  An aggregate data meta-analysis is a statistical method that pools the
summary statistics of several selected studies to estimate the outcome of
interest. When considering a continuous outcome, typically each study must
report the same measure of the outcome variable and its spread (e.g., the
sample mean and its standard error). However, some studies may instead report
the median along with various measures of spread. Recently, the task of
incorporating medians in meta-analysis has been achieved by estimating the
sample mean and its standard error from each study that reports a median in
order to meta-analyze the means. In this paper, we propose two alternative
approaches to meta-analyze data that instead rely on medians. We systematically
compare these approaches via simulation study to each other and to methods that
transform the study-specific medians and spread into sample means and their
standard errors. We demonstrate that the proposed median-based approaches
perform better than the transformation-based approaches, especially when
applied to skewed data and data with high inter-study variance. In addition,
when meta-analyzing data that consists of medians, we show that the
median-based approaches perform considerably better than or comparably to the
best-case scenario for a transformation approach: conducting a meta-analysis
using the actual sample mean and standard error of the mean of each study.
Finally, we illustrate these approaches in a meta-analysis of patient delay in
tuberculosis diagnosis.
