Table 10.4.b: Proposed tests for funnel plot asymmetry

Ntot  is the total sample size, NE and NC are the sizes of the experimental and control intervention groups, S is the total number of events across both groups and F = Ntot S. Note that only the first three of these tests (Begg 1994, Egger 1997a, Tang 2000) can be used for continuous outcomes.

Reference

Basis of test

(Begg 1994)

Rank correlation between standardized intervention effect and its standard error.

(Egger 1997a)

Linear regression of intervention effect estimate against its standard error, weighted by the inverse of the variance of the intervention effect estimate.

(Tang 2000) 

Linear regression of intervention effect estimate on 1 /ÖNtot, with weights Ntot.

(Macaskill 2001)*

Linear regression of intervention effect estimate on Ntot, with weights S×F/Ntot.

(Deeks 2005)*

Linear regression of log odds ratio on 1/ÖESS with weights ESS, where effective sample size ESS = 4NE ×NC / Ntot.

(Harbord 2006)*

Modified version of the test proposed by Egger et al., based on the ‘score’ (OE) and ‘score variance’ (V) of the log odds ratio.

(Peters 2006)*

Linear regression of intervention effect estimate on 1/Ntot, with weights S×F/Ntot.

(Schwarzer 2007)*

Rank correlation test, using mean and variance of the non-central hypergeometric distribution.

(Rücker 2008)

Test based on arcsine transformation of observed risks, with explicit modelling of between-study heterogeneity.

* Test formulated in terms of odds ratios, but may be applicable to other measures of intervention effect.