Bayesian regression in SAS software

Bayesian methods have been found to have clear utility in epidemiologic analyses involving sparse-data bias or considerable background information. Easily implemented methods for conducting Bayesian analyses by data augmentation have been previously described but remain in scant use. Thus, we provide guidance on how to do these analyses with ordinary regression software. We describe in detail and provide code for the implementation of data augmentation for Bayesian and semi-Bayes regression in SAS (R) software, and illustrate their use in a real logistic-regression analysis. For comparison, the same model was fitted using the Markov-chain Monte Carlo (MCMC) procedure. The two methods required a similar number of steps and yielded similar results, although for the main example, data augmentation ran in about 0.5% of the time required for MCMC. We also provide online appendices with details and examples for conditional logistic, Poisson and Cox proportional-hazards regression.