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. 2018 Mar 7;18(1):25.
doi: 10.1186/s12874-018-0483-0.

Dealing with missing standard deviation and mean values in meta-analysis of continuous outcomes: a systematic review

Christopher J Weir  1 , Isabella Butcher  2 , Valentina Assi  2 , Stephanie C Lewis  2 , Gordon D Murray  2 , Peter Langhorne  3 , Marian C Brady  4
Affiliations

Dealing with missing standard deviation and mean values in meta-analysis of continuous outcomes: a systematic review

Christopher J Weir et al. BMC Med Res Methodol. .

Abstract

Background: Rigorous, informative meta-analyses rely on availability of appropriate summary statistics or individual participant data. For continuous outcomes, especially those with naturally skewed distributions, summary information on the mean or variability often goes unreported. While full reporting of original trial data is the ideal, we sought to identify methods for handling unreported mean or variability summary statistics in meta-analysis.

Methods: We undertook two systematic literature reviews to identify methodological approaches used to deal with missing mean or variability summary statistics. Five electronic databases were searched, in addition to the Cochrane Colloquium abstract books and the Cochrane Statistics Methods Group mailing list archive. We also conducted cited reference searching and emailed topic experts to identify recent methodological developments. Details recorded included the description of the method, the information required to implement the method, any underlying assumptions and whether the method could be readily applied in standard statistical software. We provided a summary description of the methods identified, illustrating selected methods in example meta-analysis scenarios.

Results: For missing standard deviations (SDs), following screening of 503 articles, fifteen methods were identified in addition to those reported in a previous review. These included Bayesian hierarchical modelling at the meta-analysis level; summary statistic level imputation based on observed SD values from other trials in the meta-analysis; a practical approximation based on the range; and algebraic estimation of the SD based on other summary statistics. Following screening of 1124 articles for methods estimating the mean, one approximate Bayesian computation approach and three papers based on alternative summary statistics were identified. Illustrative meta-analyses showed that when replacing a missing SD the approximation using the range minimised loss of precision and generally performed better than omitting trials. When estimating missing means, a formula using the median, lower quartile and upper quartile performed best in preserving the precision of the meta-analysis findings, although in some scenarios, omitting trials gave superior results.

Conclusions: Methods based on summary statistics (minimum, maximum, lower quartile, upper quartile, median) reported in the literature facilitate more comprehensive inclusion of randomised controlled trials with missing mean or variability summary statistics within meta-analyses.

Keywords: Continuous outcomes; Meta-analysis; Missing mean; Missing standard deviation; Systematic review.

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Conflict of interest statement

Ethics approval and consent to participate

The research did not directly involve human participants or human tissue. Ethical approval was granted by the ethics committee of the Centre for Population Health Sciences, Usher Institute of Population Health Sciences and Informatics, University of Edinburgh. Details of ethics approval for GALA trial (data set used in illustrative meta-analysis scenarios) provided in reference [7].

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no competing interests.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures

Fig. 1
Fig. 1
Systematic review of methods to derive missing variance/SD: PRISMA Flow Diagram. Flow diagram based on: Moher D, Liberati A, Tetzlaff J, Altman DG, The PRISMA Group (2009). Preferred Reporting Items for Systematic Reviews and Meta-Analyses: The PRISMA Statement. PLoS Med 6(6): e1000097. doi:10.1371/journal.pmed1000097
Fig. 2
Fig. 2
Systematic review of methods to derive missing mean: PRISMA Flow Diagram. Flow diagram based on: Moher D, Liberati A, Tetzlaff J, Altman DG, The PRISMA Group (2009). Preferred Reporting Items for Systematic Reviews and Meta-Analyses: The PRISMA Statement. PLoS Med 6(6): e1000097. 10.1371/journal.pmed1000097
See this image and copyright information in PMC

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