Brown, B. M.; Suesse, Thomas; and Yap, Von Bing, Wilson confidence intervals for the two-sample log-odds-ratio in stratified 2 x 2 contingency tables, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 13-10, 2010, 30p.
Large-sample Wilson-type confidence intervals (CIs) are derived for a parameter of interest in many clinical trials situations: the log-odds-ratio, in a two sample experiment comparing binomial success proportions, say between cases and controls. The methods cover several scenarios: (i) results embedded in a single 2 x 2 contingency table, (ii) a series of K 2 x 2 tables with common parameter, or (iii) K tables, where the parameter may change across tables under the influence of a covariate. The calculations of the Wilson CI require only simple numerical assistance, and for example are easily carried out using Excel. The main competitor, the exact CI, has two disadvantages: It requires burdensome search algorithms for the multi-table case and results in strong over-coverage associated with long confidence intervals. All the application cases are illustrated through a well-known example. A simulation study then investigates how the Wilson CI performs among several competing methods. The Wilson interval is shortest, except for very large odds ratios, while maintaining coverage similar to Wald-type intervals. An alternative to the Wald CI is the Agresti-Coull CI, calculated from Wilson and Wald CIs, which has same length as the Wald CI but improved coverage.