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

1) The logistic model also doesn't require adjustments to the counts, so
yes, it has the same advantage as the PFT (and PAS) transformation.

2) You are doing a meta-analysis of proportions, but the analysis is
carried out on a transformed scale (like with PFT). When you use a
logistic model, you are (implicitly) doing the analysis on a logit scale.
For easier interpretation, we then typically transform the results back to
odds or directly to proportions.


Best,
Wolfgang

Thank you for your reply!
A few questions remain:
1. The reason for using FT transformation was due to many outcomes being
equal to 0 in proportions and thereby to avoid adding numbers that

distort

the estimates. Would the PAS or PLO have the same advantages as the FT
transformation in this regard?
2. The meta-regression is performed on proportions and not on relative
risks or odds. Can a meta-regression on proportions be performed in PAS

or

PLO?

Regards,
Daniel

fre. 4. okt. 2019 11.35 skrev Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer at maastrichtuniversity.nl>:

Dear Daniel,

predict(metareg, transf=transf.ipft.hm, targ=list(ni=a$total)) gives

you

the fitted values (proportions) for the 11 studies. So these are the
predicted values (based on the model) for whatever values these studies
take on for the moderator variables. If you want to compute predicted
values for other combinations of moderator values, you need to use the
'newmods' argument. For example:

predict(metareg, newmods = c(0,1,1,0),
        transf=transf.ipft.hm, targ=list(ni=a$total))

will give the predicted value (proportion) for continent = North

America,

age = infant, and pm = LA (based on your post on Stack Overflow --

https://stackoverflow.com/questions/58203464/reverse-transformation-of-double-arscine-transformed-estimates-when-doing-meta-r

-- I can see that pm has two levels, LA (reference level) and TA).

By varying one moderator and holding the other moderators constant, you
can illustrate how a moderator affects the results (you cannot just take
the model coefficients and transform them).

But: The back-transformation for the FT transformation is problematic.
Please take a look at:

https://onlinelibrary.wiley.com/doi/full/10.1002/jrsm.1348

Even though the FT transformation has some nice properties, I would
therefore avoid it (because we typically do want to back-transform in

the

end). You could either just use the 'standard' arcsine square root
transformation (measure="PAS") or maybe even better switch to a logistic
mixed-effects model, which you can fit with rma.glmm():

metareg <- rma.glmm(measure="PLO", ai=compl, nu=total, data=a,
                    mods = ~ continent + age + pm)

The results are then analyzed on the logit (log odds) scale. So, the
back-transformation to odds would be:

predict(metareg, newmods = c(0,1,1,0), transf=exp)

In fact, here, you can exponentiate the coefficients themselves, which
then reflect odds ratios:

round(exp(coef(summary(metareg))[,c("estimtate", "ci.lb", "ci.ub")]),

3)

The back-transformation to proportions would be:

predict(metareg, newmods = c(0,1,1,0), transf=transf.ilogit)

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:
r-sig-meta-analysis-bounces at r-project.org] On Behalf Of Daniel M?nsted
Shabanzadeh
Sent: Friday, 04 October, 2019 10:47
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] Back transformation of double arscine transformed
estimates in metafor

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
b<-escalc(xi=compl, ni=total, data=a, measure="PFT", add=0)

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