# [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 18:48:13 CEST 2020

```No, this is not correct. You should not apply the logit-transformation to the difference and the SE is not correct either. You should apply the logit-transformation to the two proportions individually, compute the correct SE of the logit-transformed proportions, take the difference between the two logit-transformed proportions, and then you can use the equation to get the SE of this difference. But all of this can just be done in a single step with escalc(measure="OR", ...). As I mentioned, the difference between two logit-transformed proportions is the log odds ratio.

Best,
Wolfgang

>-----Original Message-----
>From: ne gic [mailto:negic4 using gmail.com]
>Sent: Monday, 08 June, 2020 18:38
>To: Viechtbauer, Wolfgang (SP)
>Cc: r-sig-meta-analysis using r-project.org
>Subject: Re: [R-meta] Difference in Proportions Meta-Analysis
>
>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
```