Bayesian model selection for join point regression with application to age-adjusted cancer rates

The method of Bayesian model selection for join point regression models is developed. Given a set of "K"&plus;1 join point models "M"₀, "M"₁, …, "M"_{" K"} with 0, 1, …, "K" join points respec-tively, the posterior distributions of the parameters and competing models "M"_"k" are computed by Markov chain Monte Carlo simulations. The Bayes information criterion BIC is used to select the model "M"_"k" with the smallest value of BIC as the best model. Another approach based on the Bayes factor selects the model "M"_"k" with the largest posterior probability as the best model when the prior distribution of "M"_"k" is discrete uniform. Both methods are applied to analyse the observed US cancer incidence rates for some selected cancer sites. The graphs of the join point models fitted to the data are produced by using the methods proposed and compared with the method of Kim and co-workers that is based on a series of permutation tests. The analyses show that the Bayes factor is sensitive to the prior specification of the variance "σ"-super-2, and that the model which is selected by BIC fits the data as well as the model that is selected by the permutation test and has the advantage of producing the posterior distribution for the join points. The Bayesian join point model and model selection method that are presented here will be integrated in the National Cancer Institute's join point software (<externallink type="url">http://www.srab.cancer.gov/joinpoint/</externallink>) and will be available to the public. Copyright 2005 Royal Statistical Society.