Impossibility results for equating the Youden Index with average scoring rules and Tjur $R^2$-like metrics

Linard Hoessly

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arXiv · 2411.05391

Impossibility results for equating the Youden Index with average scoring rules and Tjur $R^2$-like metrics

Linard Hoessly

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Abstract

We consider the Youden index fas well as measures evaluating predicted probabilities for the maximum-likelihood estimate of a logistic regression model with predictor the classifier. We give impossibility results showing that the Youden index can not equal any average of a real scoring rule nor any metric averaging over binary outcomes (0s and 1s) for any continuous real-valued scoring rule. This shows the obstructions of such potential equivalences and highlights the distinct roles these metrics play in diagnostic assessment.

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Linard Hoessly. 2024-11-08. Impossibility results for equating the Youden Index with average scoring rules and Tjur $R^2$-like metrics. https://arxiv.org/abs/2411.05391

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