re-evaluation of random-effects meta-analysis

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 addressin...

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Published in	Journal of the Royal Statistical Society. Series A, Statistics in society Vol. 172; no. 1; pp. 137 - 159
Main Authors	Higgins, Julian P. T., Thompson, Simon G., Spiegelhalter, David J.
Format	Journal Article
Language	English
Published	Oxford, UK Oxford, UK : Blackwell Publishing Ltd 01.01.2009 Blackwell Publishing Ltd Blackwell Publishing Blackwell Royal Statistical Society Oxford University Press
Series	Journal of the Royal Statistical Society Series A
Subjects	Analysis Applications Bayesian analysis Bayesian method Confidence interval Degrees of freedom Distribution theory Eating disorders Exact sciences and technology Forecasts Gaussian distributions General topics Hypothesis Hypothesis testing Inference Justification Mathematical intervals Mathematics Meta analysis Methodology Modeling Normal distribution Null hypothesis Original Prediction Predictions Probability and statistics Probability theory and stochastic processes Random-effects models Sciences and techniques of general use Standard error Statistical methods Statistical variance Statistics Stochastic processes Systematic reviews Uncertainty Bayes estimation Random-effects models Prediction Gaussian distribution Prediction theory Non parametric estimation Statistical estimation Multivariate analysis Random distribution Stochastic process Mean estimation Prediction interval Meta-analysis Statistical method Hypothesis test Heterogeneity Statistical test Distribution function Systematic reviews Random effect Filtering theory Application
Online Access	Get full text
ISSN	0964-1998 1467-985X
DOI	10.1111/j.1467-985X.2008.00552.x

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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.
AbstractList	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. 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. 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.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. 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. [PUBLICATION 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. Copyright Journal compilation (c) 2009 Royal Statistical Society. 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. Reprinted by permission of Blackwell Publishers
Author	Higgins, Julian P. T. Thompson, Simon G. Spiegelhalter, David J.
Author_xml	– sequence: 1 givenname: Julian P. T. surname: Higgins fullname: Higgins, Julian P. T. – sequence: 2 givenname: Simon G. surname: Thompson fullname: Thompson, Simon G. – sequence: 3 givenname: David J. surname: Spiegelhalter fullname: Spiegelhalter, David J.
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20981093$$DView record in Pascal Francis https://www.ncbi.nlm.nih.gov/pubmed/19381330$$D View this record in MEDLINE/PubMed http://econpapers.repec.org/article/blajorssa/v_3a172_3ay_3a2009_3ai_3a1_3ap_3a137-159.htm$$DView record in RePEc
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PublicationDate_xml	– month: 01 year: 2009 text: January 2009
PublicationDecade	2000
PublicationPlace	Oxford, UK
PublicationPlace_xml	– name: Oxford, UK – name: Oxford – name: England
PublicationSeriesTitle	Journal of the Royal Statistical Society Series A
PublicationTitle	Journal of the Royal Statistical Society. Series A, Statistics in society
PublicationTitleAlternate	J R Stat Soc Ser A Stat Soc
PublicationYear	2009
Publisher	Oxford, UK : Blackwell Publishing Ltd Blackwell Publishing Ltd Blackwell Publishing Blackwell Royal Statistical Society Oxford University Press
Publisher_xml	– name: Oxford, UK : Blackwell Publishing Ltd – name: Blackwell Publishing Ltd – name: Blackwell Publishing – name: Blackwell – name: Royal Statistical Society – name: Oxford University Press
