[R-meta] Question on funnel plot interpretation

Dear Michael and Yefeng ,

Thank you very much for the interesting observations and orientation
provided.

- Regarding the strangeness of primary studies.
Yes indeed, it is something I noticed before that some studies have a very
low value or almost no correlation (0.001) while others have a very high
value almost maximum possible (close to 1).
 All correlations included (n = 149)  are the result of Fisher's z-to-r
transformation, and original values of r also in some cases present such
extreme values.
The primary dataset of correlations were in some cases given in the
screened studies, but for the vast majority of the correlations were
calculated by myself as Pearsons's product-moment correlation employing the
values reported by the different studies. These correlations (r) were later
transformed to z by means of Fisher's *r-to-z* transform.
Studies are very diverse, coming from different geographies, with varied
types of treatments and applying different methods.
I do not know the reason for such variability of the range of the
correlations, but it would be interesting to have a test or quantitative
way to give account of such variation in the range.

- Regarding the  the subjectivity of the interpretation of the funnel plot
and that I cannot use the function regtest()since is I am using rma.mv()
object, I also run numerical test for publication bias employing
different predictors:

1. sampling variance
2. inverse of sampling variance
3. standard error

However since for each of the cases/predictors used (see below) I got a
full model result, I assume --may be wrongly--that the value I should take
as the numerical estimation of the publication bised is the "intercept" of
the model, is this correct?

Is there a given range that might serve as a proxy indicator of potential publication
bias?

Code and model's results below.

Thanks a lot.
Kind regards,
Gabriel


 ## NUMERICAL TEST FOR PUBLICATION BIAS

## extending Egger's test to more complex models.
## "regression test for funnel plot asymmetry".

## 1. using : the sampling variance
PubB<-rma.mv(yi = yi,
             V = vi,
             mods =  vi,
             random = ~ 1 | Article / Sample_ID,
             data = dat,
             method = "REML")

PubB
# Multivariate Meta-Analysis Model (k = 149; method: REML)
#
# Variance Components:
#
#            estim    sqrt  nlvls  fixed             factor
# sigma^2.1  0.8908  0.9438     72     no            Article
# sigma^2.2  2.1970  1.4822    149     no  Article/Sample_ID
#
# Test for Residual Heterogeneity:
# QE(df = 147) = 24617.3110, p-val < .0001
#
# Test of Moderators (coefficient 2):
# QM(df = 1) = 1.4381, p-val = 0.2304
#
# Model Results:
#
#          estimate      se     zval    pval     ci.lb   ci.ub
# intrcpt    0.5620  0.2584   2.1743  0.0297    0.0554  1.0685  *
# mods      -6.7997  5.6701  -1.1992  0.2304  -17.9130  4.3135
#
# ---
#   Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1


## 2. using : the inverse of the sampling variance
PubB_1<-rma.mv(yi = yi,
             V = vi,
             mods =  1/vi,
             random = ~ 1 | Article / Sample_ID,
             data = dat,
             method = "REML")

PubB_1
# Multivariate Meta-Analysis Model (k = 149; method: REML)
#
# Variance Components:
#
#            estim    sqrt  nlvls  fixed             factor
# sigma^2.1  0.9176  0.9579     72     no            Article
# sigma^2.2  2.1797  1.4764    149     no  Article/Sample_ID
#
# Test for Residual Heterogeneity:
#   QE(df = 147) = 23656.2997, p-val < .0001
#
# Test of Moderators (coefficient 2):
# QM(df = 1) = 1.4469, p-val = 0.2290
#
# Model Results:
#
#         estimate      se    zval    pval    ci.lb   ci.ub
# intrcpt    0.0957  0.2595  0.3689  0.7122  -0.4129  0.6044
# mods       0.0040  0.0034  1.2029  0.2290  -0.0025  0.0106
#
# ---
#   Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

## 3. using : standard errors (square-root of the sampling variances)

PubB_2<-rma.mv(yi = yi,
               V = vi,
               mods =  sqrt(vi),
               random = ~ 1 | Article / Sample_ID,
               data = dat,
               method = "REML")

