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Bayesian inference of risk differences for multi-group bilateral data

  • Jinxiu Wen
  • Zhiming Li
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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.

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Cite

BibTeXRIS
BibTeX
@misc{wen2026bayesian,
  title = {{Bayesian inference of risk differences for multi-group bilateral data}},
  author = {Jinxiu Wen and Zhiming Li},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37251},
  eprint = {2609.37251},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37251},
}
RIS
TY  - UNPB
TI  - Bayesian inference of risk differences for multi-group bilateral data
AU  - Jinxiu Wen
AU  - Zhiming Li
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37251
UR  - https://arxiv.org/abs/2609.37251
AB  - 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.
ER  -