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

Daniel Mønsted Shabanzadeh dm@h@b@n @end|ng |rom gm@||@com
Sat Oct 5 17:55:46 CEST 2019

```Dear Wolfgang

The variable age_cor has 6 levels (ref. level 5)

table(a\$age_cor)
5       1       2       3       4 missing
111     140      27     113      19       8

With your code suggestion slightly modified
b<-rma.glmm(xi=compl_treat, ni=total, mods = ~age_cor, measure = "PLO",
data=a)
print(b)

Mixed-Effects Model (k = 401; tau^2 estimator: ML)

tau^2 (estimated amount of residual heterogeneity):     1.8327
tau (square root of estimated tau^2 value):             1.3538
I^2 (residual heterogeneity / unaccounted variability): 98.91%
H^2 (unaccounted variability / sampling variability):   91.85

Tests for Residual Heterogeneity:
Wld(df = 395) = 4777257347008370311248.0000, p-val < .0001
LRT(df = 395) =                      0.0000, p-val = 1.0000

Test of Moderators (coefficient(s) 2:6):
QM(df = 5) = 20.3959, p-val = 0.0011

Model Results:

estimate      se      zval    pval    ci.lb    ci.ub
intrcpt          -3.9819  0.1456  -27.3422  <.0001  -4.2674  -3.6965  ***
age_cor1          0.3358  0.1922    1.7474  0.0806  -0.0408   0.7124    .
age_cor2          0.3169  0.3093    1.0244  0.3057  -0.2894   0.9231
age_cor3          0.8528  0.2012    4.2397  <.0001   0.4586   1.2471  ***
age_cor4         -0.0370  0.3850   -0.0962  0.9234  -0.7916   0.7176
age_cormissing    0.0009  0.5648    0.0016  0.9987  -1.1061   1.1080

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

c<-predict(b, newmods=rbind(0, diag(5)), transf=transf.ilogit)
print(c)

pred  ci.lb  ci.ub  cr.lb  cr.ub
1 0.0183 0.0138 0.0242 0.0013 0.2119
2 0.0254 0.0200 0.0323 0.0018 0.2726
3 0.0250 0.0148 0.0419 0.0017 0.2772
4 0.0419 0.0322 0.0544 0.0030 0.3866
5 0.0177 0.0089 0.0349 0.0012 0.2184
6 0.0183 0.0064 0.0516 0.0011 0.2460

- Is the interpretation that line 1 represents the age_cor reference
level (level 5) proportion and the remaining levels as listed in print (b)?
- If I want to explore age_cor further, can I add multiple moderators to
the model and just increase the diag in predict?

Regards,
Daniel

MD, PhD
Department of Gastroenterology, Surgical Unit
Hvidovre Hospital
Mobile +45 2546 5251

On Sat, Oct 5, 2019 at 2:16 PM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> Dear Daniel,
>
> If level 5 is the reference level, then that is what the intercept
> represents, so the 0.0183 cannot represent level 5. You would have to
> provide the output of 'b' for me to tell you better what is being estimated
> here, but 0.0183 is the estimated proportion for whatever level the last
> coefficient represents in the model.
>
> If you want all estimated proportions for all 6 levels, then you can get
> this with a single command:
>
> predict(b, newmods=rbind(0, diag(5)), transf=transf.ilogit)
>
> The first will be for the reference level, the rest for each other level.
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: Daniel Mønsted Shabanzadeh [mailto:dmshaban using gmail.com]
> Sent: Saturday, 05 October, 2019 12:31
> To: Viechtbauer, Wolfgang (SP)
> Cc: r-sig-meta-analysis using r-project.org
> Subject: Re: [R-meta] Back transformation of double arscine transformed
> estimates in metafor
>
> Dear Wolfgang
>
> I have now run the models, but still seem to have some conversion problems
> when trying to obtain proportions from the regression model. The variable
> age_cor is categorical with 6 levels (level 5 is ref.).
>
> b<-rma.glmm(xi=compl_treat, ni=total, mods = ~age_cor, measure = "PLO",
> data=a)
> c<-predict(b, newmods=c(0,0,0,0,1), transf=transf.ilogit)
> print(c)
>
> pred  ci.lb  ci.ub  cr.lb  cr.ub
>  0.0183 0.0064 0.0516 0.0011 0.2460
>
> As far as I interpretate this results, it means that if age_cor is fixed
> at 0 in level 1-4 and level 5 is fixed at 1, the proportion is 0.0183. Is
> it not possible to obtain proportions from all levels in the variabel when
> one level is the reference? Like the case in studies with relative
> risks exploring multiple level categorical variables with one reference
> level.
>
> Regards,
> Daniel
>