Using Dual Beta Distributions to Create "Proper" ROC Curves Based on Rating Category Data.

Area of Science:

• Biostatistics
• Medical Diagnostics
• Signal Detection Theory

Background:

• Receiver operating characteristic (ROC) analysis is crucial for evaluating diagnostic systems.
• The conventional binormal (CvB) model often yields improper ROC curves lacking a consistently decreasing slope.
• Improper ROCs from the CvB model, especially with 'hooks,' can misrepresent diagnostic performance at extreme false positive rates.

Purpose of the Study:

• To introduce and assess a dual beta (DB) ROC model.
• To ensure the DB model generates ROC curves with a positive, monotonically decreasing slope, adhering to theoretical requirements.

Main Methods:

• A computer simulation study was conducted.
• The performance of the DB model was compared against the conventional binormal (CvB) and weighted power function (WPF) models.

Main Results:

• The DB model demonstrated performance equal to or exceeding the WPF model.
• Results from the DB model were less biased and closer to true values compared to the CvB model.

Conclusions:

• The DB ROC model offers a closed-form solution for the true positive and false positive rate relationship.
• It facilitates rapid ROC area calculations using spreadsheet functions.
• The DB model provides a flexible, user-friendly, and easily implementable proper ROC framework for investigators.