[R-meta] Difference in Proportions Meta-Analysis

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Mon Jun 8 17:27:07 CEST 2020

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".


>-----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
>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?
>Thanks for your help,
>On Mon, Jun 8, 2020 at 2:48 PM Michael Dewey <lists using dewey.myzen.co.uk>
>> 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
>> > 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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