MODELING OF DENGUE HEMORRHAGIC FEVER CASES IN AWS HOSPITAL SAMARINDA USING BI-RESPONSES NONPARAMETRIC REGRESSION WITH ESTIMATOR SPLINE TRUNCATED

: Research on innovations in the field of statistics implemented in the health sector. This research is the development of birespon nonparametric regression model with spline truncated approach. The purpose of this research is to model and determine the factors affecting the Dengue Hemorrhagic Fever Cases in AWS Hospital Samarinda using Bi-responses Nonparametric Regression with estimator Spline Truncated. The data used in this study were data


INTRODUCTION
Dengue Hemorrhagic Fever (DHF) is one of the diseases in Indonesia that has attracted the attention of the government. According to the World Health Organization [1] dengue is still a health problem for people around the world, especially people in tropical and sub-tropical areas.
Indonesia as one of the tropical countries in the world with high humidity is the main trigger for people affected by dengue.
The number of dengue cases itself continues to increase from year to year, recorded in [1], [2] the number of dengue cases in Southeast Asia reached 2.4 million and increased in 2019 to 4.2 million cases. According to the Indonesian experienced a significant increase to 112,954 cases compared to 2018 as many as 53,075 cases [3]. The number of cases of dengue fever in Indonesia can be seen from the number of Incidence Rates [3], [4]. Incidence Rate (IR) is the number of new cases of a disease that appear in a period of time. It is known that the IR of DHF cases in 2019 was 51.48 per 100,000 population. This shows an increase compared to previous years. In 2019 East Kalimantan was included in the highest IR category compared to 34 other provinces [3].
Dengue fever is characterized by fever for 2-7 days with a temperature of 39°C, headache, back pain and heartburn, in addition to children usually characterized by vomiting, bone and muscle pain, accompanied by bleeding, decreased platelet count <100,000 mm3, the presence of plasma leakage is marked by an increase in hematocrit 20% of the normal value [3]. According to WHO, the criteria for a person to be declared affected by dengue can be seen from the results of a complete blood examination. So that medical officers determine only based on clinical signs and 3 DENGUE HEMORRHAGIC FEVER CASES IN AWS HOSPITAL SAMARINDA symptoms on the examination of platelets, hematocrit, and hemoglobin. The platelet count itself is most often used in Indonesia as a reference to determine whether a person has dengue or not.
There are several studies that use nonparametric spline regression, among others, conducted a multivariable spline regression analysis for modeling the mortality of patients with Dengue Hemorrhagic Fever (DHF) in East Java [5]. Modeled the factors that influence the percentage of the poor and food expenditure per capita in East Java using nonparametric biresponse spline regression [6]. Performs nonparametric spline biresponse regression modeling on the percentage of poor people and the poverty depth index in East Kalimantan [7]. This research will find Modeling of Dengue Hemorrhagic Fever Cases In AWS Hospital Samarinda Using Bi-responses Nonparametric Regression with estimator Spline Truncated.

Data Source
The data used in this study were obtained from Abdul Wahab Syahrani (AWS) Hospital in 2022. The research variables used in this study are given in Table 1.

Stage of Analysis
The data analysis technique in this study used the help of R software. The analysis carried out in this study are described in the following stages.
1. Defining the response variables and the predicted predictor variables.

Patients at AWS Hospital in Samarinda
Descriptive statistics used in this study are the average value, minimum value, maximum value, and standard deviation.

Scatter Plot on Platelet Count, Hematocrit Level and Hemoglobin Level of DHF Patients
At AWS Hospital in Samarinda Figure 1 shows that the data pattern between the response variable and the predictor variable does not form a certain pattern, hence the right solution to be used in this case is to use a nonparametric approach.

