Small sample confidence intervals for the odds ratio

Numerous methods-based on exact and asymptotic distributions-can be used to obtain confidence intervals for the odds ratio in 2 x 2 tables. We examine ten methods for generating these intervals based on coverage probability, closeness of coverage probability to target, and length of confidence intervals. Based on these criteria, Cornfield's method, without the continuity correction, performed the best of the methods examined here. A drawback to use of this method is the significant possibility that the attained coverage probability will not meet the nominal confidence level. Use of a mid-P value greatly improves methods based on the exact distribution. When combined with the Wilson rule for selection of a rejection set, the resulting method is a procedure that performed very well. Crow's method, with use of a mid-P, performed well, although it was only a slight improvement over the Wilson mid-P method. Its cumbersome calculations preclude its general acceptance. Woolf's (logit) method-with the Haldane-Anscombe correction-performed well, especially with regard to length of confidence intervals, and is recommended based on ease of computation.