Table 10.4.b: Proposed tests for funnel plot asymmetry
N_{tot} is the total sample size, N_{E} and N_{C} are the sizes of the experimental and control intervention groups, S is the total number of events across both groups and F = N_{tot} – 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 /ÖN_{tot}, with weights N_{tot}. |
(Macaskill 2001)* |
Linear regression of intervention effect estimate on N_{tot}, with weights S×F/N_{tot}_{.} |
(Deeks 2005)* |
Linear regression of log odds ratio on 1/ÖESS with weights ESS, where effective sample size ESS = 4N_{E} ×N_{C} / N_{tot}. |
(Harbord 2006)* |
Modified version of the test proposed by Egger et al., based on the ‘score’ (O–E) and ‘score variance’ (V) of the log odds ratio. |
(Peters 2006)* |
Linear regression of intervention effect estimate on 1/N_{tot}, with weights S×F/N_{tot}. |
(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.