Combined relative risk in meta study I am looking at a meta study, and I've never done one (or looked at it much) before. From what I've learned about it so far, the way you calculate the compounded effect is by first calculating this $\tau^{2}$, which is a measure of the heterogeneity of the results.
If $\tau^{2}$ is in fact 0, as is the case here, we have reason to assume all studies are estimating a fixed, underlying parameter of interest, and the point estimate for the parameter of interest becomes the simple weighted average of the individual studies. Correct?
Applying that to the table below, we would have:
weights = [4.3, 3.6, 4.1, 4.3, 3.7]
y = [0.11, 0.24, 0.14, 0.12, 2.92]
and the weighted average (sum(w*y)/sum(w)) is then 0.66, by my calculation.
However, the authors claim it to be 0.24, see table. I'm sure they're correct and I'm wrong, but could someone tell me where I'm going wrong? Thanks a lot!


For risk ratios, the averaging is done on the log scale. So, if you take the log of y, then compute the weighted average, and then back-transform via exponentiation, you get the expected result (0.24). For example, in R:
w <- c(4.3, 3.6, 4.1, 4.3, 3.7)
y <- log(c(0.11, 0.24, 0.14, 0.12, 2.92))
exp(sum(w*y)/sum(w))

yields 0.2485498 (which is 0.25 when rounded, but this discrepancy is due to rounding of the weights and risk ratios shown in the figure).
