A Direct Variance Estimation (DiVE) for Meta-Analysis of Median Differences

Abstract: Meta-analyses of two-group studies that report median differences typically rely on methods that require, in addition to the median difference and sample size, summary measures of dispersion such as quartiles or ranges. Studies that do not report such statistics are often excluded from the meta-analysis. Existing two-stage approaches first estimate the asymptotic variance of the median difference within each study under parametric assumptions, and then combine these study-specific estimates to obtain the pooled median difference and its variance. We propose Direct Variance Estimation (DiVE), a method that directly estimates the variance of the pooled difference using only study-level median differences and their sample sizes. A comprehensive simulation study across a wide range of distributional scenarios shows that DiVE performs comparably to or better than conventional two-stage methods, with clear advantages when the number of studies is small. A re-analysis of published meta-analyses demonstrates that DiVE enables the inclusion of studies lacking dispersion statistics, leading to a more comprehensive and potentially less biased synthesis of evidence.