Small area estimation of receiver operating characteristic curves for ordinal data under stochastic ordering

Area of Science:

• Radiology
• Medical Imaging Analysis
• Statistical Modeling

Background:

• Radiographic image analysis is increasingly used for disease diagnosis.
• Radiological diagnostic test outcomes are often discrete ordinal data.
• Receiver Operating Characteristic (ROC) curves and Area Under the Curve (AUC) are standard performance metrics.

Purpose of the Study:

• To develop a hierarchical Bayesian model for estimating proper ROC curves and AUC with discrete ordinal data.
• To incorporate stochastic ordering into the model to ensure clinical usefulness.
• To compare the performance of the new model with a model lacking stochastic ordering.

Main Methods:

• Developed a hierarchical Bayesian model incorporating stochastic ordering.
• Applied the model to discrete ordinal diagnostic test data.
• Compared results against a model without stochastic ordering.

Main Results:

• The model with stochastic ordering accurately estimates proper ROC curves.
• Models without stochastic ordering can produce improper ROC curves (non-concave or hook shapes).
• Stochastic ordering is crucial for reliable ROC curve estimation with ordinal data.

Conclusions:

• The hierarchical Bayesian model with stochastic ordering is preferable for estimating proper ROC curves.
• This approach ensures clinical usefulness for diagnostic tests with discrete ordinal outcomes.
• Accurate ROC curve estimation is vital for reliable disease detection performance assessment.