Receiver operating characteristic curve generalization for non-monotone relationships

Area of Science:

• Biostatistics
• Medical Diagnostics
• Statistical Modeling

Background:

• Receiver operating characteristic (ROC) curves are standard for evaluating continuous diagnostic markers.
• Traditional ROC analysis assumes a monotone relationship between marker values and the condition of interest.
• Some diagnostic markers exhibit a non-monotone relationship, where both low and high values indicate a higher probability of disease.

Purpose of the Study:

• To propose a generalized ROC curve for diagnostic markers with non-monotone relationships.
• To address limitations of conventional ROC analysis in specific clinical scenarios.
• To provide a robust statistical tool for enhanced diagnostic accuracy.

Main Methods:

• A novel generalized ROC curve, denoted as [Formula: see text], is introduced.
• The method considers all pairs of cut-off points for lower and upper marker values.
• Uniform consistency and asymptotic distribution of the empirical estimator for the [Formula: see text] curve are derived.

Main Results:

• The proposed [Formula: see text] curve effectively handles non-monotone diagnostic marker relationships.
• Theoretical properties, including consistency and asymptotic distribution, are established for the empirical estimator.
• The utility of the method is demonstrated through two real-world case studies.

Conclusions:

• The generalized ROC curve offers a valuable extension for diagnostic marker evaluation.
• This approach improves diagnostic capacity when traditional assumptions are violated.
• The method provides a statistically sound framework for analyzing complex diagnostic data.