[R-meta] Funnel Plots for Multilevel Meta

[Viechtbauer, Wolfgang (SP)]

A funnel plot is simply a plot of the estimates against their standard errors (or some other measure of precision). So one can draw such a plot whether there are multiple estimates from the same study or not. Hence, funnel() in metafor will happily do so:

library(metafor)

dat <- dat.konstantopoulos2011
res <- rma.mv(yi, vi, random = ~ 1 | district/school, data=dat)
res
funnel(res)

One could indicate (with different colors or plotting symbols) which estimates belong to the same study. 

cols <- palette.colors(length(unique(dat$district)), palette="Alphabet")
cols <- cols[as.numeric(factor(dat$district))]
funnel(res, col=cols)

Then one can see how points from the same study (or in this case, 'district') cluster together.

To what extent such a plot is indicative of publication bias / small study effects is a different issue (but the same applies even to simpler meta-analyses with a single estimate per study).

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org]
>On Behalf Of Dylan Johnson
>Sent: Friday, 11 December, 2020 20:03
>To: Michael Dewey; r-sig-meta-analysis using r-project.org
>Subject: Re: [R-meta] Funnel Plots for Multilevel Meta
>
>Hi Michael,
>
>Would it not be nonsensical to have multiple effects from the same article
>in the funnel plot though?
>
>With the Egger's regression I was able to accommodate the fact that their is
>nonindependence of the effects, but am unsure how to proceed with a funnel
>plot.
>
>Dylan
>
>Dylan Johnson, MSc
>
>MA Student, School and Clinical Child Psychology
>Department of Applied Psychology and Human Development
>
>University of Toronto
>252 Bloor Street West
>
>Toronto, ON M5S 1V6
>
>From: Michael Dewey<mailto:lists using dewey.myzen.co.uk>
>Sent: December 11, 2020 6:12 AM
>To: Dylan Johnson<mailto:dylanr.johnson using mail.utoronto.ca>; r-sig-meta-
>analysis using r-project.org<mailto:r-sig-meta-analysis using r-project.org>
>Subject: Re: [R-meta] Funnel Plots for Multilevel Meta
>
>Dear Dylan
>
>Perhaps I misunderstand you but if you have the data for a regression
>type test like Egger's do you not just plot that? The funnel() function
>in metafor does that and I am sure equivalent solutions can be found in
>meta and many other packages.
>
>Michael
>
>On 11/12/2020 01:14, Dylan Johnson wrote:
>> Hello,
>>
>> Thanks everyone for helping me sort out the Egger's test with multi-level
>meta modelling!
>>
>> Is there any option in R for producing Funnel plots that are appropriate
>for the nonindependence? I imagine that the standard funnel plot would be
>deceiving if it came from a multi-level design.
>>
>> Many thanks!
>>
>> Best,
>> Dylan
>>
>> Dylan Johnson, MSc
>>
>> MA Student, School and Clinical Child Psychology
>> Department of Applied Psychology and Human Development
>>
>> University of Toronto
>> 252 Bloor Street West
>>
>> Toronto, ON M5S 1V6