Nonparametric receiver operating characteristic curve analysis with an imperfect gold standard

Area of Science:

• Biostatistics
• Diagnostic Accuracy Studies
• Medical Informatics

Background:

• Estimating diagnostic accuracy relies on reference standards, often imperfect.
• Imperfect gold standards introduce bias in receiver operating characteristic (ROC) curve and area under the curve (AUC) estimation.
• Nonparametric methods are needed to address these challenges in diagnostic accuracy studies.

Purpose of the Study:

• To develop nonparametric methods for estimating ROC curves and AUCs with imperfect reference standards.
• To address the identifiability and estimation of ROC curves and AUCs when the gold standard is prone to error.
• To propose a hypothesis-testing method for comparing AUCs when gold standard accuracy is unknown.

Main Methods:

• Nonparametric identification and estimation of ROC curves and AUCs.
• Utilizing the known or estimable accuracy of an imperfect reference standard.
• Conditional independence assumption for ROC curve identifiability.
• Hypothesis testing for comparing AUCs when gold standard accuracy is unknown.

Main Results:

• Demonstrated identifiability of ROC curves and proposed a nonparametric estimation method under conditional independence.
• Established that ROC curves are unidentifiable but the sign of AUC difference is identifiable when gold standard accuracy is unknown.
• Developed a hypothesis-testing method for relative AUC superiority.

Conclusions:

• The proposed nonparametric methods are robust and do not rely on parametric assumptions.
• Methods are applicable to continuous and ordinal biomarkers for ROC/AUC analysis.
• Validated through theoretical results, simulations, and real-world diagnostic studies.