# [R-meta] Back transformation of double arscine transformed estimates in metafor

Daniel Mønsted Shabanzadeh dm@h@b@n @end|ng |rom gm@||@com
Fri Oct 4 10:47:24 CEST 2019

```Hey

I am performing a meta-regression of multiple single arm
studies. The outcome is proportions of complications following a specific
surgical treatment which is the same for all included studies. I want to
explore if variables such as age, continent or medications have an impact
on the outcome. Since some of the identified studies have 0 complications
events I have performed Freeman-Tuckey double arscine transformation of
data.

Data transformation

Meta-regression of multiple identified studies
metareg<-rma(yi, vi, data=b, mods=~continent+age+pm)
print(metareg)

Mixed-Effects Model (k = 11; tau^2 estimator: REML)

tau^2 (estimated amount of residual heterogeneity):     0.0091 (SE = 0.0060)
tau (square root of estimated tau^2 value):             0.0952
I^2 (residual heterogeneity / unaccounted variability): 91.15%
H^2 (unaccounted variability / sampling variability):   11.30
R^2 (amount of heterogeneity accounted for):            28.85%

Test for Residual Heterogeneity:
QE(df = 6) = 78.3204, p-val < .0001

Test of Moderators (coefficient(s) 2:5):
QM(df = 4) = 7.6936, p-val = 0.1035

Model Results:

estimate      se     zval    pval    ci.lb   ci.ub
intrcpt                   0.3197  0.1079   2.9640  0.0030   0.1083  0.5311  **
continentAsia            -0.1666  0.1062  -1.5685  0.1168  -0.3747  0.0416
continentNorth America   -0.1755  0.1067  -1.6452  0.0999  -0.3845  0.0336   .
ageinfant                 0.1824  0.0741   2.4616  0.0138   0.0372  0.3277   *
pmTA                     -0.1484  0.0973  -1.5252  0.1272  -0.3392  0.0423

---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

These estimates and CI are transformed. Usually I would transform them back
to proportions with predict in presence of simple models. But I am not sure
hos to do it in multiple models.

predict(metareg, transf=transf.ipft.hm, targ=list(ni=a\$total)). This gives
us multiple lines of estimates which I cannot interpretate:

pred  ci.lb  ci.ub  cr.lb  cr.ub
1  0.0259 0.0017 0.0715 0.0000 0.1388
2  0.0202 0.0005 0.0594 0.0000 0.1245
3  0.0000 0.0000 0.0348 0.0000 0.0692
4  0.0202 0.0005 0.0594 0.0000 0.1245
5  0.1058 0.0290 0.2206 0.0056 0.2976
6  0.0175 0.0000 0.0940 0.0000 0.1478
7  0.1174 0.0380 0.2310 0.0100 0.3110
8  0.0202 0.0005 0.0594 0.0000 0.1245
9  0.0283 0.0000 0.1236 0.0000 0.1799
10 0.0259 0.0017 0.0715 0.0000 0.1388
11 0.0259 0.0017 0.0715 0.0000 0.1388

How do I obtain estimates of proportions for the impact of each variable
explored in the model?

Regards,
Daniel

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