Efficient Variance Estimation for the Polytomous Discrimination Index

Area of Science:

• Statistics
• Machine Learning
• Medical Diagnostics

Background:

• Evaluating diagnostic accuracy for multi-category outcomes is computationally challenging.
• The Polytomous Discrimination Index (PDI) is a suitable metric for nominal classifications but lacks efficient implementation, especially for variance estimation.

Purpose of the Study:

• To propose a novel asymptotic variance estimator for the PDI.
• To provide a scalable and theoretically grounded alternative to computationally intensive bootstrapping methods for PDI variance estimation.

Main Methods:

• Integration of classical U-statistic theory with combinatorics.
• Development of a novel asymptotic variance estimator for the PDI.
• Extensive simulation studies to assess performance.

Main Results:

• The proposed method offers a significant gain in computing time compared to traditional bootstrapping.
• The new variance estimator is scalable and theoretically sound.
• Efficiently reported diagnostic accuracy for deep neural networks in brain image analysis.

Conclusions:

• The novel asymptotic variance estimator addresses the computational limitations of PDI variance estimation.
• This method enables efficient and scalable accuracy assessment for multi-category diagnostic tools.
• Facilitates the application of PDI in complex real-world scenarios like deep learning-based medical image analysis.