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

[Daniel Mønsted Shabanzadeh]

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 using 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 using r-project.org] On Behalf Of Daniel Mønsted
> Shabanzadeh
> Sent: Friday, 04 October, 2019 10:47
> To: r-sig-meta-analysis using 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
>

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