Unconditional efficient one-sided confidence limits for the odds ratio based on conditional likelihood

Abstract

We compare various one-sided confidence limits for the odds ratio in a 2 × 2 table. The first group of limits relies on first-order asymptotic approximations and includes limits based on the (signed) likelihood ratio, score and Wald statistics. The second group of limits is based on the conditional tilted hypergeometric distribution, with and without mid-P correction. All these limits have poor unconditional coverage properties and so we apply the general transformation of Buehler (J. Am. Statist. Assoc. 1957; 52:482- 493) to obtain limits which are unconditionally exact. The performance of these competing exact limits is assessed across a range of sample sizes and parameter values by lookin..