# [R-meta] logarithmic scale in forest plot

Antonia Sudkaemper @@@udk@emper @end|ng |rom gm@||@com
Mon Mar 9 17:10:45 CET 2020

```Hello Wolfgang,

thank you, and apologies - mailing list is now cc'ed in.

What confuses me, however, it that for the average the numbers on the right
seem to indicate the log odds ratio (i.e. 0), but the poly in the graph
seems to show the odds ratio (i.e. 1) - I would have expected these to be
congruent?

Also, for "Study 1" and "Study 2",  do the numbers and the graph display
the odds ratio or log odds ratio? Based on the numbers and the back
transformation I am assuming the odds ratio?

Thank you very much!

All the best, Antonia

On Mon, 9 Mar 2020 at 15:31, Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> Please always cc the mailing list.
>
> For log odds ratios, the CI can be negative. After back-transformation
> (i.e., exponentiation), the CI will be >= 0.
>
> Similarly, the estimated average log odds ratio is 0 in the example.
> Hence, after back-transformation, the estimate will be 1 (exp(0) = 1).
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: Antonia Sudkaemper [mailto:a.sudkaemper using gmail.com]
> Sent: Monday, 09 March, 2020 15:05
> To: Viechtbauer, Wolfgang (SP)
> Subject: Re: [R-meta] logarithmic scale in forest plot
>
> Hello Wolfgang,
>
> I just ran this with our data and it seems to work - thank you so much!
>
> I just noticed that both in your example as well as with our data the mean
> weighted effect size lower CI is below 0 - does that make sense?
>
> Also, in your example and similar with our data, it says 0.00 as mean
> weighted effect size, but shows up in the graph at 1. Is that correct?
>
> Thanks again for your help.
>
> All the best, Antonia
>
> On Wed, 4 Mar 2020 at 15:56, Viechtbauer, Wolfgang (SP) <
> wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> Dear Antonia,
>
> You should use log odds ratios as input. In fact, we never meta-analyze
> the odds ratios directly, because they are not 'symmetric' around 1. For
> example, an OR of 2 in favor of the treatment group corresponds to an OR of
> 1/2 = 0.5 in favor of the control group, so if one were to combine these
> two ORs (assuming equal weights), one would end up with a combined OR of
> 1.25 in favor of the treatment group, but this is not logical if the two
> ORs are exact opposites of each other. On the other hand, after log
> transformation, we get log(2) = 0.6931472 and log(0.5) = -0.6931472, which
> are now symmetric around 0. Hence, the combined log OR is 0 and, after
> back-transforming (i.e., exponentiation), we get exp(0) = 1, which makes
> sense.
>
> Also, how were those standard errors (sei) computed? Are they really SEs
> of the ORs? In most cases, the SEs we can extract from papers are for the
> log odds ratios.
>
> But to answer your question, here is how it's done. Plot the log odds
> ratios and then use atransf=exp, which in essence puts the the x-axis on a
> log scale. An example:
>
> yi  <- log(c(2, 0.5))
> sei <- c(.20, .20)
> forest(yi, sei=sei, atransf=exp, ylim=c(-0.5,5))
> res <- rma(yi, sei=sei, method="FE")
>
> (And I just saw that Michael has also answered with the same concern about
> the use of the ORs.)
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: R-sig-meta-analysis [mailto:
> r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Antonia Sudkaemper
> Sent: Wednesday, 04 March, 2020 15:37
> To: r-sig-meta-analysis using r-project.org
> Subject: [R-meta] logarithmic scale in forest plot
>
> Dear Metafor Community,
>
> I hope this email finds you well.
>
> I have a question regarding the metafor package. I made a forest plot using
> the code below. I have received feedback that, as the forest plot shows
> odds ratios I should use a log scale for the x axis rather than a linear
> scale, so that the CIs are symmetric around the natural log OR. I am not
> sure how I would achieve that? Could you help me out, please? I would much
> appreciate it.
>
> All the best, Antonia
>
> #race/ethnicity
> oddsratio = c(2.07, 0.90, 1.00, 0.82, 2.25, 0.92)
> sei <- c(.43, .32, .66, .50, .70, .44)
> ci.lb <- oddsratio - 1.96*sei
> ci.ub <- oddsratio + 1.96*sei
> study<-c("Aelenei et al., 2019", "Kulich et al., 2019a", "Kulich et al.,
> 2006a", "Kulich et al., 2006b", "Ryan & Haslam, 2004a", "Ryan & Haslam,
> 2004b")
> labels<-c(-2, 0, 2, 4, 6, 8)
>
> forest(oddsratio, ci.lb=ci.lb, ci.ub=ci.ub, showweights=TRUE, refline=1,
> xlab
>        = "Odds Ratio", slab=study, alim = c(-2,8), xlim=c(-14,15),
> at=labels, cex =
>          0.9, ylim=c(-2,27))
> addpoly(x = 1.16, ci.lb=0.69, ci.ub=1.95)
>
> --
> Dr Antonia Sudkämper
> Researcher, OCR, Cambridge Assessment
>
> www.antoniasudkaemper.com
> a.sudkaemper using gmail.com
>

--
Dr Antonia Sudkämper
Researcher, OCR, Cambridge Assessment

www.antoniasudkaemper.com
a.sudkaemper using gmail.com

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://stat.ethz.ch/pipermail/r-sig-meta-analysis/attachments/20200309/9af5dd16/attachment-0001.html>

-------------- next part --------------
A non-text attachment was scrubbed...
Name: oddsratio_forest_example
Type: application/octet-stream
Size: 6624 bytes
Desc: not available
URL: <https://stat.ethz.ch/pipermail/r-sig-meta-analysis/attachments/20200309/9af5dd16/attachment-0001.obj>
```