Homogeneity test of risk differences of marginal and conditional probabilities in several incomplete correlated 2x2 tables

This article considers K pairs of incomplete correlated 2 x 2 tables in which the interesting measurement is the risk difference between marginal and conditional probabilities. A Wald-type statistic and a score-type statistic are presented to test the homogeneity hypothesis about risk differences across strata. Powers and sample size formulae based on the above two statistics are deduced. Figures about sample size against risk difference (or marginal probability) are given. A real example is used to illustrate the proposed methods.