Egger’s linear regression method intercept in meta analysis

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
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

• Comparison of Region 1 and 2 on what metric? e.g. log odds ratio, log risk ratio, risk difference ...? – onestop Feb 10 '11 at 15:27
• @onestop: I am sorry i missed your question. The comparison is on log odds ratio. Thank you for your interest. – DrWho Feb 16 '11 at 15:02

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.

• Thank you for the prompt, clear and very useful answer. I have spent almost a day trying to search internet. – DrWho Feb 10 '11 at 10:29
• @DrWho So accept it by clicking tick mark. – user88 Feb 10 '11 at 10:31

@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.

• I will try to rectify the table. I am new to this. I am trying – DrWho Feb 10 '11 at 12:35
• Thank you for your help. The 1-tailed p-value was recommended by the software Comprehensive Meta Analysis v2.2. The Data are Year 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 I will try to rectify the table.– DrWho – DrWho Feb 10 '11 at 12:54
• The data of a particular disease is Year 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 – DrWho Feb 10 '11 at 13:41