Alternative Egger's test, without using standard error

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?

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 $\overline{ES} = a + b \cdot \frac{1}{N}$.
• @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