[R-meta] Difference in Proportions Meta-Analysis

[ne gic]

Dear Wolfgang,

I have taken time to read the entire escalc documentation (
https://wviechtb.github.io/metafor/reference/escalc.html ) and I am sorry
to say I don't understand how I can do that in a single step with
escalc(measure="OR", ...) as you previously mentioned. I would like to do
this correctly following your suggestion so as to minimize any errors as I
redo steps that can be done in fewer steps.

For each of my two groups I have proportion and standard error. Could you
kindly show me how I can do this using one of the available datasets please?

Sincerely,
nelly

On Mon, Jun 8, 2020 at 6:48 PM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> 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)
> >
> >Is this still not a reasonable way to go about this?
> >
> >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?
> >>
> >>Thanks for your help,
> >>
> >>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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