Data augmentation priors for Bayesian and semi‐Bayes analyses of conditional‐logistic and proportional‐hazards regression

Data augmentation priors have a long history in Bayesian data analysis. Formulae for such priors have been derived for generalized linear models, but their accuracy depends on two approximation steps. This note presents a method for using offsets as well as scaling factors to improve the accuracy of the approximations in logistic regression. This method produces an exceptionally simple form of data augmentation that allows it to be used with any standard package for conditional-logistic or proportional-hazards regression to perform Bayesian and semi-Bayes analyses of matched and survival data. The method is illustrated with an analysis of a matched case-control study of diet and breast cancer.