Two-tailed asymptotic inferences for the odds ratio in prospective and retrospective studies: evaluation of methods of inference

Various asymptotic methods have been proposed for obtaining a two-tailed confidence interval (CI) for the odds ratio (<i>OR</i>) based on two independent samples. This paper evaluates 22 different methods, including 14 new methods or modifications of old methods. Because the CI is obtained by inversion in <i>θ</i> of the two-tailed test for <i>H</i>₀: <i>OR</i> = <i>θ</i>, this paper evaluates the tests for various values of <i>θ</i>, rather than the CIs that are obtained. The paper concludes that none of the classic methods were selected as a top method, although the Agresti logit method is an acceptable option when the sample imbalance and the true value of <i>OR</i> are moderate; however the CI so obtained is very wide. The best methods are based on the likelihood-ratio test and on the inverse sine transformation – which is a new method – after adding 0.5 to all the data; the likelihood-ratio test method has one disadvantage, which is that the CI is obtained iteratively. The paper also selects the best methods for ensuring compatibility between the conclusions for the CI and the independence test.