Bayesian design considerations for studies with an informative prior based on hierarchical modeling
*Gene Pennello, FDA/CDRH  Laura Thompson, FDA-CDRH 

Keywords: pre-posterior analysis, predictive power, Fisher information

In many Bayesian studies of medical devices, the current study is assumed to be exchangeable with one or more prior studies in a hierarchical model, enabling strength to be borrowed from the prior studies. When such a Bayesian study is proposed to support approval or clearance of a medical device, many issues need to be considered. How influential will the prior be on device performance estimates? How is the sample size for the study determined? What is the appropriate level of the type 1 error rate? In this talk, I’ll attempt to provide some guidance on these and other questions. Specifically, prior influence can be evaluated with the effective sample size, the effective number of subjects that are borrowed from the prior studies by the Bayesian analysis. The sample size for the study can be determined approximately as the usual sample size minus the prior effective sample size, where the usual sample size is powered at the prior mean or mode. The type 1 error rate is (in my view) most appropriately calculated “prior to the prior”, otherwise the advantage of using the prior will vanish.