This paper is an example of how Stan enables us to do large scale simulations of Bayesian methods to assess their repeat sampling properties. I used Stan to implement Bayesian meta-analyses using aggregate data on time to event outcomes using a rather expensive to evaluate likelihood. At first I used PROC MCMC in SAS for the example (runtime in hours to days), but then the reviewers requested a simulation study. At that stage switching to Stan seemed like the only realistic option and finally got me started with Stan.
The idea of the paper is by assuming specific distributions for event and drop-out times we can do meta-analysis about medical event occurence even when we only have the type of aggregate data that we typically get from medical journal publications. By parameterizing our analysis in terms of the parameters of survival distributions, we can also make more appropriate exchangeability assumptions about parameters of survival distributions, for which they are more appropriate than for e.g. the expected proportion of patients with an event (or the logit thereof). This is an especially interesting, if the trials vary substantially in length. “Borrowing information” through such exchangeability assumptions is very interesting when events are rare: when you have some information on what you expect in the control group, the usual claim that trials with no events in either trial arm do not tell us anything about the comparison between the treatments in the trial.
I hope this is of interest to some of you here,