Heterogeneity Measure in Meta-analysis without Study-specific Variance Information

Assessing heterogeneity between the independent studies in a meta-analysis plays a critical role in quantifying the amount of dispersion. The well-known Higgins' I2 statistic has been used most often for measuring heterogeneity. However, the problem of the within-study variances involved in this measure is discussed, which leads to misinterpretation. Alternatively, the between-study coefficient of variation, the ratio of the standard deviation of the random effects to the effect, is of interest. This current work is motivated by meta-analytic data on continuous outcomes reported only the sample means and sample sizes. No sampling variance estimate is available in the studies. In such a case, we introduce the mean difference estimator based on the profile likelihood and bootstrap methods and propose the coefficient of variation estimator for measuring the heterogeneity of the mean differences. The statistical power of the coefficient of variation is determined based on simulations. The results indicate that the estimated between-study coefficient of variation derived from maximum profile likelihood estimation has a lower bias than that obtained from bootstrap estimation. The Wald-type confidence interval using variance estimation derived from the delta method provides a suitable coverage probability and has a short length interval.