Power calculations for detecting interaction in stratified 2x2 tables

Given several 2x2 contingency tables, the first step in epidemiologic research is to test for homogeneity of odds ratios across these tables. A second problem of equal interest, but often overlooked, is to evaluate the power of detection of interaction if it is present. We address the latter issue in the context of 2x2 contingency tables. For the 2x2x2 case, given the marginal totals and the odds ratios for the respective two tables, we provide a closed form power formula for the rejection of the null hypothesis of homogeneity of the odds ratios. For several 2x2 tables, we provide a resampling approach to assessing the power for detecting interaction, if present.