Empirical Bayes estimators in hierarchical models with mixture priors

ABSTRACT

We consider subgroup analyses within the framework of hierarchical modeling and empirical Bayes (EB) methodology for general priors, thereby generalizing the normal–normal model. By doing this one obtains greater flexibility in modeling. We focus on mixture priors, that is, on the situation where group effects are exchangeable within clusters of subgroups only. We establish theoretical results on accuracy, precision, shrinkage and selection bias of EB estimators under the general priors. The impact of model misspecification is investigated and the applicability of the methodology is illustrated with datasets from the (medical) literature.

Keywords:

• Hierarchical model
• subgroups
• accuracy
• shrinkage
• mixture prior

Acknowledgments

The author thanks Martin Posch, Medical University of Vienna, and Thomas Jaki, Lancaster University, for providing the opportunity to work on the topic and for feedback on an earlier draft of the manuscript. Comments by two reviewers and an associate editor are also much appreciated.

Disclosure statement

The author has declared no conflict of interest.

Additional information

Funding

The work was funded by the UK Medical Research Council, Project No. MR/M005755/1. The views expressed are those of the author and should not be attributed to the funding institution or the organization with which the author is affiliated.