## 5 Results
### Evaluation of Conformal Prediction Methods
Ideally, a lower fraction indicates that prediction errors are more evenly distributed, reducing the likelihood of disproportionately missing readmissions. Isotonic Regression yields the lowest minority error (\(90.90\pm 14.13\%\)), suggesting that when mistakes occur, fewer are concentrated among readmitted patients. Beta and Spline calibrations approach mid-range values near 93-94%. Uncalibrated, Platt Scaling, and Spline calibrations all exceed 94-95%, indicating a larger share of errors come from those crucial positive cases. These distinctions are statistically significant (\(\chi^{2}_{\text{Friedman}}=71.88945,\ p=4.142\times 10^{-14}\)). In a high-stakes domain like sepsis, lower minority error implies the model better safeguards the subgroup in urgent need of accurate predictions. By contrast, a higher minority error portion could lead to under-detection of relapsing patients, potentially causing delays in treatment. Another key metric, shown in Figure 15, is the single prediction set ratio--the percentage of instances for which the conformal predictor returns exactly one label (fully confident) rather than an ambiguous set. Here, Isotonic Regression stands out at 91.11 \(\pm\) 13.55%, while Beta and Spline hover near 90.6-90.9%. Platt Scaling and Uncalibrated are slightly lower, around 89%. Statistical tests (\(\chi^{2}_{\text{Friedman}}=97.00886,\ p=2.2552\times 10^{-19}\)) reveal that Isotonic Regression's single-set predictions are significantly more frequent than those under uncalibrated or Platt Scaling-based conformal methods. In practice, a higher single prediction set ratio can be interpreted as fewer \"uncertain\" predictions requiring secondary review. For hospital workflows, this translates into fewer flagged patients needing additional confirmatory steps--saving time and resources, albeit with the caveat that such higher confidence can sometimes be miscalibrated. Figure 13: Friedman-Nemenyi significance test results regarding Average Coverage Gap of Split conformal prediction and calibration methods on the CatBoost model across 200 bootstrapping iterations. SCP aims to guarantee valid coverage at a pre-defined confidence level (95% in our use-case), and these results confirm that nearly all methods fulfill this target. Nonetheless, certain calibration strategies offer subtle but important trade-offs. Uncalibrated CatBoost slightly outperforms in marginal coverage and average coverage gap, but it exhibits one of the highest minority error contributions. In other words, missed admissions to the ICU account for more of its overall misclassifications. Isotonic Regression achieves the lowest minority error and the highest frequency of confident (single-label) decisions, at the cost of slightly lower coverage and a modestly larger coverage gap. Beta and Spline calibrations produce balanced, middle-ground behaviors, combining decent coverage with reasonable minority error distribution. Platt Scaling align coverage near uncalibrated levels but also share the downside of an elevated minority error fraction. For sepsis admissions to the ICU, reducing errors on the minority class could be paramount: even a small reduction in missed admissions to the ICU can translate into significantly improved patient outcomes. Hence, a method like Isotonic Regression, which shifts the error burden away from relapsing patients, may be particularly appealing. On the other hand, uncalibrated or Platt Scaling-based CP--though high in overall coverage--might inadvertently let too many high-risk patients slip by undetected. Ultimately,  
Figure 14: Friedman-Nemenyi significance test results regarding Minority Error Contribution of Split conformal prediction and calibration methods on the CatBoost model across 200 bootstrapping iterations. Figure 15: Friedman-Nemenyi significance test results regarding Single Prediction Set Ratio of Split conformal prediction and calibration methods on the CatBoost model across 200 bootstrapping iterations.