Empirical likelihood inference for area under the receiver operating characteristic curve using ranked set samples

Area of Science:

• Biostatistics
• Statistical Inference
• Diagnostic Test Evaluation

Background:

• The area under the receiver operating characteristic curve (AUC) is crucial for evaluating continuous diagnostic tests.
• Existing methods for AUC confidence intervals often require specific statistical assumptions.
• Ranked set sampling (RSS) offers enhanced data collection efficiency.

Purpose of the Study:

• To develop a novel empirical likelihood (EL) method for constructing confidence intervals for AUC.
• To leverage the efficiency of ranked set sampling (RSS) in AUC estimation.
• To provide assumption-free inference for AUC using EL and RSS.

Main Methods:

• An empirical likelihood (EL) method was developed for AUC confidence intervals.
• Data were collected using ranked set sampling (RSS) designs.
• The Mann-Whitney statistic was identified as the EL-based point estimate for AUC.

Main Results:

• The proposed EL method provides confidence intervals derived from a scaled chi-square distribution.
• Both balanced and unbalanced RSS data were accommodated by the method.
• Simulation studies and case studies demonstrated improved inference efficiency.

Conclusions:

• The EL-based method with RSS offers a statistically efficient approach for AUC inference.
• This method relaxes assumptions required by traditional non-parametric techniques.
• The approach is applicable to real-world diagnostic performance assessments, including diabetes and chronic kidney disease.