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

[Dr. Gerta Rücker]

Dear Joao,

Honestly, I don't know. Comparing the code for the forest plot with the 
rest of the code, I find it difficult to identify corresponding 
variables. For example, in the forest plot code the number of events is 
called nlameanimal, but this variable name occurs nowhere in the rest of 
the code where you always use yi. Moreover, you have two subsets, 
"Records" (11 studies) and "Locomotion Scoring Method" (22 studies), but 
it seems they are confused somewhere. I find the code extremely 
difficult to understand without knowing the data.

Best,

Gerta

Am 12.02.2020 um 18:05 schrieb 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
>
>