Considering parallel tempering and comparing post-treatment procedures in Bayesian Profile Regression Models for a survival outcome and correlated exposures

Bayesian profile regression mixture models (BPRM) allow to assess a health risk in a multi-exposed population. These mixture models cluster individuals according to their exposure profile and their health risk. However, their results, based on Monte-Carlo Markov Chain (MCMC) algorithms, turned out to be unstable in different application cases. We suppose two reasons for this instability. The MCMC algorithm can be trapped in local modes of the posterior distribution and the choice of post-treatment procedures used on the output of the MCMC algorithm leads to different clustering structures. In this work, we propose improvements of the MCMC algorithms proposed in previous works in order to avoid the local modes of the posterior distribution while reducing the computation time. We also carry out a simulation study to compare the performances of the MCMC algorithms and different post-processing in order to provide guidelines on their use. An application in radiation epidemiology is considered.