Semi-parametric maximum likelihood estimates for ROC curves of continuous-scale tests

Area of Science:

• Statistics
• Biostatistics
• Machine Learning

Background:

• Receiver Operating Characteristic (ROC) curve analysis is crucial for evaluating diagnostic tests.
• Existing methods for ROC curve estimation can be computationally intensive or lack desirable properties.
• There is a need for robust, efficient, and easily computable ROC estimators.

Purpose of the Study:

• To propose a novel semi-parametric maximum likelihood (ML) estimate for ROC curves.
• To ensure the proposed estimator possesses the property of ROC curve invariance.
• To develop a computationally accessible ROC estimation method.

Main Methods:

• Developed a new semi-parametric maximum likelihood estimation technique.
• Theoretically demonstrated sqrt[n]-consistency and asymptotic normality of the estimator.
• Conducted extensive simulation studies to assess performance.

Main Results:

• The proposed semi-parametric ML estimator for ROC curves is invariant and computationally simple.
• The estimator exhibits desirable statistical properties, including sqrt[n]-consistency and asymptotic normality.
• Simulation studies confirm the method's efficiency and robustness compared to existing approaches.

Conclusions:

• The novel semi-parametric ML estimator provides a valuable tool for ROC curve analysis.
• The method's ease of computation and robust performance make it suitable for practical applications.
• The estimator was successfully illustrated using a real-world dataset, highlighting its utility.