Two-sample aggregate data meta-analysis of medians

TL;DR

This paper develops and evaluates new methods for meta-analyzing differences of medians directly, especially effective for skewed data, enhancing the inclusion of median-reported studies in meta-analyses.

Contribution

It introduces several median-based meta-analysis methods and compares their performance to existing transformation-based approaches through simulation and real data application.

Findings

Median-based methods outperform transformation-based methods for skewed data.

Median methods provide more accurate meta-analysis results when outcomes are skewed.

Simulation confirms the robustness of median-based approaches in various scenarios.

Abstract

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.