Parametric estimates for the receiver operating characteristic curve generalization for non-monotone relationships

Area of Science:

• Biostatistics
• Medical Diagnostics
• Machine Learning

Background:

• Diagnostic procedures often rely on continuous markers to classify individuals.
• Receiver operating characteristic (ROC) curves and their area under the curve (AUC) are standard tools for evaluating marker diagnostic ability.
• Current ROC methods may not fully capture diagnostic scenarios where both low and high marker values are indicative of a condition.

Purpose of the Study:

• To revise and broaden the definition of the receiver operating characteristic curve (ROC).
• To introduce a generalized ROC curve for diagnostic markers where extreme values (low and high) are associated with the condition.
• To investigate parametric and non-parametric estimators for this generalized ROC curve.

Main Methods:

• Revising the definition of ROC curves based on specific classification subsets.
• Developing a generalized ROC curve framework to accommodate U-shaped or inverted U-shaped marker-disease relationships.
• Employing Monte Carlo simulations and real-world data analysis to assess the performance of proposed estimators.

Main Results:

• The study provides a revised framework for ROC analysis, extending its applicability.
• A generalized ROC curve is proposed and evaluated for scenarios with non-monotonic marker-disease associations.
• Parametric and non-parametric estimation methods for the generalized ROC curve demonstrate practical utility.

Conclusions:

• The generalized ROC curve offers a more comprehensive approach to evaluating diagnostic markers, particularly when extreme values are informative.
• The proposed methods provide valuable tools for biostatisticians and researchers in medical diagnostics.
• This work enhances the analytical capabilities for understanding complex marker-disease relationships.