References	O'Hagan, A. (1994) Kendall's Advanced Theory of Statistics, vol. 2B, Bayesian Inference. London: Arnold. Thompson, S. G. (1994) Why sources of heterogeneity in meta-analysis should be investigated. Br. Med. J., 309, 1351-1355. Hedges, L. V. and Olkin, I. (1985) Statistical Methods for Meta-analysis. London: Academic Press. Louis, T. A. (1991) Using Empirical Bayes methods in biopharmaceutical research. Statist. Med., 10, 811-829. Bailey, K. R. (1987) Inter-study differences-how should they influence the interpretation and analysis of results. Statist. Med., 6, 351-360. Lambert, P. C., Sutton, A. J., Burton, P. R., Abrams, K. R. and Jones, D. R. (2005) How vague is vague?: a simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS. Statist. Med., 24, 2401-2428. Whitehead, A. (2002) Meta-analysis of Controlled Clinical Trials. Chichester: Wiley. Turner, R. M., Spiegelhalter, D. J., Smith, G. C. S. and Thompson, S. G. (2008) Bias modelling in evidence synthesis. J. R. Statist. Soc. A, to be published. Tjur, T. (1998) Nonlinear regression, quasi likelihood, and overdispersion in generalized linear models. Am. Statistn, 52, 222-227. Eddy, D. M., Hasselblad, V. and Shachter, R. (1992) Meta-analysis by the Confidence Profile Method. San Diego: Academic Press. Spiegelhalter, D. J. and Best, N. G. (2003) Bayesian approaches to multiple sources of evidence and uncertainty in complex cost-effectiveness modelling. Statist. Med., 22, 3687-3709. Burr, D., Doss, H., Cooke, G. E. and Goldschmidt-Clermont, P. J. (2003) A meta-analysis of studies on the association of the platelet PlA polymorphism of glycoprotein IIIa and risk of coronary heart disease. Statist. Med., 22, 1741-1760. Welton, N. J., Ades, A. E., Carlin, J. B., Altman, D. G. and Sterne, J. A. C. (2008) Models for potentially biased evidence in meta-analysis using empirically based priors. J. R. Statist. Soc. A, to be published. Greenland, S. and O'Rourke, K. (2001) On the bias produced by quality scores in meta-analysis, and a hierarchical view of proposed solutions. Biostatistics, 2, 463-471. Knapp, G., Biggerstaff, B. J. and Hartung, J. (2006) Assessing the amount of heterogeneity in random-effects meta-analysis. Biometr. J., 48, 271-285. Gelman, A. (2006) Prior distributions for variance parameters in hierarchical models. Bayes. Anal., 1, 515-533. Smith, T. C., Spiegelhalter, D. J. and Thomas, A. (1995) Bayesian approaches to random-effects meta-analysis: a comparative study. Statist. Med., 14, 2685-2699. Lee, K. J. and Thompson, S. G. (2007) Flexible parametric models for random-effects distributions. Statist. Med., 27, 418-434. Hedges, L. V. (1987) Commentary. Statist. Med., 6, 381-385. Warn, D. E., Thompson, S. G. and Spiegelhalter, D. J. (2002) Bayesian random effects meta-analysis of trials with binary outcomes: methods for the absolute risk difference and relative risk scales. Statist. Med., 21, 1601-1623. Light, R. J. (1987) Accumulating evidence from independent studies-what we can win and what we can lose. Statist. Med., 6, 221-231. Viechtbauer, W. (2007) Confidence intervals for the amount of heterogeneity in meta-analysis. Statist. Med., 26, 37-52. Anello, C. and Fleiss, J. L. (1995) Exploratory or analytic meta-analysis: should we distinguish between them? J. Clin. Epidem., 48, 109-116. Biggerstaff, B. J. and Tweedie, R. L. (1997) Incorporating variability in estimates of heterogeneity in the random effects model in meta-analysis. Statist. Med., 16, 753-768. DerSimonian, R. and Kacker, R. (2007) Random-effects model for meta-analysis of clinical trials: an update. Contemp. Clin. Trials, 28, 105-114. Kass, R. E. and Raftery, A. E. (1995) Bayes Factors. J. Am. Statist. Ass., 90, 773-795. Higgins, J. P. T. and Whitehead, A. (1996) Borrowing strength from external trials in a meta-analysis. Statist. Med., 15, 