A Bayesian normal mixture accelerated failure time spatial model and its application to prostate cancer

In the United States, prostate cancer is the third most common cause of death from cancer in males of all ages, and the most common cause of death from cancer in males over age 75. It has been recognized that the incidence of the prostate cancer is high in African Americans, and its occurrence and progression may be impacted by geographical factors. In order to investigate the spatial effects and racial disparities for prostate cancer in Louisiana, in this article we propose a normal mixture accelerated failure time spatial model, which does not require the proportional hazards assumption and allows the multi-model distribution to be modeled. The proposed model is estimated with a Bayesian approach and it can be easily implemented in WinBUGS. Extensive simulations show that the proposed model provides decent flexibility for a variety of parametric error distributions. The proposed method is applied to 2000-2007 Louisiana prostate cancer data set from the Surveillance, Epidemiology and End Results Program. The results reveal the possible spatial pattern and racial disparities for prostate cancer in Louisiana.