A novel nonparametric confidence interval for differences of proportions for correlated binary data

Area of Science:

• Biostatistics
• Statistical Methods
• Correlated Data Analysis

Background:

• Existing confidence interval estimators for correlated proportion differences, such as Tango's score method, often result in wide intervals.
• Exact methods for small samples are computationally intensive, and recent rank-based nonparametric methods, while promising, also face computational challenges.
• There is a need for efficient and accurate confidence intervals for comparing correlated proportions.

Purpose of the Study:

• To develop a novel, computationally simple nonparametric method for constructing confidence intervals for differences in correlated proportions.
• To compare the performance of the new method against existing approaches, including Tango's score method and rank-based nonparametric methods.

Main Methods:

• A new nonparametric method utilizing the U-statistics approach is proposed for comparing correlated areas under receiver operating characteristics.
• The method features a simple analytic form and a new estimate for degrees of freedom (n-1).
• Performance is evaluated through simulation studies and illustrated with real-world examples.

Main Results:

• The proposed U-statistics-based confidence interval demonstrates good coverage properties.
• It achieves narrower confidence interval widths compared to Tango's score method.
• The new method shows improved coverage probabilities over the rank-based nonparametric confidence interval and performs well even in small samples, outperforming approximate exact unconditional methods.

Conclusions:

• The simplified nonparametric confidence interval offers a computationally efficient and accurate alternative for analyzing correlated proportion differences.
• Its ease of use and strong performance make it a practical choice for researchers and practitioners.
• The method provides a valuable tool for situations involving paired or clustered binary data.