The validity of approximation methods for interval estimation of the odds ratio.

The validity of a confidence interval is determined by the probability that the random interval covers the true parameter value. A valid interval will have coverage probabilities at least as large as the confidence coefficient for all values of the parameter. The validity of three methods for constructing an approximate confidence interval on the odds ratio parameter for 2 X 2 tables is examined in the conditional hypergeometric sampling situation. Two examples are shown for which Cornfield's method is seen to be valid over a fairly wide range of true odds ratios, while the methods of Miettinen and Woolf are often found to be invalid. A number of other examples are studied with qualitatively similar results.