Bounds for the weight of external data in shrinkage estimation
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Dynamical borrowing of information may be facilitated via shrinkage estimation in a meta-analysis framework. 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; concerns of evidence being easily overwhelmed by external data are shown to be largely unwarranted.
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