[R-meta] converting effect sizes from RR to lnRR without original data

[Viechtbauer, Wolfgang (SP)]

Thanks for the additional info. And now I see that RR refers to response ratios, not risk ratios (I thought you meant the latter). In any case, the authors do not provide any derivation or reference for this equation and I have not seen this one before. An article that discusses bias corrections for response ratios is:

Lajeunesse, M. J. (2015). Bias and correction for the log response ratio in ecological meta-analysis. Ecology, 96(8), 2056-2063.

But the equations given there are different. Let's take an example:

library(metafor)
dat <- escalc(measure="ROM", m1i=10, sd1i=2, n1i=20, m2i=5, sd2i=2, n2i=20)
c(dat$yi) # this is just log(10/5)

# correction according to the equation below
log(10/5) - 20*dat$vi / (2*(10/5)^2)

# correction based on a second-order Taylor expansion (Lajeunesse, 2015; eq 8)
log(10/5) + 1/2 * (2^2 / (20*10^2) - 2^2 / (20 * 5^2))

# correction based on the linearity of expectation rule (Lajeunesse, 2015; eq 10)
1/2 * log((10^2 + 2^2 / 20) / (5^2 + 2^2 / 20))

Best,
Wolfgang

>-----Original Message-----
>From: Diego Grados Bedoya [mailto:diegogradosb using gmail.com]
>Sent: Thursday, 29 April, 2021 9:03
>To: Viechtbauer, Wolfgang (SP)
>Cc: R meta
>Subject: Re: [R-meta] converting effect sizes from RR to lnRR without original
>data
>
>Dear Wolfgang,
>
>Thank you for your answer. There is a mistake in the online version of the article
>(https://doi.org/10.1126/sciadv.aba1715). The suggested equation is:
>
>lnRR = ln(RR) - n * SE^2 / (2 * RR^2)
>
>Greetings,
>
>Diego
>
>On Wed, 28 Apr 2021 at 12:11, Viechtbauer, Wolfgang (SP)
><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>Dear Diego,
>
>If I need to convert an RR to lnRR, I just take the log. I don't know what that
>equation is supposed to do. It might help if you would tell you where you got it
>from.
>
>Best,
>Wolfgang
>
>>-----Original Message-----
>>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>>Behalf Of Diego Grados Bedoya
>>Sent: Wednesday, 28 April, 2021 10:52
>>To: R meta
>>Subject: [R-meta] converting effect sizes from RR to lnRR without original data
>>
>>Dear all,
>>
>>I would like to convert an effect size from RR to lnRR. I do not have
>>access to the original data. I just have the effect size (RR), standard
>>error (SE) and the number of comparisons (N). I read that a direct log
>>transformation of an RR can lead to an overestimation of the effect size,
>>thus the authors proposed a correction for the log transformation as
>>
>>lnRR = ln(RR) - NSE2 x (2 RR2) - 1
>>
>>However, the formula is not fully described and there is not no further
>>reference. I was trying to make sense of it but can not get good results. I
>>wonder if you have some references or thoughts about it?
>>
>>Thank you in advance,
>>
>>Greetings,
>>
>>Diego