Bayesian clustering with regression
Seminar Room 1, Newton Institute
We consider clustering with regression, i.e., we develop a probability model for random clusters that is indexed by covariates. The two motivating applications are inference for a clinical trial and for survival of patients with breast cancer. As part of the desired inference we wish to define clusters of patients. Defining a prior probability model for cluster memberships should include a regression on patient baseline covariates. We build on product partition models (PPM). We define an extension of the PPM to include the desired regression. This is achieved by including in the cohesion a new factor that increases the probability of experimental units with similar covariates to be included in the same cluster. We discuss implementations suitable for continuous, categorical, count and ordinal covariates.