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Putting background information about relative risks into conjugate prior distributions.

Authors
  • Greenland, S
Type
Published Article
Journal
Biometrics
Publication Date
Sep 01, 2001
Volume
57
Issue
3
Pages
663–670
Identifiers
PMID: 11550913
Source
Medline
License
Unknown

Abstract

In Bayesian and empirical Bayes analyses of epidemiologic data, the most easily implemented prior specifications use a multivariate normal distribution for the log relative risks or a conjugate distribution for the discrete response vector. This article describes problems in translating background information about relative risks into conjugate priors and a solution. Traditionally, conjugate priors have been specified through flattening constants, an approach that leads to conflicts with the true prior covariance structure for the log relative risks. One can, however, derive a conjugate prior consistent with that structure by using a data-augmentation approximation to the true log relative-risk prior, although a rescaling step is needed to ensure the accuracy of the approximation. These points are illustrated with a logistic regression analysis of neonatal-death risk.

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