Tests for homogeneity of the risk difference when data are sparse

Test statistics for the homogeneity of the risk difference for a series of 2 x 2 tables when the data are sparse is proposed. A weighted least squares statistic is commonly used to test for equality of the risk difference over the tables; however, when the data are sparse, this statistic can have anticonservative Type I error rates. Simulation is used to compare the proposed test statistics to the weighted least squares statistic. The weighted least squares statistic has the most anticonservative Type I error rates of all the statistics compared. We suggest the use of one of our proposed test statistics instead of the weighted least squares statistic.