Prior data for non-normal priors

Data augmentation priors facilitate contextual evaluation of prior distributions and the generation of Bayesian outputs from frequentist software. Previous papers have presented approximate Bayesian methods using 2 x 2 tables of 'prior data' to represent lognormal relative-risk priors in stratified and regression analyses. The present paper describes extensions that use the tables to represent generalized-F prior distributions for relative risks, which subsume lognormal priors as a limiting case. The method provides a means to increase tail-weight or skew the prior distribution for the log relative risk away from normality, while retaining the simple 2 x 2 table form of the prior data. When prior normality is preferred, it also provides a more accurate lognormal relative-risk prior in for the 2 x 2 table format. For more compact representation in regression analyses, the prior data can be compressed into a single data record. The method is illustrated with historical data from a study of electronic foetal monitoring and neonatal death. Copyright (c) 2007 John Wiley & Sons, Ltd.