Exact One-Sided Confidence Bounds for the Risk Ratio in 2 x 2 Tables with Structural Zero

• Published in: Biometrical journal Vol. 49; no. 6; pp. 952 - 963
• Main Authors: LLOYD, Chris J, MOLDOVAN, Max V
• Format: Journal Article
• Language: English
• Published: Berlin Wiley-VCH 01.12.2007
• Subjects: Algorithms; Animals; Applications; Biology, psychology, social sciences; Cattle; Cattle Diseases - immunology; Cattle Diseases - microbiology; Confidence Intervals; Data Interpretation, Statistical; Drug Hypersensitivity - diagnosis; Exact sciences and technology; General topics; Humans; Mathematics; Numerical Analysis, Computer-Assisted; Odds Ratio; Pneumonia of Calves, Enzootic - immunology; Pneumonia of Calves, Enzootic - microbiology; Probability and statistics; Sciences and techniques of general use; Statistics; Tuberculosis - diagnosis; Biometrics; Statistical method; Nuisance parameter; Exact confidence limit; Life science; Confidence limit; Likelihood ratio; Ordering; Algorithm; Mean estimation; Buehler procedure
• ISSN: 0323-3847; 1521-4036; 1521-4036
• DOI: 10.1002/bimj.200710357

This paper examines exact one-sided confidence limits for the risk ratio in a 2 x 2 table with structural zero. Starting with four approximate lower and upper limits, we adjust each using the algorithm of Buehler (1957) to arrive at lower (upper) limits that have exact coverage properties and are as large (small) as possible subject to coverage, as well as an ordering, constraint. Different Buehler limits are compared by their mean size, since all are exact in their coverage. Buehler limits based on the signed root likelihood ratio statistic are found to have the best performance and recommended for practical use.