Power and Sample Size for a Collection of 2 x 2 Tables

A simple approximation is presented for the asymptotic power of the Mantel-Haenszel procedure for testing the hypothesis that the common odds ratio in a collection of 2 x 2 tables is unity. This approximation is particularly useful in evaluating the power of a study with several strata which reaches negative conclusions. The corresponding formula is also provided for estimating the sample size before such a study has begun, by approximating the margins of the stratum-specific tables with estimates obtained from pre-existing data. The approximations are good for moderate odds ratios (not greater than 6) and provide estimates which can differ by 10% to 30% from the traditional power estimates based on the overall table of totals obtained by collapsing the stratum-specific subtables.