  We consider the problem of meta-analyzing two-group studies that report the
median of the outcome. Often, these studies are excluded from meta-analysis
because there are no well-established statistical methods to pool the
difference of medians. To include these studies in meta-analysis, several
authors have recently proposed methods to estimate the sample mean and standard
deviation from the median, sample size, and several commonly reported measures
of spread. Researchers frequently apply these methods to estimate the
difference of means and its variance for each primary study and pool the
difference of means using inverse variance weighting. In this work, we develop
several methods to directly meta-analyze the difference of medians. We conduct
a simulation study evaluating the performance of the proposed median-based
methods and the competing transformation-based methods. The simulation results
show that the median-based methods outperform the transformation-based methods
when meta-analyzing studies that report the median of the outcome, especially
when the outcome is skewed. Moreover, we illustrate the various methods on a
real-life data set.