PubB_2
# Multivariate Meta-Analysis Model (k = 149; method: REML)
#
# Variance Components:
#
#            estim    sqrt  nlvls  fixed             factor
# sigma^2.1  0.8991  0.9482     72     no            Article
# sigma^2.2  2.1952  1.4816    149     no  Article/Sample_ID
#
# Test for Residual Heterogeneity:
# QE(df = 147) = 24489.6313, p-val < .0001
#
# Test of Moderators (coefficient 2):
# QM(df = 1) = 1.2528, p-val = 0.2630
#
# Model Results:
#
#           estimate      se     zval    pval    ci.lb   ci.ub
# intrcpt    0.7801  0.4374   1.7834  0.0745  -0.0772  1.6375  .
# mods      -2.6473  2.3652  -1.1193  0.2630  -7.2829  1.9883
#
# ---
#   Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1



On Wed, Jul 5, 2023 at 12:45?PM Yefeng Yang <yefeng.yang1 at unsw.edu.au>
wrote:

Dear Gabriel

Apart from Michael observation on data checking before analyses (which is
always a good practice), I add one.
The funnel plot is just a visual check of publication bias. So the
observations based on the funnel plots are inevitably subjective - I mean
you think that is "randomly scattering", while others might think not. In
contrast, Egger's test is a more objective way to test the asymmetry of a
funnel plot. Regarding how to do it, you can try to find them in the
archives associated with this mailing list.

Please be noted that whether none funnel plot and Egger's test can
indicate publication bias directly. But it is common to assume the
asymmetry of a funnel plot is caused by publication bias (or more
precisely. small study effects), after accounting for heterogeneity.

Best,
Yefeng
------------------------------
*From:* R-sig-meta-analysis <r-sig-meta-analysis-bounces at r-project.org>
on behalf of Michael Dewey via R-sig-meta-analysis <
r-sig-meta-analysis at r-project.org>
*Sent:* Wednesday, 5 July 2023 19:31
*To:* R Special Interest Group for Meta-Analysis <
r-sig-meta-analysis at r-project.org>
*Cc:* Michael Dewey <lists at dewey.myzen.co.uk>; Gabriel Cotlier <
gabiklm01 at gmail.com>
*Subject:* Re: [R-meta] Question on funnel plot interpretation

Dear Gabriel

My interpretation looking at your plots is that you have a very strange
set of primary studies. If the x-axis is really the z transformation of
r then some of  the r are .999 and some 0.001 which seems worthy of
investigation before looking further.

Michael

On 05/07/2023 09:14, Gabriel Cotlier via R-sig-meta-analysis wrote:

Hello all,

I have produced a funnel plot on the basis of an rma.mv
<http://rma.mv>() objectapplied to all the data set together ( not
subsetting  using moderators ) as follows:

image.png


When looking at the figure I tried to think that maybe one of the
following two interpretations could be the correct one:

a.  There is a kind of random scattering of the effect sizes, therefore
no symmetry is found and thus publication bised is observed.
b.  Given the randomness of the effect sizes distribution covering the
plot's space unevenly there is not a clear pattern that can indicate
publication bias is observed.

Is any of this interpretation the correct one?

Thanks a lot.
Kind regards,
Gabriel


#### CODE. ######
funnel_all <- rma.mv <http://rma.mv>(yi,
                      vi,
                      random = ~ 1 | Article / Sample_ID,
                      data=dat)
png(file = "funnel.png",
     width = 250,
     height = 200,
     res = 600,
     units = "mm")
# par(mfrow = c(2, 1))

# full data
f1 <- funnel(funnel_all,
              yaxis = "seinv",
              level = c(90, 95, 99),
              ylim = c(1, 20),
              shade = c("white", "gray55", "gray75"),
              refline = 0,
              legend = TRUE)
mtext("A", side = 3, line = 0, adj = -0.13, cex = 2)

dev.off()

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