Cost-Weighted Harmonic Score: A Unified Metric for Cost-Sensitive Classification on High-Stakes Imbalanced Data

Machine learning classifiers deployed in high-stakes domains like healthcare and finance face the dual challenges of class imbalance and asymmetric misclassification costs, which are poorly addressed by traditional evaluation metrics. The primary purpose of this study is to address this critical gap by developing and validating the Cost-Weighted Harmonic (CWH) score, a novel, bounded performance metric that unifies precision, recall, and specificity within a normalized harmonic mean, explicitly weighted by a user-defined cost ratio, for high-stakes imbalanced classification. Unlike cost-agnostic metrics (e.g., F1, HMRS) or unbounded cost-aware scores (e.g., C-score), CWH is interpretable, stable, and aligns evaluation with domain-specific risk priorities. It is integrated with threshold optimization and validated across healthcare, cybersecurity, and financial datasets, demonstrating superior stability and up to 69% performance improvement against C-score in life-critical scenarios without excessive false positives. CWH effectively bridges the gap between statistical evaluation and operational decision-making, offering practitioners a reliable tool for model selection that aligns with domain-specific risk priorities.