[R-meta] SMD and Eggers regression test for small study effects (publication bias)

[Viechtbauer, Wolfgang (SP)]

Dear Tobias,

I am not sure why the square-root of the weights (which are a function of the standard errors) would be any better. The more obvious thing to do in my opinion would be to remove that part from the standard error that creates the inherent dependence between standardized mean differences and their standard errors. In particular, the estimate of the large-sample standard error of a SMD is:

SE = sqrt(1/n1 + 1/n2 + SMD^2 / (2*(n1+n2)))

The SE involves the (squared) SMD, which leads to the inherent dependence between the SE and the SMD. An easy fix is to conduct the regression test with

sqrt(1/n1 + 1/n2)

as the 'predictor'. See also:

Pustejovsky, J. E., & Rodgers, M. A. (2019). Testing for funnel plot asymmetry of standardized mean differences. Research Synthesis Methods, 10(1), 57-71.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Tobias Saueressig
>Sent: Wednesday, 03 February, 2021 9:54
>To: Meta list
>Subject: [R-meta] SMD and Eggers regression test for small study effects
>(publication bias)
>
>Dear All,
>
>after reading that the Eggers regression test is not suitable when using a SMD as
>an effect size (https://training.cochrane.org/handbook/current/chapter-13#section-
>13-3-5-4), I found the following paper:
>
>https://onlinelibrary.wiley.com/doi/abs/10.1002/jrsm.1332
>
>My reading is that one better variant of the test is to substitute the standard
>errors with the square root of the weights.
>
>I have tried to implement that in the attached R script. (I know that the numbers
>of studies is too low for enough power of the test. This just an example).
>
>Is this the correct way to do it or are there better ways to modify the test?
>
>Regards
>
>Tobias