Usual and shortest confidence intervals on odds ratios from logistic regression

Based on the large-sample normal distribution of the sample log odds ratio and its asymptotic variance from maximum likelihood logistic regression, sh ortest 95% confidence intervals for the odds ratio are developed. Although the usual confidence interval on the odds ratio is unbiased, the shortest i nterval is not. That is, while covering the true odds ratio with the stated probability, the shortest interval covers some values below the true odds ratio with higher probability. The upper and lower limits of the shortest i nterval are shifted to the left of those of the usual interval, with greate r shifts in the upper limits. With the log odds model gamma+X beta, in whic h X is binary, simulation studies showed that the approximate average perce nt difference in length is 7.4% for n (sample size) = 100, and 3.8% for n = 200. Precise estimates of the covering probabilities of the two types of i ntervals were obtained from simulation studies, and are compared graphicall y. For odds ratio estimates greater (less) than one, shortest intervals are more (less) likely to include one than are the usual intervals. The usual intervals are likelihood-based and the shortest intervals are not. The usua l intervals have minimum expected length among the class of unbiased interv als. Shortest intervals do not provide important advantages over the usual intervals, which we recommend for practical use.