus in the family, and fasting blood glucose. From these two types of data that are analyzed using CART method, it is concluded that microalbuminuria is considered as the major factor that is related to diabetic retinopathy in patients with type 2 diabetes mellitus.
Keywords: Classification and Regression Tree, diabetes mellitus type 2, microalbuminuria
INTRODUCTION
Diabetes mellitus is a group of metabolic disorder with the characteristic of hyperglycemia that is caused by the anomaly in insulin secretion, insulin production, or both [1]. The last estimation by IDF (International Diabetes Federation) finds that there are 382 million people living with diabetes all around the world in 2013. This statistic is predicted to increase to 592 million people in 2035. In Indonesia, the proportion of diabetes mellitus in 2013 increases by almost double compared to 2007.90 % patient with diabetes mellitus suffers from type 2 diabetes mellitus [2].
An uncontrolled diabetes mellitus, in a long run, could cause microvascular complication. Diabetic retinopathy is a progressive microangiopathy that is characterized by the damage and blockage of blood vein that resulted in a disturbance in the nutrition for retina [3]. Diabetic retinopathy is the major cause of blindness in adult age, ranging from 20 years old to 74 years old [4]. The DiabCareAsia 2008 Study reports that 42 % of people suffering from diabetes mellitus di Indonesia also experiences retinopathy complication [2].
The risk of having diabetic retinopathy is proportional to the amount of time in which a person suffers from diabetes mellitus [5, 6]. It had been reported that the diastolic blood pressure and glycohemoglobin are associated with diabetic retinopathy in patients with type 2 diabetes mellitus. Other factors that are related with diabetic retinopathy is the total amount of cholesterol, creatinine clearance [7], microalbuminuria, and systolic blood pressure [8, 9]. There are also other suspected factors that are related to diabetes mellitus, such as blood glucose, lipid profile, and blood creatinine.
CART is a classification nonparametric method that employs learning sample to construct decision tree.
Decision tree constitutes of nodes that represent variable respond classes. The principle of CART algorithm is to find the best split from all available splits to separate a set of data into two parts with the maximum homogeneity.
CART method would produce classification tree if the response variable is categorical. Meanwhile, it would produce regression tree if the response variable is continual [10]. It is essential to identify factors related to diabetic retinopathy in patients with type 2 diabetes mellitus, and thus this research seeks to determine the factor related to diabetic retinopathy in patients with type 2 diabetes mellitus.
METHODS
This research is a retrospective research using medical record (status) of patient with type 2 diabetes mellitus in Cipto Mangunkusumo Hospital that is located in Jakarta. The criteria for this research sample are the outpatients of with type 2 diabetes mellitus who are above 18 years old that are currently treated in the diabetic clinic of Cipto Mangunkusumo Hospital. This research does not take into account other eye diseases that are caused by diabetes mellitus. 174 patients with type 2 diabetes mellitus are selected in this research through stratification sampling with the approval of the ethic committee.
CART method is used to determine factor related to retinopathy diabetic in patients with type 2 diabetes mellitus.
The algorithm principle of CART is to discover the best filter based on all available filters to sort a set of data into two parts with the maximum homogeneity. This method produces a decision tree composed of nodes representing variable respond classes. To measure homogeneity in a node, we need an impurity function. Let j = 1, 2 is the number of response variable classes, and !!,!!represents the probability of a random object to be classified into the first or second class. Impurity function is a symmetrical function of !!,!!. If the value of impurity function in a t node is notated as i(t), then
! ! = Φ(!!,!!) (1)
There are several way used to define i(t), such as Gini index [11]. Let ! !! stands for the probability of an object to be a member of j class in a t node. The Gini index in t node can be defined as
! ! = ! !! !(!|!)
!
!!!,!,!!!
(2) If a split s divided the object from t parent node to a child node in the right child node tR with the proportion of the amount of object that is in tR as pR, and the left child node tL with the proportion of the amount of object that is in tL as pL, so the function value decrease of impurity function is
∆! !,! = − !!!!! !! !+!! !!!!! ! !! !+!! !!!!! !!! ! (3)
∆! !,! is used as the criteria of goodness of split in a t node. A split s is considered as the best filter in t node if it has the biggest amount of ∆! !,! compared to other splits. The splitting process will stop when there is only one object left in the last node, or if all object in a class on that node. Figure 1 shows a flow chart of the CART method.
In this research, the response variable is the diabetic retinopathy status in a patient (whether the patient suffers from retinopathy or not). Meanwhile, the predictor variable that are used consist of 16 variables, which are sex, age, systolic blood pressure, diastolic blood pressure, diabetic duration, the history of diabetes mellitus in family, body mass index, fasting blood glucose, 2-hour post prandial blood glucose, glycohemoglobin, triglyceride, total cholesterol, LDL cholesterol, microalbuminuria, and blood creatinine. The data is analyzed by IBM SPSS Statistic 23 software.
FIGURE 1. Flowchart of CART method TABLE 1. Result of terminal nodes from numerical data
Node Node Gain
Response
N Percent N Percent
8 1 0.6 % 1 5.6 % 100.0 %
2 4 2.3 % 3 16.7 % 75.0 %
4 7 4.0 % 3 16.7 % 42.9 %
6 9 5.2 % 3 16.7 % 33.3 %
10 30 17.2 % 5 27.8 % 16.7 %
9 123 70.7 % 3 16.7 % 2.4 %
RESULTS
Analysis of CART Numeric Data Result
In analyzing, the data that is acquired is not categorized based on the health norm. There are six terminal nodes in this research.