Biresponse Nonparametric Regression Model with Truncated Spline
Nonparametric regression is a statistical method to determine the relationship pattern between predictor variables and response variables which form of function is unknown [8], [9], [10]. This is different from parametric regression which forces the regression curve to follow a certain model such as a linear model. The advantages of nonparametric regression, the regression curve is determined by the observational data itself without having to be forced to adjust a certain function [11], [12], [13]. In view of nonparametric regression, the data seeks its own form of estimation of the regression curve without having to be influenced by the subjectivity of the researcher, this means that the nonparametric regression model approach is very flexible and very objective [14], [15], [16].
Identification of the pattern of relationship between the two response variables and the predictor variable does not form a linear, quadratic or other relationship pattern, so the approach that can be used is nonparametric regression. The biresponse nonparametric regression models with spline truncated using two predictor variables are given in Equation (1) Biresponse nonparametric regression models with linear splines using two predictor variables and one knot point are given in Equation (3) and Equation (4) 1 = 11 1 + ∅ 21 ( 1 − 11 ) + + 12 2 + ∅ 22 ( 2 − 12 ) + (3) 2 = 11 1 + 21 ( 1 − 11 ) + + 12 2 + 22 ( 2 − 12 ) + Biresponse nonparametric regression models with linear splines using two predictor variables and two knot points are given in Equation (5)  Biresponse nonparametric regression models with linear splines using two predictor variables and three knot points are given in Equation (7) and Equation (8)

Selection of Optimum Knot Point
The selection of the best model from the spline biresponse regression can be seen from the minimum GCV [17] value and the maximum R 2 value. Table 2 shows the GCV value and R 2 value for each knot point.  Table 2 shows that the modeling that produces the smallest GCV value and the largest R 2 value is at three knot points with an R 2 value of 89. 88%. Therefore, it was decided that the best model to be chosen was a nonparametric regression model with spline truncated using three knot points.
So that the results of the knot point position for each variable and the parameter values of the three knot point linear model are obtained in Table 3 and Table 4.  The three knot points spline model can be written in the form of the following equation (9) and (10)

Interpretation of the Birespon Spline Nonparametric Regression Model
The best model for data on platelet counts of DHF patients at first check blood and after three days of treatment is birespon spline nonparametric regression model with three knot points.
The interpretation for the first response variable spline model is explained as follows: 1. If the variable of hemoglobin level in DHF patients is considered constant, then the influence of the hematocrit level on the platelet count of DHF patients at first blood check is given in Equation (11). The truncated function is given in Equation (12 (12) explains that if the hematocrit level of a DHF patient is less than 26.22%, then every 1% addition of hematocrit in a DHF patient will increase the platelet count of a DHF patient at the first blood check by 1.72%. If the hematocrit level of a DHF patient is 26.22% to less than 32.32%, then every 1% addition of hematocrit in a DHF patient will increase the platelet count of a DHF patient at the first blood check by 3.15%.
2. If the variable of hematocrit level in DHF patients is considered constant, then the influence of the hemoglobin level on the platelet count of DHF patients at first blood check is given in Equation (13).
The truncated function is given in Equation (14) { Equation (14) explains that if the hemoglobin level of a DHF patient is less than 8.03 g/dL, then every 1 g/dL addition to the hemoglobin level in a DHF patient will increase the platelet count of a DHF patient at the first blood check by 1.03 g/dL. If the hemoglobin level of a DHF patient is from 8.3 g/dL to less than 10.3 g/dL, then every 1 g/dL addition to the hemoglobin level in a DHF patient will increase the platelet count of a DHF patient at the first blood check by 0.72 g/dL.
The model for the second response variable is data on the platelet count of DHF patients after three days of treatment. The interpretation for the second response variable spline model is explained as follows: The truncated function is given in Equation (16 The truncated function is given in Equation (18) { 1.32 2 0.51 2 + 9.315 0.4 2 + 10.948 0.29 2 + 12.669 ; 2 < 11.5 ; 11.5 ≤ 2 ≤ 11.9 ; 11.9 ≤ 2 ≤ 12.3 ; 2 ≥ 12.3 Equation (18) explains that if the hemoglobin level of a DHF patient is less than 11.5 g/dL, then each addition of 1 g/dL to the hemoglobin level in a DHF patient will increase the platelet count of DHF patients after three days of treatment by 1.32 g/dL.

Model Fit Test
The comparison between the actual and predicted data on the platelet count of DHF patients at the first blood checks is given Figure 2. The pattern formed from the two lines in Figure 2 does not show a significant difference.

CONCLUSION
The best model for data on platelet counts of DHF patients at first check blood and after three days of treatment is birespon spline nonparametric regression model with three knot points. This model gave the smallest GVC value of 97.77 and R 2 of 89.86%. The graph formed by the two lines in Figure 2 does not show a significant difference. The prediction results showed a similar pattern to the actual data. The biresponse nonparametric regression model with spline truncated is generated by Equation (9) dan Equation (10).