Abstract
BackgroundRigorous, 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.MethodsWe 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.ResultsFor 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.ConclusionsMethods 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.
Highlights
Rigorous, informative meta-analyses rely on availability of appropriate summary statistics or individual participant data
Given the influential role of meta-analysis in shaping clinical guidelines and in turn patient care, it is critical that reviews summarise the available research findings with minimum bias and maximum precision, in order to provide conclusions that are of use to patients and healthcare professionals and that act as an effective guide to future research priorities
The first aim of this review was to provide an update on new developments since a previous review [5] of methods, in the meta-analysis context, of determining the variance, standard deviation (SD) or standard error (SE) where these are missing from the original trial report
Summary
Informative meta-analyses rely on availability of appropriate summary statistics or individual participant data. 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. Where continuous outcomes have a skewed distribution, incomplete reporting of the SD and mean is more widespread: often other summaries are reported, with the quartiles or minimum and maximum being given instead of the SD and the median being stated in place of the mean In such situations, the systematic reviewer must either exclude the trial from the meta-analysis – with accompanying concerns over the introduction of potential for bias and the loss of precision – or find an alternative method of deriving the missing mean or SD information based on information available in the trial report
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