COMPARISON OF EXACT, MID-P, AND MANTEL-HAENSZEL CONFIDENCE-INTERVALS FOR THE COMMON ODDS RATIO ACROSS SEVERAL 2X2 CONTINGENCY-TABLES

The exact, mid-p, and Mantel-Haenszel confidence intervals for the common odds ratio across k 2 x 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.