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[R-meta] Help with understanding the meta objecct

3 messages · Jan Pohl, Dr. Gerta Rücker, Guido Schwarzer

Jan Pohl
# 
Good day everybody,

I have a question about accessing the metacor object in the meta 
package. I have a meta-analysis where before now I just used the values 
as seen in the output, e.g., in this example I reported 0.3369 as my 
effect size:

Number of studies combined: k = 88
Number of observations: o = 5306

 ??????????????????????? COR??????????? 95%-CI???? z? p-value
Fixed effect model?? 0.3301 [ 0.3052; 0.3544] 24.35 < 0.0001
Random effects model 0.3369 [ 0.2390; 0.4281]? 6.43 < 0.0001
Prediction interval???????? [-0.5375; 0.8622]

Now I want to create some custom plots where I want to use values like 
the ES from this object. However, my problem is that I cannot find the 
ES value in the list. So, I am wondering if the value is somewhow 
transformed or if I misunderstood something?

I would greatly appreciate if somebody could help me shed light on this 
problem. Thank you very much already in advance.

Kind regards,

Jan
Dr. Gerta Rücker
# 
Dear Jan,

As seen in the output, correlation coefficients (r) are transformed for meta-analysis using Fisher's z-transformation. That is, they are not directly pooled, but transformed by

z = 0.5*log((1 + r)/(1 - r))

with inverse transformation r = (exp(2*z) - 1)/ (exp(2*z) + 1). Using the example given in the help file of metacor()

m1 <- metacor(c(0.85, 0.7, 0.95), c(20, 40, 10))

you obtain the z-transformed pooled effect size from the metacor list object by

z <- m1$TE.random

and may backtransform it by

r <- (exp(2*z) - 1)/ (exp(2*z) + 1)

which gives 0.8438764 as in the print output or the forest plot.

Best,
Gerta



UNIVERSIT?TSKLINIKUM FREIBURG
Institute for Medical Biometry and Statistics

Dr. Gerta R?cker
Guest Scientist

Stefan-Meier-Stra?e 26 ? 79104 Freiburg
gerta.ruecker at uniklinik-freiburg.de

https://www.uniklinik-freiburg.de/imbi-en/employees.html?imbiuser=ruecker


-----Urspr?ngliche Nachricht-----
Von: R-sig-meta-analysis <r-sig-meta-analysis-bounces at r-project.org> Im Auftrag von Jan Pohl via R-sig-meta-analysis
Gesendet: Donnerstag, 20. Juli 2023 14:46
An: r-sig-meta-analysis at r-project.org
Cc: Jan Pohl <jan.pohl at tu-dresden.de>
Betreff: [R-meta] Help with understanding the meta objecct

Good day everybody,

I have a question about accessing the metacor object in the meta 
package. I have a meta-analysis where before now I just used the values 
as seen in the output, e.g., in this example I reported 0.3369 as my 
effect size:

Number of studies combined: k = 88
Number of observations: o = 5306

 ??????????????????????? COR??????????? 95%-CI???? z? p-value
Fixed effect model?? 0.3301 [ 0.3052; 0.3544] 24.35 < 0.0001
Random effects model 0.3369 [ 0.2390; 0.4281]? 6.43 < 0.0001
Prediction interval???????? [-0.5375; 0.8622]

Now I want to create some custom plots where I want to use values like 
the ES from this object. However, my problem is that I cannot find the 
ES value in the list. So, I am wondering if the value is somewhow 
transformed or if I misunderstood something?

I would greatly appreciate if somebody could help me shed light on this 
problem. Thank you very much already in advance.

Kind regards,

Jan
4 days later
Guido Schwarzer
# 
Just a quick comment in addition to Gerta's post.

R package meta has some internal function to do (back)transformations. For correlations, meta:::cor2z transforms correlations to Fisher's z and meta:::z2cor back-transforms Fisher's z transformed correlations.

For example, meta:::z2cor(m1$TE.random) would provide the random effects estimate of the correlation.

Best,
Guido

P.S. I will think about making the functions for (back)transformations accessible in R package meta.