## 3 Results  
The results obtained from the experiments conducted in this study provide a comprehensive evaluation of the model's ability to predict the need for space maintainers using dental X-ray images. These results are presented to illustrate the effectiveness and reliability of the CNN in addressing the classification task. Performance metrics such as accuracy, precision, recall, F1-score, ROC AUC, and MCC were employed to assess the model's predictive capabilities. The findings highlight the model's capacity to make accurate predictions and demonstrate its potential as a valuable tool in clinical decision making for pediatric dentistry. The following sections provide a detailed analysis of these results, supported by quantitative metrics and visualizations. Figure 2 illustrates the training performance of the CNN used for predicting the need for space maintainers. The left panel shows the training accuracy over 30 epochs, with the training and validation accuracy steadily increasing as the model learns the patterns within the data. By the end of the training process, the accuracy approaches 1.0, indicating that the model has effectively captured the features necessary for accurate predictions. The right panel depicts the corresponding training loss, which consistently decreases over the epochs, reflecting the model's ability to minimize errors between predicted and actual labels. Together, these trends demonstrate \begin{table}
\begin{tabular}{c c} \hline \hline
**Metric** & **Calculation** \\ \hline Accuracy [37] & \(\dfrac{\text{TP}+\text{TN}}{\text{TP}+\text{TN}+\text{FP}+\text{FN}}\) \\ Precision [38] & \(\dfrac{\text{TP}}{\text{TP}+\text{FP}}\) \\ Recall [39] & \(\dfrac{\text{TP}}{\text{TP}+\text{FN}}\) \\ F1-Score [39] & \(\dfrac{\text{Precision}\times\text{Recall}}{\text{Precision}+\text{Recall}}\) \\ ROC AUC [40] & \(\dfrac{\text{TP}}{\text{TP}+\text{FN}}\), \(\text{FPR}=\dfrac{\text{FP}}{\text{FP}+\text{FN}}\) \\ Matthews Correlation Coefficient [40] & \(\dfrac{(\text{TP}\times\text{TN})-(\text{FP}\times\text{FN})}{\sqrt{(\text{ TP}+\text{FP})(\text{TP}\times\text{FN})(\text{TP}\times\text{FP})(\text{TN}\times\text{FN})}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of the performance metrics used in the study and their calculation methods; TP (true positives): correctly predicted positive cases, TN (true negatives): correctly predicted negative cases, FP (false positives): incorrectly predicted positive cases, and FN (false negatives): incorrectly predicted negative cases. the model's capacity to learn effectively from the training data, achieving high accuracy and low loss. The ROC curve presented in Figure 3 illustrates the model's performance in distinguishing between two classes: cases where a space maintainer is required and cases where it is not. The \(x\)-axis represents the false positive rate (1-specificity), while the \(y\)-axis represents the true positive rate (sensitivity), depicting the balance between correctly identifying positive cases and minimizing false alarms. As the decision threshold changes, the curve demonstrates how the model's sensitivity and specificity vary. The ROC curve closely approaches the top-left corner, which indicates a high discriminative ability of the model. (AUC is calculated as 0.94, signifying near-perfect classification performance. AUC values range from 0 to 1, where 0.5 suggests no discriminatory power (equivalent to random guessing), and 1.0 represents a perfect classifier. An AUC of 0.94 confirms the model's strong ability to correctly identify cases requiring a space maintainer while minimizing false positives. This high AUC value highlights the robustness and reliability of the model in making accurate predictions. Given its exceptional performance, the model has significant potential as a decision-support tool in pediatric dentistry, assisting clinicians in making informed and efficient assessments regarding the necessity of space maintainers.