Should a meta-analysis of group differences calculate Hedges’ G separately for each group, or calculate Hedges' G for the group difference? I am reading a meta-analysis where the authors state the following. (I've redacted the active drug name, as my purpose is to understand not call anyone out.)
The treatment response to placebo and [drug X] were analyzed separately per treatment group as measured from before to after treatment.
And they then report the following results
Placebo had a statistically significant association with pain intensity, with a moderate to large effect size (mean [SE] Hedges g, 0.64 [0.13]; II2 = 87.08; P < .001). The effect size of the active drug on pain intensity was large (mean [SE] Hedges g, 0.95 [0.13]; I^2 = 84.07; P < .001). However, the between-group difference for active drug and placebo was not statistically significant (q1 = 2.82; P = .09; Hedges g [active drug g – placebo g] = 0.32
I am not very familiar with the statistical methodology of meta-analyses. Is it usual in meta-analysis methodology to analyse group differences in this way: to calculate effect size separately for each group (placebo and active) and then test the difference?
Why, for example, would you not collect the effect size for the group difference in each study and then calculate the effect size for the difference?

Reading between the lines here they have looked at change in placebo and change in treated, considered them as subsets and then generated a chi-squared statistic for the difference in changes. I assume that is what q1 is as with 1 df it does have the associated p-value quoted.
The main problem I foresee here is that this loses the pairing between the placebo arm with the treated arm in the same study. That means that the comparison loses the advantage of randomisation (assuming these were randomised). That seems to me to be undesirable.
In my experience the answer to your question "Is this usual?" is clearly "No".
