  Shrinkage estimation in a meta-analysis framework may be used to facilitate
dynamical borrowing of information. This framework might be used to analyze a
new study in the light of previous data, which might differ in their design
(e.g., a randomized controlled trial (RCT) and a clinical registry). We show
how the common study weights arise in effect and shrinkage estimation, and how
these may be generalized to the case of Bayesian meta-analysis. Next we develop
simple ways to compute bounds on the weights, so that the contribution of the
external evidence may be assessed a priori. These considerations are
illustrated and discussed using numerical examples, including applications in
the treatment of Creutzfeldt-Jakob disease and in fetal monitoring to prevent
the occurrence of metabolic acidosis. The target study's contribution to the
resulting estimate is shown to be bounded below. Therefore, concerns of
evidence being easily overwhelmed by external data are largely unwarranted.
