Exact Confidence Bounds for the Risk Ratio in 2x2 Tables with Structural Zero

Chris J. Lloyd, Melbourne Business School
Max Moldovan, Melbourne Business School

Abstract

This paper examines exact one-sided confidence limits for the risk ratio in a 2x2 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.