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Inferences on lung cancer mortality rates based on reference priors under partial ordering
Author(s) -
Sonksen Michael D.,
Peruggia Mario
Publication year - 2014
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/rssc.12059
Subject(s) - prior probability , covariate , lung cancer , poisson distribution , statistics , bayesian probability , mathematics , parametric statistics , econometrics , medicine , oncology
Summary 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.