Spline Truncated Nonparametric Regression Modeling for Maternal Mortality Rate in East Java

- Maternal Mortality is the number of maternal deaths recorded during pregnancy, childbirth, and childbirth caused by pregnancy and childbirth, but not caused by accidents or falls. Since 2012 until 2015 it has been noted that maternal mortality rate has decreased from 359 to 305 maternal deaths per 100,000 live births. Despite the decline, the figure is still far from the target of the Sustainable Development Goals (SDGs) of 70 deaths per 100,000 live births. The analytical method used to determine the factors that influence maternal mortality rate is Nonparametric Spline Truncated Regression because the pattern of correlation between maternal mortality rate and each predictor variable obtained does not form a particular pattern. Based on the model obtained, the results are that all predictor variables have a significant effect on maternal mortality rate, namely the percentage of households with clean and healthy behavior, percentage of obstetric complications handling, percentage of pregnant women visits, percentage of households receiving cash assistance, and ratio of health centers and hospitals with a determination coefficient is 88 ,13 percent.


I. INTRODUCTION
ne of the indicators that represent whether or not the health of the mother one is to look at maternal mortality rate in a given area. MMR is the number of maternal deaths were recorded during pregnancy, childbirth, and childbirth are caused by pregnancy, childbirth, and postpartum, but not caused by an accident or a fall which is the number of maternal deaths in every 100,000 live births.
In 2007 there was a decrease of MMR at 228 maternal deaths which had previously 390 maternal deaths since 1991. Based on the results of the Indonesian Demographic Health Survey (IDHS) in 2012 experienced a considerable increase, reaching 359 deaths. While MMR obtained from the Inter-Census Survey in 2015 decreased, which was recorded at 305 maternal deaths per 100,000 live births [1]. Millennium Development Goals (MDGs) by 2015 for MMR is at 102 deaths per 100,000 live births. After the MDGs ended in 2015, a plan of sustainable development goals, called SDGs (Sustainable Development Goals) was formed as a change towards an improved development. If the MDG targets by 102 MMR, SDGs have a target to reduce MMR to 70 deaths per 100,000 live births. [2] There are several studies that discuss the MMR conducted by Mutfi whose results showed that the percentage of households with percentage of households with clean and healthy behavior and the percentage of obstetric complications handling significantly influenced the number of maternal deaths in the regencies / city in East Java [3]. Research conducted by Smith showed that the percentage of pregnant women who carry K4 program, the percentage of pregnant women at high risk of complications are addressed, the percentage of pregnant women who get Fe3 tablet, and the percentage of births attended by conversant health workers gave significant effect towards MMR [4].
This study aims to determine the relationship between MMR each regencies / city in East Java in 2016 with the factors suspected to influence them is the percentage of household with percentage of households with clean and healthy behavior, the percentage of treatment of obstetric complications, the percentage of visits of pregnant women, the percentage of households receiving assistance cash, and the ratio of public health centers and hospitals. The application of East Java data is because East Java province is one of nine provinces that have the largest MMR in Indonesia based on Indonesian Demographic and Health Survey in 2013 [5]. One method that serves to determine the model of the relationship between the response variable and the predictor variable is the regression method. Regression method used is Spline Truncated nonparametric regression, because it is able to estimate the data that does not have a specific pattern and have a tendency to look for the estimates of data from the patterns that are not randomly formed. In this study, the pattern acquired from the correlation between the MMR data with each of the predictor variables do not form a specific pattern, therefore that the method used apoppriate. It is expected that with this research will be able to provide policy recommendations to the government in order to suppress maternal mortality rate in East Java province.

A. Nonparametric Regression
Nonparametric regression is one method used to determine the pattern of the relationship between the response and predictor variables where the function of regression curve is unknown. Nonparametric regression model [6] in general can be shown in Equation (1) as follows. , , , Nonparametric approach is used to estimate the regression curve because the models are not determined in advance as in the parametric regression. In view of the nonparametric regression of data expected to find the regression curve without being influenced by the subjective factor of researchers.

B. Spline Truncated Nonparametric Regression
One of the nonparametric regression model used is the Spline. Spline is a segmented polynomial that has the flexibility properties. Spline depends on the point of knots. Knots point is a joint fusion point where a pattern of behavior changes from a function at different intervals [7]. In general, the function of G in the space of order m at the point Spline knots k1, k2, ..., kj is any function that can be expressed in Equation (2) as follows.
Β is parameter models with m being the order of Spline [8].

