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.