Use of the bayesmh command in Stata to calculate excess relative and excess absolute risk for radiation health risk estimates

Excess relative risk (ERR) and excess absolute risk (EAR) are important metrics typically used in radiation epidemiology studies. Most studies of long-term radiation effects in Japanese atomic bomb survivors feature Poisson regression of grouped survival data. Risks are modeled on the excess risk scale using linear and log-linear functions of regression parameters, which are generally formulated to produce both ERR and EAR as output. Given the specific assumptions underlying these models, they are dubbed ERR and EAR models, respectively. Typically, these models are fit using the Epicure software that was specifically designed to fit these models, and they are difficult to reproduce in more accessible software. The flexibility of the bayesmh command can be utilized to fit these models within a Bayesian framework, which may increase accessibility in the broader statistical and epidemiological communities. In this presentation, I detail ERR and EAR model fitting and assumptions, and I give an example of how the models can be fit in Stata using Bayesian methods.