A revisit on tests for homogeneity of the risk difference

Lipsitz et al. (1998, Biometrics 54, 148-160) discussed testing the homogen eity of the risk difference for a series of 2 x 2 tables. They proposed and evaluated several weighted test statistics, including the commonly used we ighted least squares test statistic. Here we suggest various important impr ovements on these test statistics. First, we propose using the one-sided an alogues of the test procedures proposed by Lipsitz et al. because we should only reject the null hypothesis of homogeneity when the variation of the e stimated risk differences between centers is large. Second, Re generalize t heir study by redesigning the simulations to include the situations conside red by Lipsitz et al. (1998) as special cases. Third, we consider a logarit hmic transformation of the weighted least squares test statistic to improve the normal approximation of its sampling distribution. On the basis of Mon te Carlo simulations, we note that, as long as the mean treatment group siz e per table is moderate or large (greater than or equal to 16), this simple test statistic, in conjunction with the commonly used adjustment procedure for sparse data, can be useful when the number of 2 x 2 tables is small or moderate (less than or equal to 32). in these situations, in fact, we find that our proposed method generally outperforms ail the statistics consider ed by Lipsitz et al. Finally, we include a general guideline about which te st statistic should be used in a variety of situations.