The Library
Asymptotic approximations for the radial plot in meta analysis, and a bias correction to the Egger test
Tools
Copas, John B. and LozadaCan, Claudia (2007) Asymptotic approximations for the radial plot in meta analysis, and a bias correction to the Egger test. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers).

PDF
WRAP_Copas_071w.pdf  Published Version  Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (419Kb) 
Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
Abstract
Fixed effects meta analysis can be thought of as least squares analysis of the radial plot, the plot of standardized treatment effect against precision (reciprocal of the standard deviation) for the studies in a systematic review. For example, the Egger test for publication bias is equivalent to testing the significance of the intercept in linear regression. In practice, both x and ycoordinates of the points in a radial plot are subject to sampling error, which may be correlated, and so the standard theory of least squares does not apply. For the Egger test, the actual significance levels are inflated, sometimes substantially so. We derive approximations to the sampling properties of the radial plot, assuming that the within study sample sizes are large. This leads to an asymptotic bias correction for the Egger test. A simulation study suggests that the bias correction controls the significance level of the Egger test without any appreciable loss of power in detecting nonrandom study selection. A clinical trials example is used as an illustration.
Item Type:  Working or Discussion Paper (Working Paper) 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Statistics 
Library of Congress Subject Headings (LCSH):  Metaanalysis, Least squares, Clinical trials  Mathematical models 
Series Name:  Working papers 
Publisher:  University of Warwick. Centre for Research in Statistical Methodology 
Place of Publication:  Coventry 
Date:  2007 
Volume:  Vol.2007 
Number:  No.1 
Number of Pages:  20 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
References:  Copas, J. B. and Jackson, D. (2004). A bound for publication bias based on the fraction of unpublished studies. Biometrics, 60, 146153. Egger, M., Smith, G. D., Schneider, M. and Minder, C. (1997). Bias in meta analysis detected by a simple graphical test. Brit. Med. J., 315, 629634. Galbraith, R. F. (1988). A note on graphical representation of estimated odds ratios from several clinical trials. Statist. in Med., 7, 889894. Harbord, R. M., Egger, M. and Sterne, J. A. C. (2005). A modified test for small study effects in meta analysis of controlled trials with binary endpoints. Statist. in Med., 25, 34433457. Irwig, L., Macaskill, P. and Berry, G. (1998). Bias in meta analysis detected by a simple graphical test. Graphical test is itself biased (letter to the editor). Brit. Med. J., 316, 469. Macaskill, P., Walter, S. D. and Irwig, L. (2001). A comparison of methods to detect publication bias in meta analysis. Statist. in Med., 20, 641654. Peters, J. L., Sutton, A. J., Jones, D. R., Abrams, K. R. and Rushton, L. (2006). Comparison of two methods to detect publication bias in meta analysis. J. Am. Med. Assoc., 295, 676680. Rothstein, H. R., Sutton, A. J. and Borenstein, M. (eds) (2005). Publication bias in metaanalysis. Chichester: Wiley. Shwarzer, G., Antes, G. and Shumacher, M. (2002). Inflation in Type I error rate in two statistical tests for the detection of publication bias in meta analysis with binary outcomes. Statist. in Med., 21, 24652477. Sutton, A. J., Abrams, K. R., Jones, D. R. and Sheldon, T. A. (2000). Methods for metaanalysis in medical research. Chichester: Wiley. 
URI:  http://wrap.warwick.ac.uk/id/eprint/35535 
Actions (login required)
View Item 