How to perform a double arcsine back-transformation after meta-regression with moderator analysis in RStudio


I'm conducting a meta-analysis of prevalence studies on viral infections. Prevalence can be seen as the proportion of individuals with a binary trait, thus the raw data needs to be transformed before we can start the analysis (preferably double-arcsine transformation).

Essentially, I have performed meta-regression with 3 moderators (hemisphere;dichotomous), (latitude; continuous) , (climate;dichotomous) on the double-arcsine transformed (proportion/prevalence) data. After obtaining the multi-variable meta-regression model I fail to perform a back-transformation on the regression coefficients and 95% CI to obtain the 'normal' proportion/prevalence numbers.

I have tried copying the code for the inverse of the double-arcsine transformation into the meta-regression code with the hopes of obtaining the multi-variable model with the untransformed data.

The following lines of codes were used to transform the data, conduct the meta-regression with 3 moderators, and print the output.

ies.da=escalc(xi=cases, ni=total, data=proportion, measure="PFT", add=0) metareg.3mods=rma(yi, vi, data=ies.da, mods=~hemisphere+latitude+climate) print(metareg.3mods)

The output of the lines of codes written above can be found below. I'm quite certain that the values in this output are based are based upon the transformed values and therefore still need a back-transformation (inverse double-arcsine?) in order to obtain the correct proportion values. How can I incorporate this back-transformation into the meta-regression so that RStudio provides me with a model that contains the correct proportion values?


Mixed-Effects Model (k = 22; tau^2 estimator: REML)

tau^2 (estimated amount of residual heterogeneity): 0.0067 (SE = 0.0037)

tau (square root of estimated tau^2 value): 0.0819

I^2 (residual heterogeneity / unaccounted variability): 67.46%

H^2 (unaccounted variability / sampling variability): 3.07

R^2 (amount of heterogeneity accounted for): 32.94%

Test for Residual Heterogeneity: QE(df = 18) = 66.9031, p-val < .0001

Test of Moderators (coefficient(s) 2:4): QM(df = 3) = 8.6072, p-val = 0.0350

Model Results:

Intercept: β=0.5313 SE= 0.1223 zval 4.3448 pval <0.0001 0.2916 ci.ub 0.7709

Sout hemisphere β=-0.4444 SE= 0.2116 zval -2.1001 pval 0.0357 -0.8592 ci.ub 0.-0.0297

Latitude β=-0.0055 SE= 0.0028 zval -1.9717 pval 0.0486 -0.0110 ci.ub -0.000

Tropical climate β=-0.1986 SE= 0.0701 zval -2.8340 pval 0.0046 -0.3360 ci.ub 0.-0.0613


To help us help you, could you please prepare a reproducible example (reprex) illustrating your issue? Please have a look at this guide, to see how to create one:

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