Power and commensurate priors for synthesizing aggregate and individual patient level data in network meta‐analysis

In network meta‐analysis, it is often desirable to synthesize different types of studies, featuring aggregated data and individual patient level data. However, existing methods do not sufficiently consider the quality of studies across different types of data and assume that the treatment effects are exchangeable across all studies regardless of these types. We propose Bayesian hierarchical network meta‐analysis models that allow us to borrow information adaptively across aggregated data and individual patient level data studies by using power and commensurate priors. The power parameter in the power priors and spike‐and‐slab hyperprior in the commensurate priors govern the level of borrowing information among study types. We incorporate covariate‐by‐treatment interactions to deliver personalized decision making and model any ecological fallacy. The methods are validated and compared via extensive simulation studies and then applied to an example in diabetes treatment comparing 28 oral antidiabetic drugs. We compare results across model and hyperprior specifications. Finally, we close with a discussion of our findings, limitations and future research.