Meta-analytic-predictive priors based on a single study

Meta-analytic-predictive (MAP) priors have been proposed as a generic approach to deriving informative prior distributions, where external empirical data are processed to learn about certain parameter distributions. The use of MAP priors is also closely related to shrinkage estimation (also sometimes referred to as dynamic borrowing). A potentially odd situation arises when the external data consist only of a single study. Conceptually, this is not a problem, it only implies that certain prior assumptions gain in importance and need to be specified with particular care. We outline this important, not uncommon special case and demonstrate its implementation and interpretation based on the normal-normal hierarchical model. The approach is illustrated using example applications in clinical medicine.