On ratio measures of heterogeneity for meta-analyses

As a measure of heterogeneity in meta-analysis, the coefficient of variation (CV) has been recently considered, providing researchers with a complement to the very popular $$ measure. While $$ measures the proportion of total variance that is due to variance of the random effects, the CV is the ratio of the standard deviation of the random effects to the effect of interest. Consequently, the CV provides a different measure of the extent of heterogeneity in a meta-analysis relative to the effect being measured. However, very large CV values can occur when the effect is small making interpretation difficult. The purpose of this article is two-fold. First, we consider variants of the CV that exist in the interval $$ which may be preferable for some researchers. Second, we provide interval estimators for the CV and its variants with excellent coverage properties. We perform simulation studies based on simulated and real data sets and draw comparisons between the methods. For both the CV and its transformations, we recommend confidence intervals using the propagating imprecision method or, as a simpler alternative but at the expense of slightly worse performance in terms of coverage, combining reduced-coverage confidence intervals for the two parameters. These interval estimators typically have better coverage properties for the CV measure than those previously considered.