2733-2749. Gelman, A. B., Carlin, J. S., Stern, H. S. and Rubin, D. B. (1995) Bayesian Data Analysis. Boca Raton: Chapman and Hall-CRC. Pan, G. H. and Wolfe, D. A. (1997) Test for qualitative interaction of clinical significance. Statist. Med., 16, 1645-1652. Colditz, G. A., Burdick, E. and Mosteller, F. (1995) Heterogeneity in meta-analysis of data from epidemiologic studies: Commentary. Am. J. Epidem., 142, 371-382. Detsky, A. S., Naylor, C. D., O'Rourke, K., McGeer, A. J. and Labbe, K. A. (1992) Incorporating variations in the quality of individual randomized trials into meta-analysis. J. Clin. Epidem., 45, 255-265. Laird, N. and Louis, T. A. (1989) Empirical Bayes confidence intervals for a series of related experiments. Biometrics, 45, 481-495. Robbins, H. (1983) Some thoughts on empirical Bayes estimation. Ann. Statist., 11, 713-723. Goodman, S. N. (1999) Toward evidence-based medical statistics, 2: the Bayes factor. Ann. Intern. Med., 130, 1005-1013. Hardy, R. J. and Thompson, S. G. (1998) Detecting and describing heterogeneity in meta-analysis. Statist. Med., 17, 841-856. Raudenbush, S. W. and Bryk, A. S. (1985) Empirical Bayes meta-analysis. J. Educ. Statist., 10, 75-98. Laird, N. (1978) Nonparametric maximum likelihood estimation of a mixing distribution. J. Am. Statist. Ass., 73, 805-811. Böhning, D. (2005) Meta-analysis: a unifying meta-likelihood approach framing unobserved heterogeneity, study covariates, publication bias, and study quality. Meth. Inform. Med., 44, 127-135. Morris, C. N. and Normand, S. L. (1992) Hierachical models for combining information and for meta-analysis. Bayes. Statist., 4, 321-344. Follmann, D. A. and Proschan, M. A. (1999) Valid inference in random effects meta-analysis. Biometrics, 55, 732-737. Gail, M. and Simon, R. (1985) Testing for qualitative interaction between treatment effects and patient subsets. Biometrics, 41, 361-372. Feinstein, A. R. (1995) Meta-analysis: statistical alchemy for the 21st century. J. Clin. Epidem., 48, 71-79. Thompson, S. G. and Higgins, J. P. T. (2002) How should meta-regression analyses be undertaken and interpreted? Statist. Med., 21, 1559-1574. Spiegelhalter, D., Thomas, A., Best, N. and Lunn, D. (2003) WinBUGS User Manual, Version 1.4. Cambridge: Medical Research Council Biostatistics Unit. Burr, D. and Doss, H. (2005) A Bayesian semiparametric model for random-effects meta-analysis. J. Am. Statist. Ass., 100, 242-251. Aitkin, M. (1999a) A general maximum likelihood analysis of variance components in generalized linear models. Biometrics, 55, 117-128. Glasziou, P. P. and Sanders, S. L. (2002) Investigating causes of heterogeneity in systematic reviews. Statist. Med., 21, 1503-1511. Abrams, K. R. and Sanso, B. (1998) Approximate Bayesian inference in random effects meta-analysis. Statist. Med., 17, 201-218. Bernardo, J. M. and Smith, A. F. M. (1994) Bayesian Theory. Chichester: Wiley. Greenland, S. (2005) Multiple-bias modelling for analysis of observational data. J. R. Statist. Soc. A, 168, 267-291. Hartung, J. and Knapp, G. (2001a) A refined method for the meta-analysis of controlled clinical trials with binary outcome. Statist. Med., 20, 3875-3889. Morris, C. N. (1983) Parametric empirical Bayes inference: theory and applications. J. Am. Statist. Ass., 78, 47-65. Skene, A. M. and Wakefield, J. C. (1990) Hierarchical models for multicentre binary response studies. Statist. Med., 9, 919-929. DerSimonian, R. and Laird, N. (1986) Meta-analysis in clinical trials. Contr. Clin. Trials, 7, 177-188. Egger, M., Davey Smith, G., Schneider, M. and Minder, C. (1997) Bias in meta-analysis detected by a simple, graphical test. Br. Med. J., 315, 629-634. Aitkin, M. (1999b) Meta-analysis by random effect modelling in generalized linear models. Statist. Med., 18, 2343-2351. Berkey, C. S., Hoaglin, D. C., Mosteller, F. and Colditz, G. A. (1995) A random-effects regression model for meta-analysis. Statist. Med., 14, 395-411. Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and Van Der Linde, A. (2002) Bayesian measures of model complexity and fit (with discussion). J. R. Statist. Soc. B, 64, 583-639. Peto, R. (1987) Why do we need systematic overviews of randomised trials? Statist. Med., 6, 233-240. Vangel, M. G. and Rukhin, A. L. (1999) Maximum likelihood analysis for heteroscedastic one-way random effects ANOVA in interlaboratory studies. Biometrics, 55, 129-136. Bradburn, M. J., Deeks, J. J., Berlin, J. A. and Localio, A. R. (2006) Much ado about nothing: a comparison of the performance of meta-analytical methods with rare events. Statist. Med., 26, 53-77. Hardy, R. J. and Thompson, S. G. (1996) A likelihood approach to meta-analysis with random effects. Statist. Med., 15, 619-629. Cochrane Injuries Group Albumin Reviewers (1998) Human albumin administration in critically ill patients: systematic review of randomised controlled trials. Br. Med. J., 317, 235-240. Van Houwelingen, H. C., Zwinderman, K. H. and Stijnen, T. (1993) A bivariate approach to meta-analysis. Statist. Med., 12, 2273-2284. Whitehead, A. and Whitehead, J. (1991) A general parametric approach to the meta-analysis of randomised clinical trials. Statist. Med., 10, 1665-1677. Stijnen, T. and Van Houwelingen, J. C. (1990) Empirical Bayes methods in clinical trials meta-analysis. Biometr. J., 32, 335-346. Raghunathan, T. E. and Ii, Y. C. (1993) Analysis of binary data from a multicenter clinical-trial. Biometrika, 80, 127-139. Roberts, M. E., Tchanturia, K., Stahl, D., Southgate, L. and Treasure, J. (2007) A systematic review and meta-analysis of set-shifting ability in eating disorders. Psychol. Med., 37, 1075-1084. Ohlssen, D. I., Sharples, L. D. and Spiegelhalter, D. J. (2007) Flexible random-effects models using Bayesian semi-parametric models: applications to institutional comparisons. Statist. Med., 26, 2088-2112. Hartung, J. and Knapp, G. (2001b) On tests of the overall treatment effect in meta-analysis with normally distributed responses. Statist. Med., 20, 1771-1782. Piantadosi, S. and Gail, M. H. (1993) A comparison of the power of two tests for qualitative interactions. Statist. Med., 12, 1239-1248. Böhning, D. (2000) Computer-assisted Analysis 1997; 315 1999b; 18 1989; 45 1991; 10 1999a; 55 1978; 73 1987; 6 1998; 317 2001a; 20 2001b; 20 2005; 24 1983; 11 2007; 37 2005; 25 2007; 28 1998; 17 1986; 7 2000 2005; 100 2006; 26 1999; 55 1985 1997; 16 1999; 130 1993; 80 1998; 52 1992; 45 1985; 10 1989 1992; 4 2007; 26 1994; 309 2007; 27 1990; 32 1995; 90 1995; 14 2002; 7 1998 2008 2006 1995 1994 1985; 41 1992 2006; 1 2003 2002 1996; 15 2005; 44 2001; 323 1956 1983; 78 1993; 12 2002; 64 1995; 48 2005; 168 2002; 21 2006; 48 2001; 2 1995; 142 1990; 9 2003; 22 Hardy (2023032309081474300_) 1996; 15 Raudenbush (2023032309081474300_) 1985; 10 Egger (2023032309081474300_) 1997; 315 Pauler (2023032309081474300_) 2000 Aitkin (2023032309081474300_) 1999; 18 Anello (2023032309081474300_) 1995; 48 Eddy (2023032309081474300_) 1992 Ades (2023032309081474300_) 2005; 25 Aitkin (2023032309081474300_) 1999; 55 Cochrane Injuries Group Albumin Reviewers (2023032309081474300_) 1998; 317 Goodman (2023032309081474300_) 1999; 130 Greenland (2023032309081474300_) 2001; 2 Follmann (2023032309081474300_) 1999; 55 Berkey (2023032309081474300_) 1995; 14 Louis (2023032309081474300_) 1991; 10 DerSimonian (2023032309081474300_) 1986; 7 Skene (2023032309081474300_) 1990; 9 Morris (2023032309081474300_) 1992; 4 Smith (2023032309081474300_) 1995; 14 Böhning (2023032309081474300_) 2005; 44 Gelman (2023032309081474300_) 2006; 1 Welton (2023032309081474300_) 2008 Raghunathan (2023032309081474300_) 1993; 80 Larholt (2023032309081474300_) 1989 Böhning (2023032309081474300_) 2000 Feinstein (2023032309081474300_) 1995; 48 Higgins (2023032309081474300_) 1996; 15 Turner (2023032309081474300_) 2008 Morris (2023032309081474300_) 1983; 78 Higgins (2023032309081474300_) 2002; 7 Hartung (2023032309081474300_) 2001; 20 Burr (2023032309081474300_) 2005; 100 Thompson (2023032309081474300_) 1994; 309 Spiegelhalter (2023032309081474300_) 2002; 64 Whitehead (2023032309081474300_) 2002 Kass (2023032309081474300_) 1995; 90 Spiegelhalter (2023032309081474300_) 2003; 22 Tjur (2023032309081474300_) 1998; 52 Whitehead (2023032309081474300_) 1991; 10 Thompson (2023032309081474300_) 2002; 21 Detsky (2023032309081474300_) 1992; 45 Bailey (2023032309081474300_) 1987; 6 Jüni (2023032309081474300_) 2001; 323 Vangel (2023032309081474300_) 1999; 55 Light (2023032309081474300_) 1987; 6 Biggerstaff (2023032309081474300_) 1997; 16 Knapp (2023032309081474300_) 2006; 48 Spiegelhalter (2023032309081474300_) 2003 Cox (2023032309081474300_) 2006 Bradburn (2023032309081474300_) 2006; 26 Lee (2023032309081474300_) 2007; 27 Thompson (2023032309081474300_) 1998 Gail (2023032309081474300_) 1985; 41 Pan (2023032309081474300_) 1997; 16 Glasziou (2023032309081474300_) 2002; 21 Stijnen (2023032309081474300_) 1990; 32 DuMouchel (2023032309081474300_) 1994 DerSimonian (2023032309081474300_) 2007; 28 Higgins (2023032309081474300_) 2002; 21 Viechtbauer (2023032309081474300_) 2007; 26 Greenland (2023032309081474300_) 2005; 168 Hardy (2023032309081474300_) 1998; 17 Van Houwelingen (2023032309081474300_) 1993; 12 O’Hagan (2023032309081474300_) 1994 Peto (2023032309081474300_) 1987; 6 Laird (2023032309081474300_) 1989; 45 Robbins (2023032309081474300_) 1983; 11 Gelman (2023032309081474300_) 1995 Piantadosi (2023032309081474300_) 1993; 12 Lambert (2023032309081474300_) 2005; 24 Roberts (2023032309081474300_) 2007; 37 Bernardo (2023032309081474300_) 1994 Stein (2023032309081474300_) 1956 Laird (2023032309081474300_) 1978; 73 Colditz (2023032309081474300_) 1995; 142 Hedges (2023032309081474300_) 1985 Ohlssen (2023032309081474300_) 2007; 26 DuMouchel (2023032309081474300_) 2000 Hedges (2023032309081474300_) 1987; 6 Burr (2023032309081474300_) 2003; 22 Abrams (2023032309081474300_) 1998; 17 Warn (2023032309081474300_) 2002; 21
References_xml	– reference: Stijnen, T. and Van Houwelingen, J. C. (1990) Empirical Bayes methods in clinical trials meta-analysis. Biometr. J., 32, 335-346. – reference: Cochrane Injuries Group Albumin Reviewers (1998) Human albumin administration in critically ill patients: systematic review of randomised controlled trials. Br. Med. J., 317, 235-240. – reference: Egger, M., Davey Smith, G., Schneider, M. and Minder, C. (1997) Bias in meta-analysis detected by a simple, graphical test. Br. Med. J., 315, 629-634. – reference: Hartung, J. and Knapp, G. (2001a) A refined method for the meta-analysis of controlled clinical trials with binary outcome. Statist. Med., 20, 3875-3889. – reference: Higgins, J. P. T. and Whitehead, A. (1996) Borrowing strength from external trials in a meta-analysis. Statist. Med., 15, 2733-2749. – reference: Roberts, M. E., Tchanturia, K., Stahl, D., Southgate, L. and Treasure, J. (2007) A systematic review and meta-analysis of set-shifting ability in eating disorders. Psychol. Med., 37, 1075-1084. – reference: Higgins, J. P. T. and Thompson, S. G. (2002) Quantifying heterogeneity in a meta-analysis. Statist. Med., 21, 1539-1558. – reference: Hedges, L. V. (1987) Commentary. Statist. Med., 6, 381-385. – reference: O'Hagan, A. (1994) Kendall's Advanced Theory of Statistics, vol. 2B, Bayesian Inference. London: Arnold. – reference: Smith, T. C., Spiegelhalter, D. J. and Thomas, A. (1995) Bayesian approaches to random-effects meta-analysis: a comparative study. Statist. Med., 14, 2685-2699. – reference: Goodman, S. N. (1999) Toward evidence-based medical statistics, 2: the Bayes factor. Ann. Intern. Med., 130, 1005-1013. – reference: Whitehead, A. (2002) Meta-analysis