## 5 Results and Discussion
### Predictive Models Developed Using ANN  
We also developed the predictive models using ANN--next will be called ANN model for short. We developed the ANN models using R programming with the nnet package. The nnet trains feed-forward neural networks with traditional backpropagation algorithm [26]. Feed-Forward Neural Networks (FFNN) is a type of ANN that doesn't have any feedback connection from the output to the input [27]. In FFNNN, neurons of the previous layer are entirely connected to the consecutive layer, but there are no intra-layer connections [28]. FFNN is a supervised learning method that is utilized for classification problems and consists of input, hidden, and output layers [29]. Our ANN architecture consisted of one input layer, one hidden layer, and one output layer. There were four neurons in input layer that represented hemoglobin, WBC, lymphocyte, and monocyte. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Training Data Percentage**} \\ \cline{2-4}  & **70\%** & **80\%** & **90\%** \\ \hline _Accuracy_ & 60.61\% & 60.87\% & 54.55\% \\ \hline _Sensitivity_ & 56.07\% & 59.72\% & 55.56\% \\ \hline _Specificity_ & 82.43\% & 80.67\% & 80.56\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance measurements of the Quadratic Discriminant Analysis (QDA) model. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Training Data Percentage**} \\ \cline{2-4}  & **70\%** & **80\%** & **90\%** \\ \hline _Accuracy_ & 45.45\% & 30.43\% & 27.27\% \\ \hline _Sensitivity_ & 45.73\% & 31.95\% & 27.78\% \\ \hline _Specificity_ & 72.89\% & 65.05\% & 63.10\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance measurements of the Linear Discriminant Analysis (LDA) model. There was only one hidden layer in this ANN architecture. The number of hidden layers and neurons in each hidden layer were obtained through the iteration process until the accuracy could not be furtherly improved [30]. The number of hidden layers is arbitrary. However, one hidden layer is commonly used for simple problems. The numbers of input and output neurons are determined according to the problem, while the number of hidden neurons was well optimized [20]. The problem in this research could be considered as a simple problem because it only consisted of four independent variables and the purpose was related to medical diagnosis, one of the common purposes of using ANN. That was why one hidden layer was enough for this research. Meanwhile, to ease the iteration process, we decided to use the rule of thumb in determining the hidden neurons. Based on the research conducted by [PERSON] and [PERSON] [31], one of the rules in determining the number of hidden neurons is \"the number of hidden neurons should be 2/3 of the input layer size, plus the size of the output layer\". We followed this rule when developing the ANN model. So, the number of hidden neurons is:  
\[ \begin{array}{c}\text{Hiddenneuron}=\left(\frac{2}{3}\times\text{inputneuron} \right)+\text{outputneuron}\\ =\left(\frac{2}{3}\times 4\right)+3\\ =\frac{17}{3}\\ =5.66...\\ \approx 6\end{array} \]  
Meanwhile, the number of input neurons was 4 because there were four remaining laboratory test parameters. The number of the output neuron was 3 because it represented three categories of severity level. The output that would come out was the probability values from each neuron that would sum up to 1. The probability value means the probability of a patient to suffer from dengue in a corresponding level. For example, the output value from neuron DF is 0.3, from DHF grade 1 is also 0.3, and from DHF grade 2 is 0.4. So, the patient is suffering dengue level DHF grade 2 because the probability value is the highest compared to the other two. Figure 2 was the architecture of the developed ANN predictive model.