Bayesian inference of risk differences for multi-group bilateral data

2026-09-29

AI Summary

This study addresses the poor performance of frequentist methods for clinical bilateral data in small-sample or sparse settings by constructing a Bayesian inference framework for multiple groups of bilateral data. Based on the Dallal model, objective priors—including uniform, Jeffreys, and reference priors—are derived, and range-based posterior testing procedures with corresponding decision rules are proposed. Equivalence margins are calibrated via Monte Carlo simulations to analyze risk differences. The results demonstrate that the proposed approach significantly outperforms the traditional Wald method in terms of coverage probability, interval width, and Type I error control, thereby providing a more reliable statistical tool for analyzing bilateral data with limited sample sizes.

Abstract

Bilateral data from paired body parts are common and correlated in clinical studies. Classical frequentist methods perform poorly in small or sparse datasets. This paper develops a Bayesian framework for bilateral data with multiple groups under Dallal's model. We derive three objective priors (uniform, Jeffreys', and Bernardo's reference priors) and propose a range-based posterior testing procedure, combined with a decision rule, to test the homogeneity of risk differences, with the equivalence margin calibrated. Monte Carlo simulations evaluate empirical Type I error rates, powers, and interval estimation properties. Results show that the Bayesian methods achieve accurate coverage probabilities, narrower confidence intervals, and better Type I error control than the frequentist Wald approach, especially in small-sample and sparse-data settings. We illustrate the methodology with two real datasets. The proposed framework provides a robust and flexible tool for multi-group bilateral data analysis.

Problem

• Bayesian inference
• bilateral data
• risk differences
• small-sample
• sparse data

Innovation

• Bayesian inference
• Bilateral data
• Dallal's model
• Objective priors
• Risk differences