Based on Table 1, from these six terminal nodes that are produced, the nodes that represent the class of patients with type 2 diabetes mellitus with a positive status in diabetic retinopathy are the eighth node and the second node.
Based on Fig. 2, the characteristic of patients with type 2 diabetes mellitus with retinopathy diabetic complication is as follows:
• If patients with type 2 diabetes mellitus are detected to have microalbuminuria score more than 5714.5mg/g, the patients is predicted to have diabetic retinopathy.
Yes No
Start
!=!!≤!!" ; i = 1, 2, …, 16; z = 1, 2, …, 174
argmax
!!!!!"−!! !(!|!)!
!!!
+!!!! !(!|!!)!
!!!
Finish
!!,!!, and !(!|!)=!(!,!)/!(!)
• If patients with type 2 diabetes mellitus are detected to have microalbuminuria score less than 5714.5mg/g, creatinine blood less or equal with 4.59 g/dL, glycohemoglobin less or equal with 11.05 mg/dL, and triglyceride more than 411.5 mg/dL, the patient is predicted to have diabetic retinopathy.
FIGURE 2. Classification tree result (Numeric data)
TABLE 2. The truth classification level (Numeric data)
Observed Predicted
Negative RD Positive RD Percent Correct
Negative RD 155 1 99.4 %
Positive RD 14 4 22.2 %
Overall Percentage 97.1 % 2.9 % 91.4 %
TABLE 3. Result of terminal nodes from categorical data
Node Node Gain Response
N Percent N Percent
13 3 1.7 % 2 11.1 % 66.7 %
3 9 5.2 % 2 11.1 % 22.2 %
14 23 13.2 % 5 27.8 % 21.7 %
16 23 13.2 % 4 22.2 % 17.4 %
4 21 12.1 % 3 16.7 % 14.3 %
12 13 7.5 % 1 5.6 % 7.7 %
8 18 10.3 % 1 5.6 % 5.6 %
11 44 25.3 % 0 0.0 % 0.0 %
15 20 11.5 % 0 0.0 % 0.0 %
TABLE 4. The truth classification level (Categoriy data)
Observed Predicted
Negative RD Positive RD Percent Correct
Negative RD 155 1 99.4 %
Positive RD 16 2 11.1 %
Overall Percentage 98.3 % 1.7 % 90.2 %
Based on Table 2, the risk of classification error in predicting new object class by using classification tree that are produced is 8.6 %.
Analysis of CART Categorical Data Result
In analyzing, the data that is acquired is categorized based on the norm healthy that are contained in [3]. There are nine terminal nodes are created from the classification tree that are produced.
Based on Table 3, from the nine terminal nodes, only the terminal node (Node 13) represents the class with positive diabetic retinopathy.
The characteristics of patients with type 2 of diabetes mellitus that are predicted to have diabetic retinopathy, based on Fig. 3, are:
1. patients with microalbuminuria score ≤ 300 mg/g,
2. patients with 2-hour post prandial blood glucose score > 200 mg/dL, 3. patients that have family members with diabetes history
4. having the fasting blood glucose score ≤ 126 mg/dL
Based on Table 4, the risk of classification error in predicting new object class by using classification tree that are produced is 9.8 %.
FIGURE 3. Classification tree result (Category data)
DISCUSSION
Analyzing two types of data result in the strength and weakness of each analysis. Based on numeric data, microalbuminuria is a main factor related to diabetic retinopathy. Patients with type 2 diabetes mellitus are predicted to have diabetic retinopathy if they:
• have microalbuminuria score more than 5714.5mg/g, or
• have microalbuminuria score less than 5714.5mg/g, creatinine blood less or equal with 4.59 g/dL, glycohemoglobin less or equal with 11.05 mg/dL, and triglyceride more than 411.5 mg/dL
The result produces the value limit that are considered abnormal (microalbuminuria level is higher, beyond the normal level). Moreover, the characteristic from the second point tends to be not suited to the medical diagnosis.
The validity of numeric data classification tends to be higher compared to the classification of categorical data classification.
If the value of each independent variable is categorized based on health norm, it can be seen that microalbuminaria is a main factor related to diabetic retinopathy. The characterizations of patients with type 2 diabetes mellitus that are predicted to have diabetic retinopathy are:
1. having microalbuminuria score ≤300 mg/g,
2. having post-prandial blood glucose score > 200 mg/dL 3. having family members with diabetes history
4. having the fasting blood glucose score ≤ 126 mg/dL
These fourth characteristics tend to contradict medical diagnosis.
The result of CART method analysis using numeric or categorical data shows similar main factor, which is microalbuminuria. Microalbuminuria indicates the existence of microvascular complication in kidney and eyes (retina) [12]. A patient is considered to have microalbuminuria status if his or her score of microalbuminuria random test ranges from 30 to 300 mg/g. Martín-Merino et al. [8] also displays that microalbuminuria is a factor related to diabetic retinopathy.
CONCLUSIONS
The result of CART method from numeric and categorical independent variable data shows similar factor in diabetic retinopathy. The main factor related to diabetic retinopathy in patients with type 2 diabetes mellitus that are treated in Cipto Mangunkusumo Hospital at Jakarta in 2016 is the patient’s score of microalbuminuria.
ACKNOWLEDGMENTS
This research was supported by PITTA Universitas Indonesia year 2017 research grant (690/UN2.R3.1/HKP.05.00/2017).
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