Efficient Variance Estimation for the Polytomous Discrimination Index

2026-07-31

AI Summary

This study addresses the computational burden associated with variance estimation of the Polytomous Discrimination Index (PDI) in multiclass diagnostic accuracy assessment, which traditionally relies on expensive resampling methods such as bootstrap. To overcome this limitation, the authors propose a novel asymptotic variance estimator by integrating U-statistic theory with combinatorial mathematics, yielding a scalable and theoretically rigorous approach. The proposed method substantially reduces computational complexity while avoiding the high overhead of conventional resampling techniques. Both simulation studies and real-world neuroimaging analyses demonstrate that the new estimator enables efficient evaluation of multiclass diagnostic performance of deep neural networks, achieving significant reductions in computation time without compromising statistical reliability.

Abstract

Evaluating diagnostic accuracy for multi-category outcomes remains a significant challenge, primarily due to computational limitations in existing performance metrics. The Polytomous Discrimination Index (PDI) has emerged as an order-agnostic solution suitable for nominal classifications. However, its broader adoption has been constrained by the lack of efficient implementation, especially for its variance estimation, which typically would require computationally intensive bootstrapping procedures. In this work, we address this limitation by proposing a novel asymptotic variance estimator for the PDI. Our method integrates classical $U$-statistic theory with recent advances in combinatorics, offering a scalable and theoretically grounded alternative. To assess the performance of the proposed approach, we conduct extensive simulation studies and observe remarkable gain in computing time. We further apply our method to a real-world brain image analysis where deep neural networks are used as a diagnostic tool. We can efficiently report the accuracy of the neural networks with different depth specifications.

Problem

• Polytomous Discrimination Index
• variance estimation
• computational efficiency
• multi-category outcomes
• diagnostic accuracy

Innovation

• Polytomous Discrimination Index
• asymptotic variance estimation
• U-statistic
• computational efficiency
• multi-category classification