Meta-analysis model for multivariate datasets

Modeling
1

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:

  1. A meta-analysis is usually represented as a hierarchical model, sometimes with random effects per study.

  2. 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.

  3. 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?

  4. 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?

2

In the sense that individual studies would contribute to a shared, overall (group-level) effect, that’s the general idea.

I’m not sure what “feature” refers to here, most of the times this seems to be confusing terminology from the Machine Learning that just means (independent) variable, but it seems like it may be something different here.

In general I believe meta-analyses will plug in sample size or estimated standard deviation (which in theory have a well-defined relationship) as a proxy for confidence in that study, which is like weighing their likelihoods (did you have any other suggestions for the weighted likelihoods implementation)?

I’m not sure if there are specific references to meta-analyses or how detailed they were in the references you read, but here’s a reference that could be useful: A re-evaluation of random-effects meta-analysis - PubMed.