I have access to summary statistics from several published trials. Each of these trials estimated an effect on thousands of features. For each feature, I only have access to the effect, standard error and sample size.
I have skimmed through several books (Gelman 2007, Gelman 2014, etc.) as well as the documentation of Stan and several R packages to gather ideas on how to model this as a meta-analysis:
A meta-analysis is usually represented as a hierarchical model, sometimes with random effects per study.
In my case probably I should do one meta-analysis for each feature and tie them together to benefit from partial pooling across individual feature meta-analyses.
How shall I model effects and standard errors? One quick thought is to use a measurement error structure. That is, the effect is a single observation drawn from a normal distribution with known standard deviation (equal to the given standard error) and unknown mean. Is this how brms would implement a se() aterm?
Sample sizes from each individual study are usually modeled using the observed standard error as I outlined above. Any other alternatives (perhaps involving a weighted likelihood)?
Any other thoughts?