## 5 Results
### Evaluation of Calibration Approaches (RQ2)  
Following the classifier comparison, we now explore how various calibration methods alter the CatBoost model's probability outputs. In Table 4, we report classification  
Figure 5: Friedman-Nemenyi significance test results regarding MCC of machine learning models across 200 bootstrapping iterations. performance (AUROC, AUPRC) alongside calibration-specific measures (LogLoss, ECE, MCE) averaged over 200 bootstrap iterations. Figures 6-10 summarize the corresponding Friedman-Nemenyi significance test results for each metric. As expected, none of the post-hoc calibration techniques significantly boosts AUROC or AUPRC over the uncalibrated CatBoost. Platt Scaling and Beta match the uncalibrated baseline in AUROC (both at \(\sim\)0.8506 \(\pm\) 0.05), while Spline and Isotonic Regression appear slightly lower (\(\sim\)0.835). The Friedman test for AUROC (\(\chi^{2}_{\text{[PERSON]}}=153.9573\), \(p=1.9185\times 10^{-31}\)) affirms that at least one method differs notably; however, the Nemenyi post-hoc analysis pinpoints Isotonic Regression and Spline Calibration as significantly less effective than Beta, Platt Scaling, and the uncalibrated model. A similar observation arises with AUPRC (\(\chi^{2}_{\text{[PERSON]}}=32.9493,\ p=3.8516\times 10^{-6}\)): Isotonic Regression obtains the top mean AUPRC (0.6825 \(\pm\) 0.09), but Beta, Platt Scaling, and uncalibrated CatBoost remain very close behind (\(\sim\)0.6807 \(\pm\) 0.09). The fact that these methods do not provide consistent improvement in rank-based metrics (AUROC) or minority-class performance (AUPRC) aligns with existing literature: calibration primarily targets how well probabilities match actual outcome frequencies, rather than enhancing the underlying discrimination. In some instances (e.g., Spline or Isotonic Regression vs. uncalibrated CatBoost), a minor dip in AUROC/AUPRC is the price of improved calibration. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Calibration Method** & **AUROC** & **AUPRC** & **Log Loss** & **ECE** & **MCE** \\ \hline Beta & **0.8506 (\(\pm\)0.05)** & 0.6807 (\(\pm\)0.09) & 0.1995 (\(\pm\)0.04) & 0.0327 (\(\pm\)0.01) & 0.6248 (\(\pm\)0.18) \\ Isotonic Regression & 0.8345 (\(\pm\)0.05) & **0.6825 (\(\pm\)0.09)** & 0.4194 (\(\pm\)0.27) & **0.0318 (\(\pm\)0.01)** & **0.4663 (\(\pm\)0.24)** \\ Platt Scaling & **0.8506 (\(\pm\)0.05)** & 0.6807 (\(\pm\)0.09) & 0.1981 (\(\pm\)0.03) & 0.0333 (\(\pm\)0.01) & 0.6260 (\(\pm\)0.19) \\ Spline & 0.8355 (\(\pm\)0.06) & 0.6731 (\(\pm\)0.09) & 0.2001 (\(\pm\)0.03) & 0.0384 (\(\pm\)0.02) & 0.6008 (\(\pm\)0.17) \\ Uncalibrated & **0.8506 (\(\pm\)0.05)** & 0.6807 (\(\pm\)0.09) & 0.2062 (\(\pm\)0.05) & 0.0413 (\(\pm\)0.01) & 0.6108 (\(\pm\)0.16) \\ Venn-Abers & 0.8474 (\(\pm\)0.05) & 0.6806 (\(\pm\)0.09) & 0.2068 (\(\pm\)0.03) & 0.0490 (\(\pm\)0.01) & 0.4883 (\(\pm\)0.16) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average Performance of CatBoost Model Across 200 Bootstrap Samples with Different Calibration Methods Applied. Figure 6: Friedman-Nemenyi significance test results regarding AUROC of calibration methods on the CatBoost model across 200 bootstrapping iterations. LogLoss gauges the magnitude of misalignment between predicted probabilities and actual outcomes--severely penalizing instances assigned incorrect high-confidence scores. Notably, Platt Scaling yields the lowest mean LogLoss (0.1981 \(\pm\) 0.03), followed closely by Beta (0.1995 \(\pm\) 0.04) and Spline (0.2001 \(\pm\) 0.03). By contrast, Isotonic Regression exhibits a substantially higher mean LogLoss (0.4194 \(\pm\) 0.27). The Friedman test (\(\chi^{2}_{\text{Friedman}}=178.8486,\ p=9.4262\times 10^{-37}\)) indicates these differences are highly significant, and the subsequent Nemenyi comparisons identify Isotonic as significantly worse than nearly all other calibration methods in this regard. From a clinical perspective, lower LogLoss translates into more reliable estimation of readmission risk across the entire probability spectrum.