Combining posteriors from multiple imputation


I am running a network meta-analysis which seems to be an unending treasure trove of new learning opportunities, the newest of which is the issue of combining posteriors from multiple imputation. I am running a meta-regression that appears to have a relationship with treatment effect in scatterplots, but the covariate of interest is missing from ~20% of studies. I know the best answer is that I need to learn to code my imputation into stan, but these are secondary analyses on a project that I really need to finish to make room for other deadlines.

By any stretch, is it at all safe to simply run my model on the five imputed datasets, concatenate the posteriors, and then derive my quantiles of interest? This seems on it’s face to do what I’m looking for (i.e. account for uncertainty from the imputation), but I am not a statistician and always have a healthy amount of skepticism towards solutions that seem too easy.


That is considered the right thing to do following multiple imputation. But you have to do the convergence diagnostics separately for each imputed dataset that you are conditioning on.


A slightly more cautious approach that lets you leverage domain knowledge would be to carry out the full analysis on multiple imputed datasets and determine whether they all reach the same conclusions. If they do you’ve shown the result is insensitive to the details of the imputation and that’s what you’re looking for anyway. The fine distinction here is that even if the model parameters converge to the same distribution, the derived quantities you use for your analysis may not. I’m not sure if this is different than Ben’s suggestion.