Putting background information about relative risks into conjugate prior distributions.
- Authors
- 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.