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Asymptotic approximations for the radial plot in meta analysis, and a bias correction to the Egger test
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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, Vol.2007 (No.1).

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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  
Official Date:  2007  
Dates: 


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Status:  Not Peer Reviewed  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 

URI:  http://wrap.warwick.ac.uk/id/eprint/35535 
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