I´m performing a prognostic effect meta-analysis of SMD in the metafor R package. Data includes means and SD for each arm (exposed vs unexposed groups) for several studies that used different scales.
I wish to backtranformed the final estimate to the natural scale, multiplying the MD by the pooled SD.
Is there a function in metafor to extract this pooled SD from the model? or to yield the backtransformed SD? What formula would you use?
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$\begingroup$ To anyone interested: Metafor includes a function transf.dtomd: transformation of standardized mean differences to mean differences given a known standard deviation (which needs to be specified via the targs argument). $\endgroup$– san festeinCommented May 6 at 22:07
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One can just multiply the pooled standardized mean difference by a given standard deviation. Say a meta-analysis of studies comparing the cognitive abilities of children exposed to lead with those unexposed yields a pooled standardized mean difference of $d = -0.20$. Then this implies a $-0.20 \times 15 = 3$ points deficit on average in terms of IQ scores (since IQ tests are normed to have an SD of 15). So this kind of back-transformation makes most sense when the d value reflects a construct (in this example, cognitive abilities) for which one can take a known SD for some kind of scale that can be argued to be a reflection of this construct (in this example, IQ scores).
