[R-meta] Subgroup analysis results are different if I conducted each subgroup separately in metarate in R

Greetings all
I am doing a single arm meta-analysis of *incidence rate (IR)* using
Poisson regression and doing subgroup analysis using `meta` and `metafor`
packages in `R`.
Upon reviewing subgroup analysis results, I noticed* it is different if I
conducted each subgroup separately.* If there is any possible explanation
for that, it will be greatly appreciated.

Furthermore, I need  to know ***what is the used statistical test to get
the `interaction-P value` or `subgroup difference P value*`** is which is
`0.0432` in the following dataset (in random effect model).

I reviewed this [link][1] but I couldn't get what I need there.


Here is my code and sample dataset
```
library(meta); library(metafor)
data<-read.table(text="studlab Subgroup_2gps Mean.FU popXFU event
DeBonis.2014 Adult 11.5 1552.5 13
Fucci.2007 Adult 6.5 416 4
Ram.2020 Pediatrics 5.583333 290.33333 4
Kadirogullari.2019 Pediatrics 1.616667 90.53333 2
Kashiyama.2014 Pediatrics 3.275 180.125 1
Tomita.2005 Pediatrics 6.708333 134.16667 1
Lawrie.2006 Pediatrics 3.1 291.4 16
Maeda.2019 Pediatrics 5.5 203.5 1
Zussa.1997 Pediatrics 3.05 350.75 2
Murashita.2013 Pediatrics 7.5 562.5 6
David.2013 Pediatrics 10.1 1070.6 30
Bourguignon.2016 Pediatrics 3.4 98.6 3
Phillips.2000 Pediatrics 0.9 66.6 5
Pfannmuller.2013 Pediatrics 4.3 498.8 5
Totaro.1999 Adult 3.833333 199.33333 3
", sep="\t", header=T)


mr <- metarate(event,popXFU, data= data,# subset= data$Subgroup_2gps==
"Neochords " ,
               studlab = studlab, method = "GLMM",model.glmm = "CM.EL",
method.ci = "Poisson",   irscale = 1000)
mr2<- update (mr, byvar=Subgroup_2gps);forest(mr2); mr2

# Results for subgroups (random effects model):
#   k  events             95%-CI  tau^2    tau
# Subgroup_2gps = Adult        3  9.3998 [ 6.0643; 14.5697]      0      0
# Subgroup_2gps = Pediatrics  12 18.6089 [11.3291; 30.5666] 0.4500 0.6708
#
# Test for subgroup differences (random effects model):
#   Q d.f. p-value
# Between groups   4.09    1*  0.0432*

## It gave me IR of 18.6089 [11.3291; 30.5666] for random effect for
Pediatrics subgroup

#============================================================================================
mr <- metarate(event,popXFU, data= data, subset= data$Subgroup_2gps==
"Pediatrics" ,
               studlab = studlab, method = "GLMM",model.glmm = "CM.EL",
method.ci = "Poisson",   irscale = 1000);mr
## It gave me IR of 15.9876 [ 9.5438; 26.7820] for random effect
```
Any guidance will be greatly appreciated.


  [1]:
https://stats.stackexchange.com/questions/340621/why-am-i-getting-different-means-when-conducting-multilevel-meta-analysis-with-f

*Link to my question on* Cross Validated:
https://stats.stackexchange.com/questions/590438/subgroup-analysis-results-are-different-if-i-conducted-each-subgroup-separately

--
Best Regards;
Sincerely
Mohamed Rahouma
<https://www.google.com./url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0CCkQFjAB&url=https%3A%2F%2Fsincerely.com%2F&ei=neObVayoG4v0-QH0xIrQBg&usg=AFQjCNGzY8IeWvSHsGzJCztf4BSaSxH76g&bvm=bv.96952980,d.cWw>