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McGrath S, Zhao X, Ozturk O, Katzenschlager S, Steele R, Benedetti A. metamedian: An R package for meta-analyzing studies reporting medians. Res Synth Methods 2024; 15:332-346. [PMID: 38073145 DOI: 10.1002/jrsm.1686] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2023] [Revised: 11/15/2023] [Accepted: 11/16/2023] [Indexed: 01/05/2024]
Abstract
When performing an aggregate data meta-analysis of a continuous outcome, researchers often come across primary studies that report the sample median of the outcome. However, standard meta-analytic methods typically cannot be directly applied in this setting. In recent years, there has been substantial development in statistical methods to incorporate primary studies reporting sample medians in meta-analysis, yet there are currently no comprehensive software tools implementing these methods. In this paper, we present the metamedian R package, a freely available and open-source software tool for meta-analyzing primary studies that report sample medians. We summarize the main features of the software and illustrate its application through real data examples involving risk factors for a severe course of COVID-19.
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Affiliation(s)
- Sean McGrath
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts, USA
| | - XiaoFei Zhao
- MOE Key Laboratory of Bioinformatics, Bioinformatics Division, BNRIST and Department of Automation, Tsinghua University, Beijing, China
| | - Omer Ozturk
- Department of Statistics, The Ohio State University, Columbus, Ohio, USA
| | | | - Russell Steele
- Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada
| | - Andrea Benedetti
- Department of Epidemiology, Biostatistics, and Occupational Health, McGill University, Montreal, Quebec, Canada
- Respiratory Epidemiology and Clinical Research Unit (RECRU), McGill University Health Centre, Montreal, Quebec, Canada
- Department of Medicine, McGill University, Montreal, Quebec, Canada
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McGrath S, Katzenschlager S, Zimmer AJ, Seitel A, Steele R, Benedetti A. Standard error estimation in meta-analysis of studies reporting medians. Stat Methods Med Res 2023; 32:373-388. [PMID: 36412105 DOI: 10.1177/09622802221139233] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
We consider the setting of an aggregate data meta-analysis of a continuous outcome of interest. When the distribution of the outcome is skewed, it is often the case that some primary studies report the sample mean and standard deviation of the outcome and other studies report the sample median along with the first and third quartiles and/or minimum and maximum values. To perform meta-analysis in this context, a number of approaches have recently been developed to impute the sample mean and standard deviation from studies reporting medians. Then, standard meta-analytic approaches with inverse-variance weighting are applied based on the (imputed) study-specific sample means and standard deviations. In this article, we illustrate how this common practice can severely underestimate the within-study standard errors, which results in poor coverage for the pooled mean in common effect meta-analyses and overestimation of between-study heterogeneity in random effects meta-analyses. We propose a straightforward bootstrap approach to estimate the standard errors of the imputed sample means. Our simulation study illustrates how the proposed approach can improve the estimation of the within-study standard errors and consequently improve coverage for the pooled mean in common effect meta-analyses and estimation of between-study heterogeneity in random effects meta-analyses. Moreover, we apply the proposed approach in a meta-analysis to identify risk factors of a severe course of COVID-19.
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Affiliation(s)
- Sean McGrath
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA, USA
| | | | - Alexandra J Zimmer
- Department of Epidemiology, Biostatistics, and Occupational Health, 5620McGill University, Montreal, Quebec, Canada.,McGill International TB Centre, Montreal, Quebec, Canada
| | - Alexander Seitel
- Division of Intelligent Medical Systems, 28333German Cancer Research Center (DKFZ), Heidelberg, Germany
| | - Russell Steele
- Department of Mathematics and Statistics, 5620McGill University, Montreal, Quebec, Canada
| | - Andrea Benedetti
- Department of Epidemiology, Biostatistics, and Occupational Health, 5620McGill University, Montreal, Quebec, Canada.,Respiratory Epidemiology and Clinical Research Unit (RECRU), 54473McGill University Health Centre, Montreal, Quebec, Canada.,Department of Medicine, 5620McGill University, Montreal, Quebec, Canada
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