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A simplified regression equation $ES=\frac{a+b}{n_1+n_2}$ has been suggested as an alternative to Egger's regression equation $\frac{ES}{SE}=\frac{a+b}{SE}$, where ES=Effect Size, $n_1$=sample size of the patients, $n_2$=sample size of the controls, SE=Standard Error.

This alternative test, that was presented by Peters et al. in their 2006 paper in JAMA, is supposed to be better than Egger's test when the ES is the lnOR.

This alternative test could also be valuable in cases Standard Error (SE) cannot be calculated, as SE is not taking part in the equation.

Could this alternative Egger's test be used with the other types of Effect Size? When the ES is the SMD? When the ES is the RR? When the ES is the Pearson's correlation coefficient?

Staty Despair
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Yes, I think that this approach can be use with other types of effect sizes as long as they are (approximately) normally distributed (that's why you use $log(OR)$; to be more precise, the errors of the linear regression model need to be $N(0,1)$).

Your regression equation is wrong. It is $\overline{ES} = a + b \cdot \frac{1}{N}$.

Furthermore, it is a weighted regression. So, unfortunately, you still need the standard errors. Macascill et al (2001: 644) write: "The observations are weighted by the inverse variance of the estimate to allow for possible heteroscedasticity (FIV)". However, since I know that you can compute the standard errors, this shouldn't be a problem (trust the authors ;-).

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Bernd Weiss
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  • Thanks. I think is enough to test for normal distribution with a Kolmogorov-Smirnov test on the effect size. What do you mean "the errors of the linear regression model have to be N(0,1)? Weighted regression? This means that I have to weight for SE my dependend variable? I've recently heard about this guy, Peters et al. 2006 JAMA wrote that they modified his test, Macascill's test, to produce the alternative Egger's regression. Unfortunatelly I don't have access to full text of Macascill et al. paper, but Peters et al modification does not include weighting as far as I understand their paper. – Staty Despair Feb 24 '11 at 01:25
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    Peters et al (678) write: "In preference to Egger’s regression test, we recommend a simple weighted linear regression with lnOR as the dependent variable and the inverse of the total sample size as the independent variable." No, this does not mean that you have to weight your dependent variable. Just estimate a WLS regression model. – Bernd Weiss Feb 24 '11 at 01:34
  • Do you mean I have to use "SE" as the Weight Variable in SPSS WLS regression model? – Staty Despair Feb 24 '11 at 16:34
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    @Staty Despair: No, its in my answer: "...are weighted by the inverse variance of the estimate...", i.e. $w_i = \frac{1}{SE_i^2}$. – Bernd Weiss Feb 24 '11 at 16:40