of Controlled Clinical Trials. Chichester: Wiley. – reference: DerSimonian, R. and Laird, N. (1986) Meta-analysis in clinical trials. Contr. Clin. Trials, 7, 177-188. – reference: Burr, D., Doss, H., Cooke, G. E. and Goldschmidt-Clermont, P. J. (2003) A meta-analysis of studies on the association of the platelet PlA polymorphism of glycoprotein IIIa and risk of coronary heart disease. Statist. Med., 22, 1741-1760. – reference: Hardy, R. J. and Thompson, S. G. (1996) A likelihood approach to meta-analysis with random effects. Statist. Med., 15, 619-629. – reference: Whitehead, A. and Whitehead, J. (1991) A general parametric approach to the meta-analysis of randomised clinical trials. Statist. Med., 10, 1665-1677. – reference: Abrams, K. R. and Sanso, B. (1998) Approximate Bayesian inference in random effects meta-analysis. Statist. Med., 17, 201-218. – reference: Knapp, G., Biggerstaff, B. J. and Hartung, J. (2006) Assessing the amount of heterogeneity in random-effects meta-analysis. Biometr. J., 48, 271-285. – reference: Eddy, D. M., Hasselblad, V. and Shachter, R. (1992) Meta-analysis by the Confidence Profile Method. San Diego: Academic Press. – reference: Higgins, J., Thompson, S., Deeks, J. and Altman, D. (2002) Statistical heterogeneity in systematic reviews of clinical trials: a critical appraisal of guidelines and practice. J. Hlth Serv. Res. Poly, 7, 51-61. – reference: Jüni, P., Altman, D. G. and Egger, M. (2001) Assessing the quality of controlled clinical trials. Br. Med. J., 323, 42-46. – reference: Peto, R. (1987) Why do we need systematic overviews of randomised trials? Statist. Med., 6, 233-240. – reference: Thompson, S. G. and Higgins, J. P. T. (2002) How should meta-regression analyses be undertaken and interpreted? Statist. Med., 21, 1559-1574. – reference: Turner, R. M., Spiegelhalter, D. J., Smith, G. C. S. and Thompson, S. G. (2008) Bias modelling in evidence synthesis. J. R. Statist. Soc. A, to be published. – reference: Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and Van Der Linde, A. (2002) Bayesian measures of model complexity and fit (with discussion). J. R. Statist. Soc. B, 64, 583-639. – reference: Louis, T. A. (1991) Using Empirical Bayes methods in biopharmaceutical research. Statist. Med., 10, 811-829. – reference: Burr, D. and Doss, H. (2005) A Bayesian semiparametric model for random-effects meta-analysis. J. Am. Statist. Ass., 100, 242-251. – reference: Viechtbauer, W. (2007) Confidence intervals for the amount of heterogeneity in meta-analysis. Statist. Med., 26, 37-52. – reference: Bradburn, M. J., Deeks, J. J., Berlin, J. A. and Localio, A. R. (2006) Much ado about nothing: a comparison of the performance of meta-analytical methods with rare events. Statist. Med., 26, 53-77. – reference: Morris, C. N. (1983) Parametric empirical Bayes inference: theory and applications. J. Am. Statist. Ass., 78, 47-65. – reference: Warn, D. E., Thompson, S. G. and Spiegelhalter, D. J. (2002) Bayesian random effects meta-analysis of trials with binary outcomes: methods for the absolute risk difference and relative risk scales. Statist. Med., 21, 1601-1623. – reference: Vangel, M. G. and Rukhin, A. L. (1999) Maximum likelihood analysis for heteroscedastic one-way random effects ANOVA in interlaboratory studies. Biometrics, 55, 129-136. – reference: Follmann, D. A. and Proschan, M. A. (1999) Valid inference in random effects meta-analysis. Biometrics, 55, 732-737. – reference: Bailey, K. R. (1987) Inter-study differences-how should they influence the interpretation and analysis of results. Statist. Med., 6, 351-360. – reference: Laird, N. and Louis, T. A. (1989) Empirical Bayes confidence intervals for a series of related experiments. Biometrics, 45, 481-495. – reference: Anello, C. and Fleiss, J. L. (1995) Exploratory or analytic meta-analysis: should we distinguish