Confidence Intervals for the Risk Difference in Combined Unilateral and Bilateral Data Incorporating a Distribution-Based Approach

2026-06-30

AI Summary

This study addresses the limitations of existing confidence interval methods based on asymptotic normality, which fail to adequately capture the skewed sampling distribution of risk difference estimators in small-sample settings—particularly in paired-organ studies with unilateral and bilateral binary outcomes. To overcome the restrictive normality assumption, this work proposes a distribution-driven approach that explicitly models the true sampling distribution of the risk difference. The method integrates a modified MOVER procedure accounting for within-subject correlation with Monte Carlo simulation. Extensive simulations demonstrate that the proposed intervals achieve coverage probabilities close to the nominal level across various parameter configurations, with widths comparable to existing methods while more accurately reflecting distributional skewness in small samples. Its inferential consistency and practical utility are further corroborated through applications to two real datasets.

Abstract

Combined unilateral and bilateral binary outcomes frequently arise in studies involving paired organs. The risk difference is a clinically interpretable measure for comparing treatment effects between groups. Existing confidence interval methods are primarily based on asymptotic normality and may fail to adequately reflect finite-sample distributional features, particularly skewness. To address this issue, we propose a distribution-based confidence interval derived from the probability distribution of the risk difference estimator and a modified MOVER procedure that accounts for intra-subject correlation. Their performances are compared with those of commonly used asymptotic methods through extensive simulation studies. Across a broad range of parameter settings, all methods exhibited satisfactory performance as sample size increased. The proposed distribution-based interval achieved coverage probabilities close to the nominal level with interval widths comparable to those of existing procedures. In small sample settings, it was able to capture skewness in the sampling distribution that was not reflected by methods relying on asymptotic normality. Analyses of two real-world datasets demonstrated the practical applicability of the competing methods and yielded consistent inferential conclusions. The proposed approach provides an alternative framework for interval estimation of the risk difference in studies involving combined unilateral and bilateral binary outcomes.

Problem

• risk difference
• confidence interval
• bilateral data
• skewness
• finite-sample distribution

Innovation

• risk difference
• distribution-based confidence interval
• MOVER
• bilateral binary outcomes
• intra-subject correlation