Construction of confidence intervals for risk difference with paired correlated data using saddlepoint approximation

Area of Science:

• Biostatistics
• Clinical Trial Methodology
• Statistical Inference

Background:

• Correlated binary outcomes in paired organs require specialized statistical methods.
• Intra-subject dependencies are common in clinical studies with paired data (e.g., eyes, ears).
• Existing methods like Wald, likelihood ratio, score, and MOVER may lack accuracy in small samples or rare events.

Purpose of the Study:

• To propose a novel saddlepoint approximation (SA) method for confidence intervals (CI) of risk differences in paired binary data.
• To evaluate the performance of the SA method against conventional approaches under Donner's correlation model.
• To address the need for robust statistical inference in small-sample settings with correlated outcomes.

Main Methods:

• Development of a saddlepoint approximation (SA) method incorporating higher-order moment information.
• Simulation studies to compare SA with Wald, likelihood ratio, score, and MOVER methods.
• Evaluation metrics included empirical coverage probability (ECP) and mean interval width (MIW) under varying correlation levels.
• Application to real-world clinical trial data (otitis media).

Main Results:

• The SA method consistently achieved empirical coverage probabilities near the nominal 95% level.
• SA produced narrower confidence intervals compared to conventional methods, especially under high correlation.
• Likelihood and score tests showed undercoverage, while Wald and MOVER intervals were overly conservative.
• The SA method demonstrated improved accuracy and robustness in small-sample and rare-event scenarios.

Conclusions:

• The proposed saddlepoint approximation (SA) method offers a superior approach for constructing confidence intervals for risk differences in paired binary data.
• SA provides more accurate and precise inferences than traditional methods, particularly in challenging small-sample or high-correlation settings.
• This method fills a crucial gap in statistical inference for correlated bilateral outcomes, enhancing clinical trial data interpretation.