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      A re-evaluation of random-effects meta-analysis

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          Abstract

          Meta-analysis in the presence of unexplained heterogeneity is frequently undertaken by using a random-effects model, in which the effects underlying different studies are assumed to be drawn from a normal distribution. Here we discuss the justification and interpretation of such models, by addressing in turn the aims of estimation, prediction and hypothesis testing. A particular issue that we consider is the distinction between inference on the mean of the random-effects distribution and inference on the whole distribution. We suggest that random-effects meta-analyses as currently conducted often fail to provide the key results, and we investigate the extent to which distribution-free, classical and Bayesian approaches can provide satisfactory methods. We conclude that the Bayesian approach has the advantage of naturally allowing for full uncertainty, especially for prediction. However, it is not without problems, including computational intensity and sensitivity to a priori judgements. We propose a simple prediction interval for classical meta-analysis and offer extensions to standard practice of Bayesian meta-analysis, making use of an example of studies of ‘set shifting’ ability in people with eating disorders.

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          Bias in meta-analysis detected by a simple, graphical test

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            Quantifying heterogeneity in a meta-analysis.

            The extent of heterogeneity in a meta-analysis partly determines the difficulty in drawing overall conclusions. This extent may be measured by estimating a between-study variance, but interpretation is then specific to a particular treatment effect metric. A test for the existence of heterogeneity exists, but depends on the number of studies in the meta-analysis. We develop measures of the impact of heterogeneity on a meta-analysis, from mathematical criteria, that are independent of the number of studies and the treatment effect metric. We derive and propose three suitable statistics: H is the square root of the chi2 heterogeneity statistic divided by its degrees of freedom; R is the ratio of the standard error of the underlying mean from a random effects meta-analysis to the standard error of a fixed effect meta-analytic estimate, and I2 is a transformation of (H) that describes the proportion of total variation in study estimates that is due to heterogeneity. We discuss interpretation, interval estimates and other properties of these measures and examine them in five example data sets showing different amounts of heterogeneity. We conclude that H and I2, which can usually be calculated for published meta-analyses, are particularly useful summaries of the impact of heterogeneity. One or both should be presented in published meta-analyses in preference to the test for heterogeneity. Copyright 2002 John Wiley & Sons, Ltd.
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              Meta-analysis in clinical trials

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                Author and article information

                Journal
                J R Stat Soc Ser A Stat Soc
                rssa
                Journal of the Royal Statistical Society. Series A, (Statistics in Society)
                Blackwell Publishing Ltd
                0964-1998
                1467-985X
                January 2009
                : 172
                : 1
                : 137-159
                Affiliations
                Medical Research Council Biostatistics Unit Cambridge, UK
                Author notes
                Julian P. T. Higgins, Medical Research Council Biostatistics Unit, Institute of Public Health, Robinson Way, Cambridge, CB2 0SR, UK. E-mail: julian.higgins@ 123456mrc-bsu.cam.ac.uk
                Article
                10.1111/j.1467-985X.2008.00552.x
                2667312
                19381330
                c0aa6b67-e23d-4596-bb41-8daadb56906d
                © 2009 The Royal Statistical Society and Blackwell Publishing Ltd

                Re-use of this article is permitted in accordance with the Creative Commons Deed, Attribution 2.5, which does not permit commercial exploitation.

                History
                : March 2008
                : March 2008
                Categories
                Original Articles

                Statistics
                random-effects models,systematic reviews,prediction,meta-analysis
                Statistics
                random-effects models, systematic reviews, prediction, meta-analysis

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