Egger's regression test for funnel-plot asymmetry in a meta-analysis using metafor My meta-analysis investigates the association between dietary intake of a micronutrient on the risk of being diagnosed with a disease (binary outcome).
I am trying to test for funnel-plot asymmetry of the studies I have included using an Egger's regression test, which is noted as the regtest() function in the metafor package.
Having read through the guide provided on the regtest() function , it appears  I have an option of specifying either a 'weighted regression with multiplicative dispersion', which is a classical Egger's test, or a 'mixed-effects meta-regression model'.
I would appreciate if anyone could shed some light on which I should specify in my meta-analysis. Would the 'mixed-effects meta-regression model' be more appropriate for my meta-analysis which uses a random-effects model that accounts for between-study heterogeneity?
The provided reference Sterne and Egger (2005) in the guide explains that the first model may underestimate between-study heterogeneity, but I am not sure of the implication of this to my meta-analysis. I do get rather different p-values when I compare both methods.
I will share my outputs below.
> regtest(dietres,model="lm", predictor="sei") ##Classical Egger's Test

Regression Test for Funnel Plot Asymmetry
Model:     weighted regression with multiplicative dispersion
Predictor: standard error
Test for Funnel Plot Asymmetry: t = -2.0149, df = 17, p = 0.0600 Limit
Estimate (as sei -> 0):   b = 0.0515 (CI: -0.0493, 0.1524)

> regtest(dietres,model="rma", predictor="sei") ##mixed effects

meta-regression model
Regression Test for Funnel Plot Asymmetry
Model:     mixed-effects meta-regression model Predictor: standard
error
Test for Funnel Plot Asymmetry: z = -2.3660, p = 0.0180 Limit Estimate
(as sei -> 0):   b = 0.0683 (CI: -0.0333, 0.1700)

 A: As noted in the question, the weighted regression model with a multiplicative dispersion term is what Matthias Egger originally suggested, but it's not the type of model we typically use in meta-analyses. So there is a bit of a disconnect between using this model for the regression test and using the standard types of models for the main analysis. Hence, in Sterne and Egger (2005), the use of a standard mixed-effects meta-regression model is described for the purposes of the regression test for funnel plot asymmetry. For consistency with other analyses, I would personally also favor using this model. Also, the logic of the regression test then generalizes easily to more complex situations (e.g., for a multilevel meta-analysis), which would not work for the multiplicative model.
This aside, I would say that the two tests provide pretty consistent results in your case though. Yes, one p-value is just below .05 while the other is just above, but if I may quote Rosnow and Rosenthal (1989) here:

[...] surely, God loves the .06 nearly as much as the .05.

(or .02 and .06 in your case).
