Two-tailed asymptotic inferences for the odds ratio in cross-sectional studies: evaluation of fifteen old and new methods of inference

Abstract

ABSTRACT Various asymptotic methods of obtaining a confidence interval (CI) for the odds ratio (OR) have been proposed. Surprisingly, insofar as we know, the behavior of these methods has not been evaluated for data proceeding from a cross-sectional study (multinomial sampling), but only for data that originate in a prospective or retrospective study (two independent binomials sampling). The paper evaluates 15 different methods (10 classic ones and 5 new ones). Because the CI is obtained by inversion in θ of the two-tailed test for H0(θ): OR = (null hypothesis), this paper evaluates the tests for various values of θ, more than the CIs that are obtained. The following statements are valid only for the two-tailed inferences based on 20 ≤ n ≤ 200 and 0.05≤ OR≤20, since these are the limitations of the study. The two best methods are the classic Cornfield chi-squared method for 0.2≤ OR≤5 and, in other cases, the new method of Sterne for chi-squared; but the adjusted likelihood ratio method is a good alternative to the two previous methods, especially to the first when the sample size is large. The three methods require iterative calculations to obtain the CI. If one is looking for methods that are simple to apply (that is, ones that admit a simple, explicit solution), the best option is the Gart logit method for 1/3≤ OR≤3 and, if in other cases, the Agresti logit method. The Cornfield chi-squared and Gart logit methods should not be used outside the specified interval OR. The paper also selects the best methods for realizing the classic independence test (θ = 1).