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. 2020 Sep;29(9):2520-2537.
doi: 10.1177/0962280219889080. Epub 2020 Jan 30.

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

Sean McGrath  1 , XiaoFei Zhao  1 , Russell Steele  2 , Brett D Thombs  3   4   5   6   7   8   9 , Andrea Benedetti  1   5   6 ; DEPRESsion Screening Data (DEPRESSD) Collaboration
Affiliations

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

Sean McGrath et al. Stat Methods Med Res. 2020 Sep.

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.

Keywords: Meta-analysis; first quartile; maximum value; median; minimum value; third quartile.

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Conflict of interest statement

Declaration of conflicting interests

All authors have completed the ICJME uniform disclosure form at www.icmje.org/coi_disclosure.pdf (available on request from the corresponding author) and declare: no support from any organisation for the submitted work other than that described above; no financial relationships with any organizations that might have an interest in the submitted work in the previous three years with the following exceptions: JCNC Is a steering committee member and/or consultant of Astra Zeneca, Bayer, Lilly, MSD and Pfizer. She has received sponsorships and honorarium for giving lectures and providing consultancy and her affiliated institution has received research grants from these companies; UH declares that within the last three years, he was an advisory board member for Lundbeck and Servier; a consultant for Bayer Pharma; a speaker for Pharma and Servier; and received personal fees from Janssen Janssen and a research grant from Medice, all outside the submitted work; MI declares that he has received a grant from Novartis Pharma, and personal fees from Meiji, Mochida, Takeda, Novartis, Yoshitomi, Pfizer, Eisai, Otsuka, MSD, Technomics, and Sumitomo Dainippon, all outside of the submitted work; KI declares that she has received honorarium for speaker fees for educational lectures for Sanofi, Sunovion, Janssen and Novo Nordisk. No other relationships or activities that could appear to have influenced the submitted work.

Figures

Figure 1:
Figure 1:
ARE of the Luo/Wan (red line, hollow circle), QE (blue line, solid triangle), and BC (green line, solid circle) methods in scenario S1. The panels in the left and right columns present the ARE of the sample mean estimators and sample standard deviation estimators, respectively.
Figure 2:
Figure 2:
ARE of the Luo/Wan (red line, hollow circle), QE (blue line, solid triangle), and BC (green line, solid circle) methods in scenario S2. The panels in the left and right columns present the ARE of the sample mean estimators and sample standard deviation estimators, respectively.
Figure 3:
Figure 3:
Forest plot from the meta-analysis of mean PHQ-9 scores. The study-specific estimates represent the true sample means and their 95% CIs. The pooled estimate shown was obtained using the true-study-specific sample means and standard deviations. In the “Mean PHQ-9” column, the true study-specific sample means and their 95% CIs as well as the pooled mean and its 95% CI are given.
See this image and copyright information in PMC

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