Meta-analysis in R with standard errors instead of standard deviations {metafor}

Question

This is the formula I would need to use to perform a meta-analysis in R using the package metafor:

REmodel <- rma(m1i=elev.mean,m2i=amb.mean,sd1i=?,
               sd2i=?,n1i=?,n2i=?,data=NPPsiteWide,
               measure="ROM")

Note that sd and n refers to standard deviations and sample size. The problem is that the dataset I am using (data gathered by others) contains se values, but not sd and n.

Is there any way I can still do the meta-analysis using the data I have without sd and n? Thanks

EDIT:

After following Wolfgang’s suggestion below, it seems I am doing something wrong because rma can’t calculate vi (all NA’s), and returns this error:

REmodel <- rma(m1i=elev.mean,m2i=amb.mean,sd1i=elev.se,
               sd2i=amb.se,n1i=1,n2i=1,data=db,
               measure="ROM",subset=Myc=="AM”)


Error in rma(m1i = elev.mean, m2i = amb.mean, sd1i = elev.se, sd2i = amb.se,  : 
          Processing terminated since k = 0.
        In addition: Warning message:
        In rma(m1i = elev.mean, m2i = amb.mean, sd1i = elev.se, sd2i = amb.se,  :
          Studies with NAs omitted from model fitting.

Answer 1

The outcome measure used is the (log-transformed) ratio of means (often called the response ratio in the ecology literature), which is given by $$y = \ln\left[\frac{\bar{x}_1}{\bar{x}_2}\right] = \ln[\bar{x}_1] - \ln[\bar{x}_2].$$ The large-sample approximation to the sampling variance of $y$ is given by $$Var[y] = \frac{SD_1^2}{n_1 \bar{x}_1^2} + \frac{SD_2^2}{n_2 \bar{x}_2^2}$$ (see, for example, Hedges et al., 1999). Since $$SE[\bar{x}_1] = \frac{SD_1}{\sqrt{n_1}} \quad \mbox{and} \quad SE[\bar{x}_2] = \frac{SD_2}{\sqrt{n_2}},$$ it follows that $$Var[y] = \frac{SE_1^2}{\bar{x}_1^2} + \frac{SE_2^2}{\bar{x}_2^2}.$$ So, you could easily compute this by hand based on the information you have.

But there is an even simpler trick. All that you have to do is feed the SEs to the escalc() or rma() functions and at the same time set the sample sizes to 1. An example:

library(metafor)
escalc(measure="ROM", m1i=15.6, m2i=12.2, sd1i=3.82, sd2i=3.22, n1i=15, n2i=20, digits=6)
escalc(measure="ROM", m1i=15.6, m2i=12.2, sd1i=3.82/sqrt(15), sd2i=3.22/sqrt(20), n1i=1, n2i=1, digits=6)

Both give you:

          yi         vi
1 0.24583496 0.00748055

Hedges, L. V., Gurevitch, J., & Curtis, P. S. (1999). The meta-analysis of response ratios in experimental ecology. Ecology, 80(4), 1150-1156.