The Performance of Three Approximate Confidence Limit Methods for the Odds Ratio

The performance of three approximate confidence limit methods for the odds ratio, R, is studied at the 95% level in the unconditional sample space. There are: the method proposed by Cornfield (Proceedings of the 3rd Berkeley Symposium 1956;4:135-48), the logit method with 1/2 corrections first considered by Woolf (Ann Hum Genet 1955;19:251-3), and the test-based method proposed by Miettinen (Am J Epidemiol 1976;103:226-35). Cornfield's method comes closest to attaining the normal confidence coefficient. The logit method typically has actual confidence coefficients somewhat too large with disparate tail areas. The latter is ascribed in part to the enhanced skewness induced by the logit transformation itself. The test-based method has actual coefficients uniformly less than nominal when R not equal to 1. This underestimation is worse in finite samples than Halperin found it to be asymptotically. Although the Cornfield and test-based methods have the same confidence coefficients for R = 1, the test-based method is more likely to cover distant values of R not equal to 1 when in fact R = 1. It is concluded that Cornfield's method without the continuity correction is the preferred approximate method in the unconditional space as, with the continuity correction, it was previously found to be in the conditional space.