Revisiting and expanding the meta-analysis of variation: The log coefficient of variation ratio

Meta-analyses are often used to estimate the relative average values of a quantitative outcome in two groups (eg, control and experimental groups). However, they may also examine the relative variability (variance) of those groups. For such comparisons, two relatively new effect size statistics, the log-transformed "variability ratio" (the ratio of two standard deviations; lnVR) and the log-transformed "coefficients of variation ratio" (the ratio of two coefficients of variation; lnCVR) are useful. In practice, lnCVR may be of most use because a treatment may affect the mean and the variance simultaneously. We propose new estimators for lnCVR and lnVR, including for when the two groups are dependent (eg, cross-over and pre-test-post-test designs). Through simulation, we evaluated the bias of these estimators and make recommendations accordingly. We use the methods to demonstrate that: (a) lifestyle interventions have a heterogenizing effect on gestational weight gain in obese women and (b) low-glycemic index (GI) diets have a homogenizing effect on glycemic control in diabetics. We also find that the degree to which dependence among samples is accounted for can impact parameters such as τ² (ie, the between-study variance) and I² (ie, the proportion of the total variability due to between-study variance), and even the overall effect, and associated qualitative interpretations. Meta-analytic comparison of the variability between two groups enables us to ask completely new questions and to gain fresh insights from existing datasets. We encourage researchers to take advantage of these convenient new effect size measures for the meta-analysis of variation.