[R-meta] Mismatch between output from sub-group analysis and forest plot
Gerta Ruecker
ruecker @end|ng |rom |mb|@un|-|re|burg@de
Wed Feb 12 18:00:13 CET 2020
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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