title: Exact confidence intervals for the relative risk and the odds ratio.
abstract: 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.
authors.affiliation: College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China.|Department of Mathematics and Statistics, Wright State University, Dayton, Ohio, U.S.A.
authors.forename: Weizhen
authors.initials: W
authors.lastname: Wang
authors.affiliation: Department of Environmental and Occupational Health, University of Nevada Las Vegas, Las Vegas, Nevada, U.S.A.
authors.forename: Guogen
authors.initials: G
authors.lastname: Shan
mesh_terms: D016010:Binomial Distribution; D001699:Biometry / Q000379:methods; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data; D016001:Confidence Intervals; D006801:Humans; D016555:Matched-Pair Analysis; D015233:Models, Statistical; D016017:Odds Ratio; D012306:Risk; D018401:Sample Size
keywords: Binomial distribution; Coverage probability; Multinomial distribution; Set inclusion