Homogeneous clustering method for data on tumor incidence due to dose levels

In a typical animal epidemiological experiment, a hazardous chemical compound induces the tumor of interest and the onset times are closely related to the dose levels of the compound. Here, we focus on homogeneous clustering of the tumor onset probability vectors due to dose levels. We applied a Bayesian nonparametric prior to probability vectors defined on the simplex dimension of the tumor onset times. The nonparametric formulation specifies various clusterings of the tumor onset probability vectors. These provide a natural comparison of the probability vectors according to dose levels. Most types of tumors are unobservable until a pathology examination at the time of death; their corresponding onset times are therefore often unknown, and Bayesian analysis of tumor incidence data is problematic. To overcome this difficulty, we used a data augmentation algorithm with latent variables indicating the onset times of the tumor. These latent variables with the given priors provide convenient conjugate forms of the conditional densities used in the Gibbs sampling. We analyzed data from a rodent carcinogenicity study.