  Meta-analytic methods may be used to combine evidence from different sources
of information. Quite commonly, the normal-normal hierarchical model (NNHM)
including a random-effect to account for between-study heterogeneity is
utilized for such analyses. The same modeling framework may also be used to not
only derive a combined estimate, but also to borrow strength for a particular
study from another by deriving a shrinkage estimate. For instance, a
small-scale randomized controlled trial could be supported by a non-randomized
study, e.g. a clinical registry. This would be particularly attractive in the
context of rare diseases. We demonstrate that a meta-analysis still makes sense
in this extreme two-study setup, as illustrated using a recent trial and a
clinical registry in Creutzfeld-Jakob disease. Derivation of a shrinkage
estimate within a Bayesian random-effects meta-analysis may substantially
improve a given estimate even based on only a single additional estimate while
accounting for potential effect heterogeneity between the studies.
Alternatively, inference may equivalently be motivated via a model
specification that does not require a common overall mean parameter but
considers the treatment effect in one study, and the difference in effects
between the studies. The proposed approach is quite generally applicable to
combine different types of evidence originating e.g. from meta-analyses or
individual studies. An application of this more general setup is provided in
immunosuppression following liver transplantation in children.
