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)


1 Answer 1


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).

  • $\begingroup$ Thank you Wolfgang for your helpful and quick response. I have just two more questions... 1) Could I then say that the mixed-effects meta-regression model works well even for the fixed effect model in the main analysis? 2) Apart from the borderline p-values here, could I also be comparing the beta estimates, suggesting that there is weak/no evidence of small-study effects (as both happen to contain 0) ? $\endgroup$
    – Wei Qi Loh
    Mar 23, 2022 at 16:12
  • $\begingroup$ 1) I don't understand that question. 2) No, the limit estimate has nothing to do with saying if there are or are not small-study effects. $\endgroup$
    – Wolfgang
    Mar 23, 2022 at 18:26
  • $\begingroup$ Ah, do let me try to rephrase my question. 1) Is it appropriate to specify model='rma' when using regtest() for studies in a meta-analysis that was conducted on a fixed-effects model i.e. where method was set as "FE" using the function rma()? 2) I had understood in Sterne and Egger (2005) that the p-value from Egger's regression test is for the hypothesis that 𝑏0 = 0; Why is it not possible to look at the CI of b for an evidence of small-study effects then? Am I misunderstanding the b and CI in the output? $\endgroup$
    – Wei Qi Loh
    Mar 24, 2022 at 6:30
  • $\begingroup$ 1) Got it. Yes. regtest() then also uses a fixed-effects with moderators model for the regression test. 2) There are two ways to do the multiplicative model, one where the intercept is the test and one where the slope is the test. regtest() uses the latter. The intercept is the limit estimate, which is the projected estimated effect for a study with infinite precision. $\endgroup$
    – Wolfgang
    Mar 24, 2022 at 6:44

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