C. Optimum Knot Point Selection
The best Spline estimator is obtained by using optimal knot point. Knot point is the joint point where there is a change of behavior patterns or curves function. Optimal knot point can be obtained using methods Generalied Cross Validation (GCV) [7]. GCV method has asymptotically optimal properties, which means it can be used for large samples. The asymptotically optimal trait not shared by other methods, such as Cross Validation (CV) [9]. Additionally, it has the invariant nature of the transformation, which means the data can be transformed if the residual assumption are not fulfilled. Best spline regression model derived from optimal knots point to see the smallest GCV value. GCV method can be written as follows [6],

I -A
where I is the identity matrix, n is a lot of observation,

D. Maternal Mortality
MMR is the number of maternal deaths were recorded during pregnancy, childbirth, and postpartum hildbirth are caused by pregnancy, childbirth, postpartum and or its management, but not caused by an accident or a fall which is the number of maternal deaths in every 100,000 births. Factors that could cause the death of the mother during pregnancy is maternal age, parity, health services, antenatal care, helper, facilities and infrastructure, as well as social, economic, and cultural [10].

A. Data source
The data used in this research is secondary data obtained from the East Java Provincial Health Profile 2016 published by the East Java Health Departement and there is a secondary data obtained from the Central Bureau of Statistics. The research unit with the regencies / cities in East Java with a number of observations were 38 consisting of 9 cities and 29 counties in 2016.

B. Research variable
The variables used in this study is shown in Table 1 below. Percentage of household with percentage of households with clean and healthy behavior x2 Percentage of obstetric complications handling x3 Percentage of pregnant women visit x4 Percentage of households receiving cash assistance x5 The ratio of public health centers and hospitals

C. Step Research
The method used in this study is Truncated Spline Nonparametric Regression. Here are the steps of analysis used in this research according to the research objectives. 1. Analyzing the characteristics of MMR in regencies / cities in East Java. i. MMR describe each Regency / city in East Java and the factors suspected of influencing it. ii. Creating a scatter plot between the response variable with each of the predictor variables to determine the pattern of relationships that occur. 2. MMR model in Regencys / cities in East Java by using spline Nonparametric Regression Truncated method i. Choosing the optimal knots point based on the value of the minimum GCV. ii. Getting the best spline regression model with the point of optimal knots. iii. To test the significance of parameters simultaneously and partially. iv. To test the assumption of residual identical, independent and normally distributed (IIDN) of spline regression model. v. Creating a model interpretation and draw conclusions.

A. MMR Data Characteristics and Factors Affecting
Data MMR in East Java province in 2016 and the factors influencing it allegedly will be described using the mean, variance, minimum and maximum values. Here is the MMR data characteristics and factors that influence allegedly shown in Table 2. Based on Table 2, Y is a variable MMR in East Java in 2016 where the average maternal mortality rate in East Java province in 2016 amounted to 99.86 maternal deaths per 100,000 live births in every regencies / city with a large variance value, means that the county / city there are certain high maternal mortality rate and low. It can be seen from the value of the minimum and maximum MMR in East Java, which is the lowest MMR is the Madiun City, while a highest MMR is Blitar City. Truncated spline nonparametric regression model with point five knots with the nonparametric components can generally be written as follows.
Further after obtaining value knots with GCV most optimum value for each predictor variable is to compare the value of the GCV of each spline nonparametric regression model to determine the best knots. Here are the smallest GCV value of each knot point results shown in Table 3. GCV value of each model of each knot in Table 3 shows that the value of the minimum GCV is a model with a combination of spline knots. The combination of knots optimum point is three knots point to a variable percentage of household with percentage of households with clean and healthy behavior, the percentage of obstetric complications handling, pregnant women visit, and a variable ratio of health centers and hospitals, as well as two point knots for variable households receiving cash assistance. It can be concluded that the spline nonparametric regression model with a combination of knots by the number of model parameters as many as 20 parameters.

D. Parameter Estimation
Based on the results of the calculation to obtain the minimum GCV value, the model is best spline spline knots combination. The combination of the knot point is for the variables x1, x2, x3, and x5 is a three-point knots, while the X4 is two point knots. Thus, the parameter estimates for nonparametric regression models with a combination of knots using OLS method is as follows.

E. Regression Parameter Testing
There are two tests used parameters, namely the simultaneous test and partial test. The test results simultaneously displayed in Table 4 with the following hypotheses. H0 : β1 = ... = β19 = 0 H1 : At least there is one βj ≠ 0, j = 1,2, ..., 19 Based on test results in partial or individual parameters using the t test statistic of all the variables that go into the model a significant effect. There are seven parameters that are not significant because the p-value is higher than the value of α, which is β4, β5, β10, β11, β12, β13, and β16. Meanwhile, 13 other parameters have been significant for p-value less than the INFERENSI, Vol. 2(1), March 2019, ISSN: 0216-308X value α, namely β0, β1, β2, β3, β6, β7, β8, β9, β14, β15, β17, β18, β19. Although there is not a significant parameter, all five predictor variables remained significant effect on the Maternal Mortality Rate (MMR) due to any predictor variables are significant parameters.

