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 2x2 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 2x2 table form of the prior data. When prior normality is preferred, it also provides a more accurate lognormal relative-risk prior in for the 2x2 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.