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

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 =[Formula: see text] (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).

One-tailed asymptotic inferences for the difference of proportions: Analysis of 97 methods of inference.

Two-tailed asymptotic inferences for the difference d = p2 - p1 with independent proportions have been widely studied in the literature. Nevertheless, the case of one tail has received less attention, despite its great practical importance (superiority studies and noninferiority studies). This paper assesses 97 methods to make these inferences (test and confidence intervals [CIs]), although it also alludes to many others. The conclusions obtained are (1) the optimal method in general (and particularly for errors α = 1% and 5%) is based on arcsine transformation, with the maximum likelihood estimator restricted to the null hypothesis and increasing the successes and failures by 3/8; (2) the optimal method for α = 10% is a modification of the classic model of Peskun; (3) a more simple and acceptable option for large sample sizes and values of d not near to ±1 is the classic method of Peskun; and (4) in the particular case of the superiority and inferiority tests, the optimal method is the classic Wald method (with continuity correction) when the successes and failures are increased by one. We additionally select the optimal methods to make compatible the conclusions of the homogeneity test and the CI for d, both for one tail and for two (methods which are related to arcsine transformation and the Wald method).