Inferences on lung cancer mortality rates based on reference priors under partial ordering

type="main" xml:id="rssc12059-abs-0001"> We present a novel analysis of a landmark table of dose–response mortality counts from lung cancer in men. The data were originally collected by Doll and Hill. Our inferences are based on Poisson models for which the rates of occurrence are partially ordered according to two covariates. The partial ordering of the mortality rates enforces the well-established knowledge that lung cancer mortality rates are higher for older men and for heavier smokers. The ordered group reference priors that we use in our analyses generalize a class of reference priors that we previously derived for models of count data in which the rates of occurrence in different categories are completely ordered with respect to the values of a single covariate. The reference models for the lung cancer data based on the proposed priors are more flexible than and can be superior, in terms of goodness of fit, to a Bayesian version of several parametric models derived from a mathematical theory of carcinogenesis that have appeared in the literature.