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

[Joao Afonso]

Dear Gerta,

Thank you so much for all the insights and guidance. I was looking at
the figures and there is still one thing I can't make sense of which
relates to this part of the code:

> print(pes.lcmbi, digits=3) #display recomputed summary effect size

This hopefully is the part of the code that provide the
back-transformed pooled estimate of prevalence as it outputs the
following:

  pred ci.lb ci.ub cr.lb cr.ub
 0.283 0.206 0.368 0.168 0.415

I would expect to see this in the forest plot, yet what the plot provides is

 0.29 (0.24-0.34)

Any thoughts?

Many thanks once again. Have a great evening,

On Wed, Feb 12, 2020 at 5:00 PM Gerta Ruecker
<ruecker using imbi.uni-freiburg.de> wrote:
>
> 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



-- 
João Afonso
DVM, MSc Veterinary Epidemiology
PhD Student
Department of Infection and Global Health
University of Liverpool
+351914812305