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

Douglas Mossman1, Hongying Peng2

  • 1Department of Psychiatry and Behavioral Neuroscience, University of Cincinnati College of Medicine, Cincinnati, OH, USA. (DM)

Medical Decision Making : an International Journal of the Society for Medical Decision Making
|April 26, 2015
PubMed
Summary

A new dual beta (DB) Receiver Operating Characteristic (ROC) model provides more accurate diagnostic performance analysis than the conventional binormal (CvB) model. This proper ROC model offers a flexible and simpler alternative for researchers.

Keywords:
binormal assumptiondistributionproper ROCreceiver operating characteristicβ

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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.