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Exact confidence intervals for the relative risk and the odds ratio

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  • Weizhen Wang
  • Guogen Shan

Abstract

type="main" xml:lang="en"> For comparison of proportions, there are three commonly used measurements: the difference, the relative risk, and the odds ratio. Significant effort has been spent on exact confidence intervals for the difference. In this article, we focus on the relative risk and the odds ratio when data are collected from a matched-pairs design or a two-arm independent binomial experiment. Exact one-sided and two-sided confidence intervals are proposed for each configuration of two measurements and two types of data. The one-sided intervals are constructed using an inductive order, they are the smallest under the order, and are admissible under the set inclusion criterion. The two-sided intervals are the intersection of two one-sided intervals. R codes are developed to implement the intervals. Supplementary materials for this article are available online.

Suggested Citation

  • Weizhen Wang & Guogen Shan, 2015. "Exact confidence intervals for the relative risk and the odds ratio," Biometrics, The International Biometric Society, vol. 71(4), pages 985-995, December.
    • Handle: RePEc:bla:biomet:v:71:y:2015:i:4:p:985-995
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    Cited by:

    1. Guogen Shan, 2016. "Exact sample size determination for the ratio of two incidence rates under the Poisson distribution," Computational Statistics, Springer, vol. 31(4), pages 1633-1644, December.
    2. Schaarschmidt, Frank & Gerhard, Daniel & Vogel, Charlotte, 2017. "Simultaneous confidence intervals for comparisons of several multinomial samples," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 65-76.
    3. Sören Möller & Linda Juel Ahrenfeldt, 2021. "Estimating Relative Risk When Observing Zero Events—Frequentist Inference and Bayesian Credibility Intervals," IJERPH, MDPI, vol. 18(11), pages 1-9, May.
    4. Natalie DelRocco & Yipeng Wang & Dongyuan Wu & Yuting Yang & Guogen Shan, 2023. "New Confidence Intervals for Relative Risk of Two Correlated Proportions," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 1-30, April.

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