[R-meta] Back transformation of arcsine transformed data in meta-regression

[Daniel Mønsted Shabanzadeh]

Hey

I am performing a meta-regression analysis with both a continuous and a
categorical variable and use the arcsine transformation.

b<-rma(xi=compl_treat, ni=total, mods = ~age_cor+year, measure = "PAS",
data=a)
print(b)

Mixed-Effects Model (k = 425; tau^2 estimator: REML)

tau^2 (estimated amount of residual heterogeneity):     0.0165 (SE = 0.0013)
tau (square root of estimated tau^2 value):             0.1286
I^2 (residual heterogeneity / unaccounted variability): 99.57%
H^2 (unaccounted variability / sampling variability):   230.02
R^2 (amount of heterogeneity accounted for):            4.23%

Test for Residual Heterogeneity:
QE(df = 418) = 42191.1379, p-val < .0001

Test of Moderators (coefficients 2:7):
QM(df = 6) = 24.6125, p-val = 0.0004

Model Results:

                estimate      se     zval    pval    ci.lb   ci.ub
intrcpt           3.0578  1.5361   1.9907  0.0465   0.0471  6.0684    *
age_cor1          0.0206  0.0175   1.1769  0.2392  -0.0137  0.0549
age_cor2          0.0276  0.0271   1.0189  0.3082  -0.0255  0.0807
age_cor3          0.0738  0.0184   4.0149  <.0001   0.0378  0.1098  ***
age_cor4         -0.0170  0.0340  -0.4991  0.6177  -0.0837  0.0497
age_cormissing   -0.0292  0.0506  -0.5785  0.5629  -0.1283  0.0698
year             -0.0014  0.0008  -1.8830  0.0597  -0.0029  0.0001    .

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



Using the usual back transformation gives strange estimates of proportions.
Since i have added the continuous variable "year" it has been looking odd.

c<-predict(b, newmods=rbind(0, diag(6)), transf=transf.iarcsin)
print(c)

    pred  ci.lb  ci.ub  cr.lb  cr.ub
1 1.0000 0.0022 1.0000 0.0013 1.0000
2 1.0000 0.0037 1.0000 0.0025 1.0000
3 1.0000 0.0044 1.0000 0.0031 1.0000
4 1.0000 0.0145 1.0000 0.0121 1.0000
5 1.0000 0.0009 1.0000 0.0004 1.0000
6 1.0000 0.0005 1.0000 0.0001 1.0000
7 1.0000 0.0022 1.0000 0.0013 1.0000


What is the mistake here? Any other way of transforming the data back to
proportions?
Ideas appreciated.

Regards,
Daniel

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