Defining an Ethical Explainability Metric for Measuring AI Trustworthiness in Connected Healthcare Systems

Leveraging Artificial Intelligence (AI) ethically in connected healthcare systems requires a quantifiable framework that measures not only outcome correctness, but also the clarity, auditability, and ethical acceptability of model explanations in high-stakes clinical and cybersecurity workflows. This manuscript first presents a narrative review of ethical risks and countermeasures in Healthcare Internet of Things (HIoT) and explains why existing performance metrics are insufficient for trustworthy deployment. We then formalize a quantitative metric called Ethical Explainability (Ee) as a composite index integrating (1) a Human Agreement Ratio (HAR), capturing concordance between AI recommendations (and their rationale) and a calibrated expert consensus, and (2) an Entropy Reduction Index (ERI), capturing the proportional reduction in expert uncertainty after receiving an explanation, operationalized via probability-elicitation questionnaires mapped to Shannon entropy. Designed for HIoT security monitoring, Ee links transparency with governance-ready evidence of trustworthiness for human–AI collaboration.