Simultaneous interval estimates of the odds ratio in studies with two or more comparisons

More than one odds ratio estimate will often arise from a single epidemiologic study. Examples of designs where this may occur include those where there is more than one case or control group, and investigations of several risk factors as part of the same study. Various methods for presenting multiple interval estimates are discussed, including: the naive method, the Bonferroni method, the Dunn method, the Scheffé method, and the Dunnett method. For rectangular regions the Dunnett method gives a region with the most appropriate confidence level, but this region contains a different set of odds ratio estimates than are implied by the usual significance tests. A confidence ellipse circumscribed by the Scheffé limits gives the best agreement with the significance tests. Each of these methods is illustrated with a numerical example.