Extending the coefficient of variation for measuring heterogeneity following a meta-regression

Meta-regression is often used to form hypotheses about what is associated with heterogeneity in a meta-analysis and to estimate the extent to which effects can vary between cohorts and other distinguishing factors. However, study-level variables, called moderators, that are available and used in the meta-regression analysis will rarely explain all of the heterogeneity. Therefore, measuring and trying to understand residual heterogeneity is still important in a meta-regression, although it is not clear how some heterogeneity measures should be used in the meta-regression context. The coefficient of variation, and its variants, are useful measures of relative heterogeneity. We consider these measures in the context of meta-regression which allows researchers to investigate heterogeneity at different levels of the moderator and also average relative heterogeneity overall. We also provide CIs for the measures and our simulation studies show that these intervals have good coverage properties. We recommend that these measures and corresponding intervals could provide useful insights into moderators that may be contributing to the presence of heterogeneity in a meta-analysis and lead to a better understanding of estimated mean effects.