Is the Risk Difference Really a More Heterogeneous Measure?

There are claims in the literature that the risk difference is a more heterogeneous measure than the odds ratio or risk ratio. These claims are based on surveys of meta-analyses showing that tests reject the null hypothesis of homogeneity more often for the risk difference than for the ratio measures. Discussions of this point have neglected the fact that homogeneity tests can have different levels of statistical power (i.e., different probabilities of rejecting the null when it is false) across different scales. We give hypothetical examples in which there is arguably equal heterogeneity across risk difference and odds ratio measures but in which the risk difference homogeneity test rejects more often, and therefore has higher power, than the odds ratio homogeneity test. These examples suggest that current empirical evidence for the claim that the risk difference is more heterogeneous is not at present satisfactory. Further research could consider other approaches to empirical comparisons of the heterogeneity of the three measures.