[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:

[R-meta] Question on funnel plot interpretation

Thread (12 messages)