Estimating the sample mean and standard deviation from commonly reported quantiles in meta-analysis

TL;DR

This paper introduces two new methods to estimate the sample mean and standard deviation from reported quantiles in meta-analyses, especially when data are skewed and not normally distributed.

Contribution

The paper proposes novel estimation techniques that improve accuracy over existing methods for non-normal data in meta-analyses.

Findings

Proposed methods outperform existing ones on non-normal data

Simulation studies demonstrate improved estimation accuracy

Empirical assessments confirm practical usefulness

Abstract

Researchers increasingly use meta-analysis to synthesize the results of several studies in order to estimate a common effect. When the outcome variable is continuous, standard meta-analytic approaches assume that the primary studies report the sample mean and standard deviation of the outcome. However, when the outcome is skewed, authors sometimes summarize the data by reporting the sample median and one or both of (i) the minimum and maximum values and (ii) the first and third quartiles, but do not report the mean or standard deviation. To include these studies in meta-analysis, several methods have been developed to estimate the sample mean and standard deviation from the reported summary data. A major limitation of these widely used methods is that they assume that the outcome distribution is normal, which is unlikely to be tenable for studies reporting medians. We propose two novel approaches to estimate the sample mean and standard deviation when data are suspected to be non-normal. Our simulation results and empirical assessments show that the proposed methods often perform better than the existing methods when applied to non-normal data.