• Bayesian analysis;
  • Data augmentation;
  • Epidemiologic methods;
  • Exponential regression;
  • Interpretation;
  • Logistic regression;
  • Log-linear models;
  • Odds ratio;
  • Poisson regression;
  • Relative risk;
  • Risk assessment;
  • Risk regression

Summary. 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.