Tests for homogeneity of the risk ratio in a series of 2x2 tables

We often apply the risk ratio to measure the strength of a causal relationship between a suspected risk factor and a disease of interest. In this paper we consider testing the homogeneity of risk ratio over a series of 2x2 tables. In addition to the classical weighted least squares (CWLS) test procedure, we consider two test procedures using simple transformations of the CWLS statistic and develop three other asymptotically weighted test procedures. On the basis of Monte Carlo simulation, we conclude that the commonly-used CWLS test procedure is generally conservative, especially when the number of 2x2 tables is large and the mean group size per table is moderate or small. We further find that two of the test procedures discussed here can not only generally outperform the CWLS test procedure, but also perform well in a variety of situations considered in this paper. Finally, we illustrate the use of these testing procedures with an example of six randomized trials that assess the effects of aspirin on the prevention of death in post-myocardial infarction patients.