Equivalence of binormal likelihood-ratio and bi-chi-squared ROC curve models

Area of Science:

• Medical Imaging
• Biostatistics
• Diagnostic Test Evaluation

Background:

• A fundamental assumption for diagnostic decision variables is a monotone relationship with their likelihood ratio.
• This assumption is often violated when using the binormal receiver operating characteristic (ROC) curve model, leading to improper ROC curves.
• Improper ROC curves can exhibit 'hooks', lack concavity, and cross the chance line, causing issues in diagnostic accuracy assessment.

Purpose of the Study:

• To address the complexities in understanding the binormal likelihood-ratio (binormal-LR) model for ROC curve estimation.
• To provide a more accessible framework for developing and analyzing binormal-LR ROC curves.
• To demonstrate the equivalence between the binormal-LR model and a bi-chi-squared model.

Main Methods:

• The study establishes the equivalence between the binormal-LR model and a bi-chi-squared model.
• This equivalence is demonstrated by showing that both models generate the same families of ROC curves.
• The bi-chi-squared formulation is utilized to simplify the development and explanation of binormal-LR ROC curve properties.

Main Results:

• The binormal-LR model is shown to be mathematically equivalent to the bi-chi-squared model.
• This equivalence allows for the use of well-known distributions within the bi-chi-squared framework.
• The bi-chi-squared formulation simplifies the derivation and understanding of binormal-LR ROC curve characteristics.

Conclusions:

• The bi-chi-squared model provides a more intuitive and manageable approach to understanding binormal-LR ROC curves.
• This formulation facilitates a clearer analysis of diagnostic decision variables and their relationship with likelihood ratios.
• The findings offer a valuable tool for researchers and practitioners in diagnostic test evaluation and biostatistics.