F. Residual Assumptions Testing
Residual assumptions that must be fulfilled for a model of the nonparametric regression residuals spline is assuming identical, independent and normally distributed. identical residuals assumptions test using the statistic test. Assumption testing of independent residuals using the Durbin-Watson test. While testing the residual assuming normal distribution using the Kolmogorov -. Glejser statistic test test results can be seen in Table 6 with the following hypotheses.

G. Model Interpretation
Based on nonparametric models obtained previously, here is a model and interpretation of the truncated spline nonparametric regression model best on Maternal Mortality in East Java with five variables were significant predictors.
The percentage of households on the condition of percentage of households with clean and healthy behavior less than 33.04 if the addition of 1 unit of the MMR will be decreased by 13.893 per 100,000 live births. Regencies / cities included in the category of percentage of household with percentage of households with clean and healthy behavior less than 33.04 is Malang Regency, Bondowoso Regency, Situbondo Regency, Probolinggo Regency, and Batu City.
The percentage of households on the condition of percentage of households with clean and healthy behavior in between 33.04 and 34.04 in the event increments of 1 unit of the MMR will be an increase of 73.68 per 100,000 live births. Regencies / cities included in the category of percentage of household with percentage of households with clean and healthy behavior in between 33.04 and 34.04 is Trenggalek Regency.
The percentage of households on the condition of percentage of households with clean and healthy behavior in between 34.04 and 35.31 in the event increments of 1 unit of the MMR will be decreased by 129.687 per 100,000 live births. Regencies / cities included in the category of percentage of household with percentage of households with clean and healthy behavior in between 34.04 and 35.31 is Lumajang Regency, Sampang Regency, and Pamekasan Regency.
The percentage of households on the condition of percentage of households with clean and healthy behavior is higher than 35.31 if the addition of 1 unit of the MMR will increase by 29.436 per 100,000 live births. Regencies / cities included in the category of percentage of household H0 : ρ = 0 (autocorrelation does not happen) H0 : ρ ≠ 0 (autocorrelation does happen) INFERENSI, Vol. 2(1), March 2019, ISSN: 0216 On the condition of the percentage of households receiving cash transfers between 6.25 and 11.78 in the event increments of 1 unit of the MMR will be decreased by 52.148 per 100,000 live births. Regencies / cities included in the category of percentage of households receiving cash transfers between 6.25 and 11.78 are Ponorogo Regency .
On the condition of the percentage of households receiving cash transfers over from 11.78 in the event increments of 1 unit of the MMR will be decreased by 1,063 per 100,000 live births. Regencies / cities included in the category of percentage of households receiving cash transfers of less than 6.25 was Lamongan Regency. 5 On the condition of public health centers and hospitals ratio between 8 and 8.29 in case of an addition of 1 unit of the MMR will increase by 372.566 per 100,000 live births. Regencys / cities included in the category of public health centers and hospitals ratio between 8 and 8.29 are Trenggalek Regency.
On the condition of public health centers and hospitals ratios between 8.29 and 8.58 in case of an addition of 1 unit of the MMR will be decreased by 720.651 per 100,000 live births. Regencys / cities included in the category of health centers and hospitals ratios between 8.29 and 8.58 are Regency Pacitan, Malang, and Madiun.
While the Regency / city are included in the category of health centers and hospitals ratio greater than 8.29 is Nganjuk Regency, Madiun Regency, Sumenep Regency, Kediri City, Blitar City, Probolinggo City, Pasuruan City, Mojokerto City, and Surabaya City.

V. CONCLUSION
Maternal Mortality Rate data characteristics in East Java province reached an average of 99.86 maternal deaths per 100,000 live births. Regencies / cities with the highest maternal mortality rate is the city of Blitar, which is 236 maternal deaths per 100,000 live births, while the Regencies / cities with the lowest maternal mortality rate is the City of Madiun, which amounted to 38 maternal deaths per 100,000 live births. The best spline truncated nonparametric regression model produced by using a combination of knots, where all predictor variables significantly influence the MMR, namely the percentage of household with percentage of households with clean and healthy behavior (x1), the percentage of treatment of obstetric complications (x2), the percentage of visits of pregnant women (x3), The percentage of households receiving cash assistance (x4), and the ratio of public health centers and hospitals (x5). The coefficient of determination obtained by the truncated spline nonparametric regression model with a combination of knots point of 88.13 percent. Suggestions for further research is to add other alleged predictor variables that able to affect maternal mortality rate, thus the information in order to effort the decrease of maternal mortality rate will be improved.