Confidence interval construction for proportion ratio in paired studies based on hybrid method

Area of Science:

• Biostatistics
• Statistical Inference
• Correlated Data Analysis

Background:

• Confidence intervals are crucial for estimating proportion ratios in paired samples.
• Existing score-based intervals for correlated proportions often lack closed-form solutions, requiring complex iterative methods.
• There is a need for simpler, explicit methods for constructing confidence intervals in such scenarios.

Purpose of the Study:

• To develop and evaluate a novel hybrid method for constructing confidence intervals for the ratio of two correlated proportions.
• To provide an alternative to iterative score-based confidence intervals that offers explicit solutions.
• To assess the performance of the proposed hybrid method through simulation studies.

Main Methods:

• A hybrid method combining individual confidence intervals for two proportions was proposed.
• The hybrid method generates a confidence interval for the ratio of correlated proportions.
• Fieller's theorem was utilized in conjunction with Wilson score intervals to form the hybrid confidence intervals.

Main Results:

• The proposed hybrid confidence intervals possess explicit solutions, eliminating the need for iterative procedures.
• Simulation studies demonstrated that the hybrid Wilson score confidence intervals, utilizing Fieller's theorem, perform well.
• The method was illustrated using three real-world examples, showcasing its practical applicability.

Conclusions:

• The hybrid method provides a practical and explicit approach for confidence interval construction for proportion ratios in paired samples.
• This method offers a valuable alternative to existing complex interval estimation techniques for correlated proportions.
• The proposed confidence intervals are reliable and suitable for application in various research settings involving paired data.