# Machine Learning in Medical Triage: A Predictive Model for Emergency Department Disposition
## 3 Results  
The performance metrics of the selected GBM model on test data are presented in Table 2. The Receiver Operating Characteristic (ROC) curve for the GBM model is depicted in Figure 1. Under the ROC Curve area (AUC ROC) is a broadly recognized metric in machine learning and statistics, indicating the model's capacity to differentiate between positive and negative classes, representing the probability that the model will rank a randomly selected positive instance higher than a randomly selected negative instance [38; 39; 40]. For this dataset, the GBM model achieved an AUC of 0.8256, suggesting an 82.56% likelihood that the classifier will prioritize a randomly chosen positive instance over a randomly chosen negative one. We now briefly review some key metrics for reporting classifier quality before actually presenting the results of our investigation. The _Area Under the Curve (AUC)_ serves as a quantification of a binary classifier's ability to discriminate between classes and functions as a condensed representation of the ROC curve, with greater AUC values corresponding to the better performance of the model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**AUC** & **AUCPR** & **MSE** & **RMSE** & **LOGLOSS** & **MEAN PER-CLASSEROR** \\ \hline
0.8256 & 0.8722 & 0.1677 & 0.4095 & 0.5005 & 0.2939 \\ \hline \hline \end{tabular}  
* Reported on test data. Mean Square Error (MSE), Root Mean Square Error (RMSE), Area Under the Curve (AUC), Area Under the Precision-Recall Curve (AUCPR).  
\end{table} 
Table 2: Model Metrics Binomial: GBM **. **  
Figure 1: Receiver Operating Characteristic (ROC) Curve for the Gradient Boosting Machine (GBM) model. The ROC curve illustrates the performance and predictive accuracy of a Gradient Boosting Machine (GBM) model. The curve plots the true positive rate (sensitivity) against the false positive rate (1-specificity) at various classification thresholds. The closer the ROC curve is to the top-left corner, the better the model’s discriminatory power. The area under the ROC curve (AUC) quantifies the model’s overall performance, with a higher AUC indicating better predictive accuracy. The ROC curve for the GBM model visually represents its trade-off between sensitivity and specificity, helping to determine the optimal classification threshold for decision-making. Additionally, a precision-recall curve is employed to assess the effectiveness of binary classification algorithms, particularly in scenarios characterized by a class imbalance. Similar to ROC curves, precision-recall curves offer a visual depiction of a classifier's performance across various thresholds, as opposed to a single metric. To create a precision-recall curve, the precision and recall are computed and graphed for a single classifier using a range of thresholds. A model attains a perfect _Area Under the Precision-Recall Curve_ (_AUPRC_) when it successfully identifies all positive examples (achieving perfect recall) without mistakenly classifying any negative instances as positive (achieving perfect precision). The _Mean Squared Error_ (_MSE_) quantifies the proximity of a regression line to a given set of data points. It represents a risk function that corresponds to the expected value of the squared error loss. The MSE is calculated by averaging the squared errors between the data points and the function's predictions. Ideally, the MSE values should be close to zero. Another primary performance metric for a regression model is the _Root Mean Squared Error_ (_RMSE_) which evaluates the average disparity between the model-predicted values and actual values. The RMSE evaluates the model's predictive accuracy, with lower values indicating a more effective model. Ideally, if a model consistently predicts the exact expected value, the RMSE would be zero. A notable advantage of the RMSE is that it expresses error in the same units as the predicted variable, making interpretation straightforward.