Egger’s linear regression method intercept in meta analysis

Question

In Meta analysis, how to interpret the Egger’s linear regression method intercept (B0) 10.34631, 95% confidence interval (1.05905, 19.63357), with t=3.54535, df=3. The 1-tailed p-value (recommended) is 0.01911, and the 2-tailed p-value is 0.03822. I am a medical doctor. *Updated* The data are comparison of Regions 1 and 2

          Region 1      Region 2         Region 3           
        Cases   Dead    Cases   Dead     Cases  Dead    Total cases Total dead cases
2006    2320    528     1484    108       73    3       3877            639
2007    3024    645     1592    75        32    1       4648            721
2008    3012    537     1920    53         3    0       4935            590
2009    3073    556     1477    40       246    8       4796            604
2010    3540    494     1460    26       138    1       5138            521
Total  14969    2760    7933    302      492    13     23394            3075

Answer 1

I suppose you are not interested in "hardcore" statistical explanation. So, more the intercept deviates from zero, the more pronounced the asymmetry. If the p-value of the intercept is 0.1 or smaller, the asymmetry is considered to be statistically significant. More here.

Answer 2

@Andrej has already given an answer, i.e there is evidence of funnel plot asymmetry.

@DrWho, I would be interested in the reference that suggests using a one-tailed test.

The following can give you an idea of the underlying logic of applying this regression model to test for publication bias:

Most of these regression approaches are using the so-called standard normal deviate (SND) which is defined as effect size divided by its standard error ($ES_i / SE_i$). The inverse standard error (“precision”) serves as predictor variable. Then, an unweighted OLS regression is estimated. When there is no evidence of funnel plot asymmetry, the intercept should not significantly differ from zero, i.e. $H_0: b_0 = 0$. In other words, the intercepts provide a measure of funnel plot asymmetry (Sterne/Egger 2005: 101). This is due to two reasons:

(1) Since the standard error depends on sample size, the inverse standard error for small studies will be close to zero.

(2) Even though small studies may produce large effect sizes, the SND will be small since the standard error will be large. Again, for small studies, the SND will be close to zero. For large studies, however, we will observe large SNDs and the inverse standard errors will also be large (Egger et al 1997: 629f.).

Egger, M., G. Davey Smith, M. Schneider, C. Minder (1997), Bias in meta-analysis detected by a simple, graphical test British Medical Journal 315: 629-634.

Sterne, J.A.C., B.J. Becker, M. Egger (2005), The funnel plot. S. 75-98 in: H.R. Rothstein, A.J. Sutton, M. Borenstein (Hrsg.), Publication Bias in Meta-Analysis. Prevention, Assessment and Adjustments, The Atrium, Southern Gate, Chichester: John Wiley & Sons, Ltd.