[R-meta] Transformation of meta-regression coefficients to ORs

[Viechtbauer, Wolfgang (SP)]

Just as a (late) follow-up:

If you are meta-analyzing ORs and then fit a meta-regression model, the coefficients cannot be converted to ORs (one can compute predicted ORs, but that's something different). The coefficients can be converted to ratios of ORs (by exponentiation, as illustrated in my previous answer) and that is something that people do occasionally do.

Best,
Wolfgang

-----Original Message-----
From: dirk.richter using upd.unibe.ch [mailto:dirk.richter using upd.unibe.ch] 
Sent: Wednesday, 03 July, 2019 17:53
To: Viechtbauer, Wolfgang (SP); r-sig-meta-analysis using r-project.org
Subject: AW: [R-meta] Transformation of meta-regression coefficients to ORs

Dear Wolfgang,

It is a log OR effect size. As we had univariate ORs in our paper for all
potential moderators and then reported the coefficients of the multivariate
regression analysis, the reviewer requested to make the effect sizes
comparable. Is there any specific reason why multivariate regression
analyses usually do not report ORs or RRs but betas? Wouldn't that help to a
better understanding and interpretation?

Anyway, perfect answer, the code worked smoothly and correctly. Many thanks
once again!

Best wishes from Switzerland,
Dirk

-----Ursprüngliche Nachricht-----
Von: Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer using maastrichtuniversity.nl> 
Gesendet: Dienstag, 2. Juli 2019 11:50
An: dirk.richter using upd.unibe.ch; r-sig-meta-analysis using r-project.org
Betreff: RE: [R-meta] Transformation of meta-regression coefficients to ORs

Dear Dirk,

What effect size / outcome measure are you using for your analysis? If you
are meta-analyzing logit transformed proportions, then exponentiating a beta
coefficient will give you the odds ratio for the corresponding predictor.
For example:

library(metafor)

dat <- escalc(measure="PLO", xi=xi, ni=ni, data=dat.debruin2009) dat

res <- rma(yi, vi, mods = ~ scq + ethnicity + patients + select + sens,
data=dat) res

round(exp(coef(summary(res))[-1,c("estimate", "ci.lb", "ci.ub")]), 2)

                 estimate ci.lb ci.ub
scq                  1.06  1.02  1.10
ethnicityother       0.39  0.19  0.80
patientsstarting     1.41  0.81  2.46
selectyes            0.72  0.38  1.38
sens<400             0.66  0.33  1.31

So, per one-unit increase in SCQ, the odds (in this case, of having an
undetectable viral load) goes up by 6% (95% CI: 2% to 10%), or in other
words, the odds ratio is 1.06 (95% CI: 1.02 to 1.10). Since we are comparing
studies with different levels of SCQ, it might be more appropriate to say
that in studies where SCQ is one point higher, the odds of an undetectable
viral load are 6% higher (and if we want to be even more precise, we really
should that "are on average 6% higher"). Similarly, in studies where the
majority of participants are non-Caucasian, the odds are on average 61%
lower (95% CI: 20% to 81%), or in other words, the odds ratio is 0.39 (95%
CI: 0.19 to 0.80).

But this only works for logit transformed proportions as the outcome. 

For other ratio-type outcome measures that are log transformed (e.g., log
risk ratios and log odds ratios), exponentiating a coefficient gives you a
ratio as well, but it is actually the ratio of two ratios. For example:

dat <- escalc(measure="OR", ai=tpos, bi=tneg, ci=cpos, di=cneg,
data=dat.bcg) dat

res <- rma(yi, vi, mods = ~ ablat + year, data=dat) res

round(exp(coef(summary(res))[-1,c("estimate", "ci.lb", "ci.ub")]), 2)

      estimate ci.lb ci.ub
ablat     0.97  0.95  0.99
year      1.01  0.98  1.03

So, in studies that are one more degree away from the equator (i.e., where
absolute latitude increases by one unit), the odds ratio (i.e., the ratio of
a TB infection in those vaccinated compared to those not vaccinated) goes
down on average by 3% (95% CI: 1% to 5%), or the ratio of odds ratios is
0.97 (95% CI: 0.95 to 0.99).

Those are essentially the two cases where you can go from the coefficients
to either an odds ratio or a ratio of odds ratios (the latter can also be
done, for example, with risk ratios -- then you get a ratio of risk ratios).

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org]
On Behalf Of dirk.richter using upd.unibe.ch
Sent: Saturday, 29 June, 2019 16:52
To: r-sig-meta-analysis using r-project.org
Subject: [R-meta] Transformation of meta-regression coefficients to ORs

Dear mailing list members

A reviewer of a paper I have authored has requested to transform the beta
estimates of a meta-regression result into odds ratios. The analysis was
conducted with the metafor rma.mv function. Although I understand the point
of this suggestion, I have looked into several textbooks and review articles
and have not found anything in this regard.
Before I start searching for a code to do this, I would like to kindly ask
for opinions on this issue. And if it is reasonable to do so I would be
grateful to see a coding example.

Many thanks in advance,
Dirk Richter

UNIVERSITÄRE PSYCHIATRISCHE DIENSTE BERN (UPD) AG ZENTRUM PSYCHIATRISCHE
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Dirk Richter, Dr. phil. habil.
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E-Mail: dirk.richter using upd.unibe.ch 

Bern University Hospital for Mental Health Center for Psychiatric
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