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 I 2 measure. While I 2 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 0 , 1 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.

The diamond ratio: A visual indicator of the extent of heterogeneity in meta-analysis.

The result of a meta-analysis is conventionally pictured in the forest plot as a diamond, whose length is the 95% confidence interval (CI) for the summary measure of interest. The Diamond Ratio (DR) is the ratio of the length of the diamond given by a random effects meta-analysis to that given by a fixed effect meta-analysis. The DR is a simple visual indicator of the amount of change caused by moving from a fixed-effect to a random-effects meta-analysis. Increasing values of DR greater than 1.0 indicate increasing heterogeneity relative to the effect variances. We investigate the properties of the DR, and its relationship to four conventional but more complex measures of heterogeneity. We propose for the first time a CI on the DR, and show that it performs well in terms of coverage. We provide example code to calculate the DR and its CI, and to show these in a forest plot. We conclude that the DR is a useful indicator that can assist students and researchers to understand heterogeneity, and to appreciate its extent in particular cases.