Why do we treat study standard errors as known in a meta-analysis?

I wonder if anyone knows why it is that we treat study standard errors as known when conducting a meta-analysis? When conducting analysis of trial data, the error is treating as a quantity to be estimated (at least in the Bayesian code I've seen). In a meta-analysis however, we might say:

y[i]  ~ N(delta,sigma[i])
delta ~ N(u,tau)


leaving sigma as data instead of identifying it as a parameter. Is there a reason for this? Would we just never get stable estimates? Are there any consequences to this approach (i.e., underestimating uncertainty?)

• I think there is a typo in your formula. Apr 10 '18 at 15:23
• This is because meta-analysis uses the aggregated data. If the meta-analysis is performed using a random effect model, the estimate of between-study heterogeneity is produced in response to the amount of errors estimated from analysis of trial data. I think your code should be changed. (y[i] ~ N(u,sigma) -> y[i] ~ N(u,sigma[i]), sigma[i] was data which was extracted from the original article along with y[i].) Apr 11 '18 at 1:16
• @J-HYoon, why not turn that into an official answer? Otherwise this Q looks unanswered. Apr 11 '18 at 13:44