[R-meta] Mismatch between output from sub-group analysis and forest plot

[Gerta Ruecker]

Dear Joao,

This is what I suspected in one of my previous e-mails. It is all right. 
While metafor gives the results transformed, that is, on the 
arcsin(sqrt())-scale, the forest plot provides results conveniently on 
the original probability scale (backtransformed). You can (roughly) 
switch between both measures by using

  * arcsin(sqrt(x)) (from the forest plot to the text output), or vice versa
  * sin^2(x) (from the text output to the forest plot).

It is only rough here (1) because the package used the Freeman-Tukey 
transformation which is more complicated and (2) because of rounding error.

See some calculations inline below.

Best,

Gerta

Am 12.02.2020 um 11:47 schrieb Joao Afonso:
> Dear all,
>
> Once again I am sorry for posting this message again but I forgot to
> send the outputs.
>
> Again I am conducting a meta-analysis on prevalence and incidence
> data. As there is plenty of heterogeneity I am doing a sub-group
> analysis. However I
> am finding the output of the same and forest plots produced to have
> different values for the pooled estimates. I am using the double
> arcsine transformation and then have the data back-transformed to
> produce the estimates.
[...]
> Random-Effects Model (k = 11; tau^2 estimator: DL)
>
> tau^2 (estimated amount of total heterogeneity): 0.027 (SE = 0.021)
> tau (square root of estimated tau^2 value):      0.164
> I^2 (total heterogeneity / total variability):   99.93%
> H^2 (total variability / sampling variability):  1428.81
>
> Test for Heterogeneity:
> Q(df = 10) = 14288.143, p-val < .001
>
> Model Results:
>
> estimate     se   zval   pval  ci.lb  ci.ub
>     0.506  0.051  9.905  <.001  0.406  0.606  ***
>
This apparently corresponds to the smaller subgroup where the forest 
plot shows  0.23 [0.0.16; 0.31], but gives the untransformed result on 
the arcsin(sqrt()) scale. In fact:

arcsin(sqrt(0.23 [0.16; 0.31]) = 0.5 [0.41; 0.59]

[...]

>
> Random-Effects Model (k = 22; tau^2 estimator: DL)
>
> tau^2 (estimated amount of total heterogeneity): 0.011 (SE = 0.007)
> tau (square root of estimated tau^2 value):      0.104
> I^2 (total heterogeneity / total variability):   99.23%
> H^2 (total variability / sampling variability):  130.14
>
> Test for Heterogeneity:
> Q(df = 21) = 2732.942, p-val < .001
>
> Model Results:
>
> estimate     se    zval   pval  ci.lb  ci.ub
>     0.600  0.024  25.359  <.001  0.553  0.646  ***
>
Again: arcsin(sqrt(0.32 [0.26; 0.38]) = 0.60 [0.54; 0.66] (similar to 
what metafor shows, differences due to rounding and the Freeman-Tukey 
transformation).

Analogous for the whole group.

[...]


-- 

Dr. rer. nat. Gerta Rücker, Dipl.-Math.

Institute of Medical Biometry and Statistics,
Faculty of Medicine and Medical Center - University of Freiburg

Stefan-Meier-Str. 26, D-79104 Freiburg, Germany

Phone:    +49/761/203-6673
Fax:      +49/761/203-6680
Mail:     ruecker using imbi.uni-freiburg.de
Homepage: https://www.imbi.uni-freiburg.de/persons/ruecker/person_view


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