Joseph Rickert and I put together an experiment trying to both run a standard meta-analysis and then reproduce similar results directly using Bayesian methods. I think it came out really interesting and we share it here at R Works and also here on Github.

A meta-analysis is an attempt to estimate an effect by combining several pre-existing studies. For our example we try to estimate the effectiveness of the calcium channel blocker amlodipine as compared to a placebo in improving work capacity in patients with angina from eight studies. We think the extra Bayesian analysis gives a great on-ramp or opportunity to work out what happens during a meta-analysis. In the Bayesian version we are estimating the distribution of the unknown true effect size that is most compatible with the observed study summaries (and any priors we dial in).

For our example we get the following estimates of the posterior distribution of effect for both treatment and control groups (and hence the difference).

This has the grace that it is directly answering a desired question: what are the likely or plausible values of the effect size that would lead to the observed data. Such an analysis can be tweaked to respect different distributional requirements or assumptions.

Please check it out!