Comparing Ordinal Loss Functions for Heart Disease Severity Prediction

Ordinal classification problems are common in domains where class labels follow a natural order, such as disease severity prediction. For these problems, standard classification methods fail to explicitly account for ordinal relationships between classes. In this paper, we analyse and compare different ordinal approaches for heart disease severity prediction using the Cleveland Heart Disease dataset, where the target variable represents ordered severity levels. Ten ordinal-aware loss functions were evaluated using repeated stratified cross-validation, complemented by a linear regression baseline, non-linear sensitivity analysis, statistical testing, and interpretability analysis. The results show that no single loss function or model formulation consistently outperformed all others across all metrics. The linear regression baseline achieved the best aggregate performance for standard accuracy, accuracy within one adjacent class, AMAE, MMAE, and RPS, but failed to identify the extreme severity classes. Among the ordinal classification losses, different losses favoured different aspects of performance: triangular obtained the highest standard accuracy, EMD achieved the highest accuracy within one adjacent class and GMES, exponential obtained the highest MES and Min Sensitivity, and MCE achieved the lowest RPS among ordinal classification losses. These findings highlight the importance of selecting loss functions according to the clinical objective of interest and of evaluating ordinal prediction models using complementary metrics. The quantitative results are complemented with SHAP-based interpretability analysis and illustrative natural language explanations.