Numerical Results on Approximate Confidence Limits for the Odds Ratio

Summary Consider the comparison of two binomial variates with parameters p1 and p2. The parameter of non-centrality for the Fisher–Irwin exact test is the odds ratio, ψ = p1q2/p2q1, where qi = 1 – pi, i = 1, 2. Exact confidence limits for ψ may be calculated (Fisher, 1935, 1962; Cornfield, 1956) and several authors have suggested approximate methods. The various approximate methods are reviewed and, from both theoretical and numerical results, we find that Cornfield's approximate method and Method II of Gart (1962) yield the better approximations under various conditions. An F-test alternative to the exact test of 2 × 2 tables (Gart, 1962) is found to be accurate in small numbers.