## 3 Results
### Validation of Developed Models  
To evaluate the validity of the models, we utilized a separate set of validation data comprising 30% of the total dataset. This approach allowed us to assess the performance of the machine learning models on data that were not used during the model development phase. Regarding the probabilities provided by the models, we presented their distribution in a comparative boxplot in Figure 14. All models exhibited a high discrimination ability. The random forest and logistic regression models provided probabilities for acidotic cases distributed across a wide range, while the neural network models produced probabilities confined to a narrower range. Figure 14: Probabilities distributions. Figure 13: Estimation error in neural network training. The calibration of the models is in accordance with the analyzed distribution of probabilities. Figure 15 displays calibration curves, where the \(x\)-axis corresponds to the predicted probabilities and the \(y\)-axis represents the actual occurrence of acidosis. The logistic regression and classification tree models demonstrate good calibration. However, the random forest model tends to overestimate low probabilities and underestimate high probabilities. The perceptron with one hidden layer tends to overestimate high probabilities, while the two-hidden-layer neural network underestimates low probabilities and overestimates high probabilities. Regarding the discrimination ability, all models exhibit excellent discrimination with AUC values very close to or above 0.9. The highest AUC is achieved by the random forest model with an AUC of 0.971 (0.948, 0.993), which shows no statistically significant difference compared to the logistic regression model (0.968 (0.940, 0.996), \(p\) = 0.846), the neural network with one hidden layer (0.962 (0.35, 0.988), \(p\) = 0.352), or the neural network with two hidden layers (0.925 (0.883, 0.967), \(p\) = 0.063). However, the random forest model demonstrates superiority over the classification tree model (0.896 (0.839, 0.952), \(p\) = 0.004). The ROC curves are displayed in Figure 16.  
Although we observed similar behavior in terms of AUC values, it is crucial for the predictive models to be effective in detecting acidic cases, especially at high sensitivity values. Table 4 summarizes the specificities for high sensitivity values. When considering a sensitivity value of 0.9, the logistic regression model performs the best with a specificity of 0.928. It is followed by the neural network with one hidden layer (0.916, \(p\) = 0.712), random forest (0.892, \(p\) = 0.182), classification tree (0.817, \(p\) < 0.001), and the neural network with two hidden layers (0.782, \(p\) < 0.001). Figure 15: Calibration curves. Upper panel: Logistic regression (**left**); classification tree (**center**); random forest (**right**). Lower panel: Neural network with one hidden layer (**left**); two-hidden-layer neural network (**center**). In order to effectively prioritize the identification of acidotic cases, our study emphasizes logistic regression, random forest, and one-hidden-layer perceptron as the most optimal models. However, a crucial question remains: to what extent can these models help reduce the number of unnecessary cesarean sections? This important aspect can be examined by analyzing the clinical utility curves presented in Figure 17. The \(x\)-axis represents the potential threshold acidosis probability points used to classify individuals as acidotic or non-acidotic. On the \(y\)-axis, we present the percentage of acidosis cases misclassified below the selected cut-off point (indicated by a solid line) and the percentage of cesarean sections that could be avoided (depicted with a dotted line). By analyzing the clinical utility curve, we can determine the number of cesarean sections that could be avoided by detecting a certain percentage of acidemia cases.