between them? J. Clin. Epidem., 48, 109-116. – reference: Feinstein, A. R. (1995) Meta-analysis: statistical alchemy for the 21st century. J. Clin. Epidem., 48, 71-79. – reference: Greenland, S. (2005) Multiple-bias modelling for analysis of observational data. J. R. Statist. Soc. A, 168, 267-291. – reference: Greenland, S. and O'Rourke, K. (2001) On the bias produced by quality scores in meta-analysis, and a hierarchical view of proposed solutions. Biostatistics, 2, 463-471. – reference: Bernardo, J. M. and Smith, A. F. M. (1994) Bayesian Theory. Chichester: Wiley. – reference: Robbins, H. (1983) Some thoughts on empirical Bayes estimation. Ann. Statist., 11, 713-723. – reference: Colditz, G. A., Burdick, E. and Mosteller, F. (1995) Heterogeneity in meta-analysis of data from epidemiologic studies: Commentary. Am. J. Epidem., 142, 371-382. – reference: Böhning, D. (2005) Meta-analysis: a unifying meta-likelihood approach framing unobserved heterogeneity, study covariates, publication bias, and study quality. Meth. Inform. Med., 44, 127-135. – reference: Raudenbush, S. W. and Bryk, A. S. (1985) Empirical Bayes meta-analysis. J. Educ. Statist., 10, 75-98. – reference: DerSimonian, R. and Kacker, R. (2007) Random-effects model for meta-analysis of clinical trials: an update. Contemp. Clin. Trials, 28, 105-114. – reference: Ades, A. E., Lu, G. and Higgins, J. P. T. (2005) The interpretation of random-effects meta-analysis in decision models. Med. Decsn Mak., 25, 646-654. – reference: Biggerstaff, B. J. and Tweedie, R. L. (1997) Incorporating variability in estimates of heterogeneity in the random effects model in meta-analysis. Statist. Med., 16, 753-768. – reference: Skene, A. M. and Wakefield, J. C. (1990) Hierarchical models for multicentre binary response studies. Statist. Med., 9, 919-929. – reference: Aitkin, M. (1999a) A general maximum likelihood analysis of variance components in generalized linear models. Biometrics, 55, 117-128. – reference: Detsky, A. S., Naylor, C. D., O'Rourke, K., McGeer, A. J. and Labbe, K. A. (1992) Incorporating variations in the quality of individual randomized trials into meta-analysis. J. Clin. Epidem., 45, 255-265. – reference: Glasziou, P. P. and Sanders, S. L. (2002) Investigating causes of heterogeneity in systematic reviews. Statist. Med., 21, 1503-1511. – reference: Kass, R. E. and Raftery, A. E. (1995) Bayes Factors. J. Am. Statist. Ass., 90, 773-795. – reference: Raghunathan, T. E. and Ii, Y. C. (1993) Analysis of binary data from a multicenter clinical-trial. Biometrika, 80, 127-139. – reference: Spiegelhalter, D., Thomas, A., Best, N. and Lunn, D. (2003) WinBUGS User Manual, Version 1.4. Cambridge: Medical Research Council Biostatistics Unit. – reference: Hardy, R. J. and Thompson, S. G. (1998) Detecting and describing heterogeneity in meta-analysis. Statist. Med., 17, 841-856. – reference: Laird, N. (1978) Nonparametric maximum likelihood estimation of a mixing distribution. J. Am. Statist. Ass., 73, 805-811. – reference: Morris, C. N. and Normand, S. L. 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SubjectTerms	Analysis Applications Bayesian analysis Bayesian method Confidence interval Degrees of freedom Distribution theory Eating disorders Exact sciences and technology Forecasts Gaussian distributions General topics Hypothesis Hypothesis testing Inference Justification Mathematical intervals Mathematics Meta analysis Methodology Modeling Normal distribution Null hypothesis Original Prediction Predictions Probability and statistics Probability theory and stochastic processes Random-effects models Sciences and techniques of general use Standard error Statistical methods Statistical variance Statistics Stochastic processes Systematic reviews Uncertainty
Title	re-evaluation of random-effects meta-analysis
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