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

Sat Oct 5 12:30:47 CEST 2019

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

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

On Fri, Oct 4, 2019 at 1:30 PM Wolfgang Viechtbauer <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> 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 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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