# [R-meta] Difference in Proportions Meta-Analysis

ne gic neg|c4 @end|ng |rom gm@||@com
Mon Jun 8 18:37:55 CEST 2020

```Sorry, that was a typing mistake:
I transformed the proportions using qlogis, then back transformed them
using the plogis.

Here is literally what I have done:

On excel:

1. Calculated the difference in proportions between arm1 and arm2 (arm1 -
arm2) to get arm12_prop_diff
2. Used the formula you provided to calculate the "joint" standard error
(se_diff)

In R:

# Import the excel data.

gastric_data\$arm12_prop_diff <- as.numeric(gastric_data\$arm12_prop_diff)
gastric_data\$se_diff <- as.numeric(gastric_data\$se_diff)

# Log transformation
gastric_data\$arm12_prop_qlogs_diff <- qlogis(gastric_data\$arm12_prop_diff)

# fit random-effects model
pes.da=rma(yi = arm12_prop_qlogs_diff, sei = se_diff, slab=author ,
data=gastric_data, method="REML")
forest(pes.da, xlab = "2-year survival difference (%)",
order=order(gastric_data\$arm12_prop_diff), atransf=plogis)

On Mon, Jun 8, 2020 at 5:27 PM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> I am not sure I really understand what you did. arm1_prop_plogis and
> arm2_prop_plogis actually sound like they are plogis()-transformed
> proportions, which doesn't make sense (plogis() is the inverse-logit
> transformation). The logit transformation is qlogis(). Not sure how you
> computed arm1_se and arm2_se. Why not use escalc(measure="PLO", ...), which
> will do things correctly for you?
>
> But if you want to compare the two groups within studies directly, then
> you need to use measures such as the risk difference (measure="RD"), the
> log transformed risk ratio ("RR"), or the log transformed odds ratio
> ("OR"). In fact, the difference between two logit-transformed proportions
> *IS* the log transformed odds ratio.
>
> So, just use escalc(measure="OR", ...) and then pass the 2x2 table counts
> via arguments 'ai', 'bi', 'ci', 'di' (or the 'event' counts via arguments
> 'ai' and 'ci' and the group sizes via 'n1i' and 'n2i'). See help(escalc)
> and search for "OR".
>
> Best,
> Wolfgang
>
> >-----Original Message-----
> >From: R-sig-meta-analysis [mailto:
> r-sig-meta-analysis-bounces using r-project.org]
> >On Behalf Of ne gic
> >Sent: Monday, 08 June, 2020 15:09
> >To: Michael Dewey
> >Cc: r-sig-meta-analysis using r-project.org
> >Subject: Re: [R-meta] Difference in Proportions Meta-Analysis
> >
> >Dear Michael,
> >
> >Thanks. I am using metafor (or rather planning to for this).
> >
> >Initially I had performed two separate single arm meta-analysis of
> >proportion as follows to get an estimate for each of the arms:
> >
> >rma(yi = arm1_prop_plogis, sei = arm1_se, slab=author_year ,
> >data=gastric_data, method="REML")
> >
> >rma(yi = arm2_prop_plogis, sei = arm2_se, slab=author_year ,
> >data=gastric_data, method="REML")
> >
> >But then it was pointed out that it would be more interesting to
> >meta-analyze the difference in proportions from both arms, and hence my
> >question.
> >
> >So what I have done is:
> >
> >   1. Calculate the raw proportion differences i.e. before using the R
> >   function "qlogis"
> >   2. Calculate a single SE from the SE of both arms using the equation
> >   provided by Wolfgang.
> >
> >Then the two outputs are what I hope to provide as inputs to rma exactly
> as
> >I had done before for the single arm analysis.
> >
> >Is there a more direct way to do this? or am I missing something?
> >
> >
> >Sincerely,
> >nelly
> >
> >On Mon, Jun 8, 2020 at 2:48 PM Michael Dewey <lists using dewey.myzen.co.uk>
> >wrote:
> >
> >> Dear Nelly
> >>
> >> I am not sure what software you use but both meta and metafor provide
> >> analysis of risk differences (which is what differences in proportions
> >> are) so you may get what you want directly there.
> >>
> >> Michael
> >>
> >> On 08/06/2020 11:36, ne gic wrote:
> >> > Dear List,
> >> >
> >> > I aim to perform a meta-analysis and present a forest plot of the
> >> > difference in proportions between two groups.
> >> >
> >> > For each group I have proportion and standard error (SE).
> >> >
> >> > It's straightforward to get the difference in the proportions, but am
> >not
> >> > sure how to handle the SEs, I presume I can't just subtract them. Is
> >> there
> >> > a formula on how to handle SEs?
> >> >
> >> > Sincerely,
> >> > nelly
>

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