"Proper" Binormal ROC Curves: Theory and Maximum-Likelihood Estimation.

Area of Science:

• Biostatistics
• Medical Imaging Analysis
• Machine Learning Evaluation

Background:

• The conventional binormal model is widely used for Receiver Operating Characteristic (ROC) curve analysis.
• This model assumes latent normal decision-variable distributions.
• However, it can produce curve-fitting artifacts, such as "hooks," with small or ordinal datasets.

Purpose of the Study:

• To develop a "proper" binormal model to address limitations of the conventional binormal model.
• To introduce a new maximum-likelihood (ML) estimation algorithm for fitting ROC curves.
• To overcome curve-fitting artifacts in ROC analysis, particularly "hooks" near unit square corners.

Main Methods:

• Development of a "proper" binormal statistical model.
• Implementation of a novel maximum-likelihood (ML) estimation algorithm.
• Extensive simulation studies to evaluate algorithm reliability and model performance.

Main Results:

• The new algorithm for the "proper" binormal model demonstrated high reliability in simulations.
• ML estimates from the proper and conventional binormal models were nearly identical when no "hook" was present.
• The proper binormal model consistently produced ROC curves with monotonic slopes, avoiding degenerate fits.

Conclusions:

• The "proper" binormal model and its ML estimation algorithm effectively resolve "hook" artifacts in ROC curve fitting.
• This approach ensures more reliable ROC curve analysis, especially for challenging datasets (small N, ordinal categories).
• The developed method offers a robust alternative for accurate ROC analysis in various scientific applications.