Clustering blood donors via mixtures of product partition models with covariates

Motivated by the problem of accurately predicting gap times between successive blood donations, we present here a general class of Bayesian nonparametric models for clustering. These models allow for the prediction of new recurrences, accommodating covariate information that describes the personal characteristics of the sample individuals. We introduce a prior for the random partition of the sample individuals, which encourages two individuals to be co-clustered if they have similar covariate values. Our prior generalizes product partition models with covariates (PPMx) models in the literature, which are defined in terms of cohesion and similarity functions. We assume cohesion functions that yield mixtures of PPMx models, while our similarity functions represent the denseness of a cluster. We show that including covariate information in the prior specification improves the posterior predictive performance and helps interpret the estimated clusters in terms of covariates in the blood donation application.