Comparison of Exact, Mid-p, and Mantel.Haenszel Confidence Intervals for the Common Odds Ratio Across Several 2 . 2 Contingency Tables

This department includes the two sections New Developments in Statistical Computing and Statistical Computing Software Reviews; suitable contents for each of these sections are described under the respective section heading.Articles submitted for the department, outside the two sections, should not be highly technical and should be relevant to the teaching or practice of statistical computing.The exact, mid-p, and Mantel.Haenszel confidence intervals for the common odds ratio across k 2 . 2 contingency tables were compared, in terms of their coverage and length characteristics.A network algorithm was crucial to making the simulations computationally feasible for the exact and mid-p methods.The Mantel.Haenszel method used a variance estimator.Although the exact method is the only one to guarantee, theoretically, that the interval will not undercover the true odds ratio, the mid-p method was seen, empirically, to also preserve coverage.At the same time it produced shorter intervals.In small samples with large underlying odds ratios, the Mantel.Haenszel method was often degenerate because the test statistic attained a boundary value.However a hybrid Mantel.Haenszel approach, whereby the exact interval was used at the boundary values, was shown to preserve nominal coverage and had a shorter average length than either the exact or mid-p intervals.