A Unified Framework for Statistical Inference and Study Design of Comparative F ₁ and F _β Scores under Paired Classifier Evaluations

Background and objective

The F ₁ score and its generalized F _β score are widely used to evaluate machine learning and artificial intelligence (AI) models in healthcare, particularly for imbalanced clinical datasets. In practice, competing prediction models are commonly evaluated on the same patient cohort, resulting in correlated classifier decisions. However, existing approaches for statistical inference of F ₁ -related metrics typically assume independent classifier decisions or lack integrated procedures for comparative evaluation, power analysis, and sample size determination in paired validation studies.

Methods

We propose psF1pair, a unified framework for confidence interval estimation, hypothesis testing, and power and sample size calculation for comparative F ₁ and F _β scores under paired evaluation designs. Dependence between classifiers is modeled using a four-component multinomial representation of the joint decision process, allowing explicit estimation and incorporation of classifier correlations commonly encountered when AI models are evaluated on the same patient cohort. Exact distributions are used for small sample settings, while asymptotic approximations are employed for computational efficiency in large studies.

Results

Simulation studies demonstrated that the proposed confidence intervals achieved nominal coverage probabilities across a wide range of sample sizes and correlation settings. Estimated power closely agreed with empirical power, with discrepancies generally below 3%. Compared with existing methods, psF1pair showed competitive or superior statistical power while maintaining appropriate type I error rates across a broad range of scenarios. Applications to skin cancer classification and breast cancer screening demonstrated that accounting for classifier correlation produced narrower confidence intervals and improved statistical efficiency.

Conclusions

psF1pair provides a practical and rigorous framework for evaluation and study planning of medical AI systems using F ₁ and F _β metrics. The method supports comparative benchmarking, uncertainty quantification, and sample size determination for future validation studies. An open-source R package is freely available.

Highlights

• Unified statistical inference and study-design framework for comparative F ₁ and F _β scores under paired evaluation designs.

• Explicit modeling of dependence between classifiers evaluated on the same dataset using a multinomial framework.

• Open-source R package supporting comparative evaluation and validation studies of predictive and AI models.