# Usmile likelihood evaluation provides robust threshold free assessment of binary classification models for balanced and imbalanced datasets

## TL;DR

A new method called U-smile LE evaluates binary classification models without thresholds, improving performance in imbalanced datasets like medical diagnostics.

## Contribution

The U-smile LE method introduces a threshold-free metric (rLR) and class-specific decomposition for better evaluation in imbalanced settings.

## Key findings

- U-smile LE outperformed AUC-based selection in minority-class detection by 16% in AUC-PR and 21% in F1-score.
- U-smile LE provides interpretable insights into class-specific predictor contributions during variable selection.
- The method works with logistic regression and random forest models, offering a model-agnostic evaluation framework.

## Abstract

Current metrics for binary classification, like the Area Under the Receiver Operating Characteristic curve (AUC-ROC) or Log Loss, provide a global performance score. However, they do not quantify predictive quality separately for event and non-event classes. This limitation is particularly critical in imbalanced settings like medical diagnostics. To address it, we introduce the U-smile Likelihood Evaluation (LE) method, a substantial extension of the original U-smile framework. The U-smile LE method is based on a new metric called the relative Likelihood Ratio (rLR). This single score measures overall model strength without needing a classification threshold. We decompose this score into two class-specific components: \documentclass[12pt]{minimal}
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\begin{document}$$\:{rLR}_{0}$$\end{document} for non-event class, visualizing them simultaneously in a compact U-shaped plot. We validated the U-smile LE method on synthetic datasets with varying class imbalance and a real-world clinical Heart Disease dataset. In severely imbalanced scenarios (90/10 class distribution), stepwise variable selection guided by U-smile LE outperformed traditional AUC-based selection, improving minority-class detection by 16% in the Area Under the Precision-Recall curve (AUC-PR) and 21% in F1-score. The evolution of U-smile patterns during variable selection provided clear, interpretable insight into class-specific contributions of individual predictors. Demonstrated with both logistic regression and random forest models, U-smile LE offers an explainable, model-agnostic framework for evaluating binary classifiers, especially valuable where class imbalance and interpretability are key concerns.

The online version contains supplementary material available at 10.1038/s41598-026-40545-z.