Putting background information about relative risks into conjugate prior distributions.
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.
Greenland
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Department of Epidemiology, UCLA School of Public Health, and Topanga, California 90290, USA.
D001499:Bayes Theorem; D001699:Biometry; D004812:Epidemiologic Methods; D006801:Humans; D007226:Infant Mortality; D007231:Infant, Newborn; D016015:Logistic Models; D012044:Regression Analysis; D012306:Risk