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

Thu, Apr 29, 2021 12:54 AM

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

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

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