Bayesian Nonparametric Modeling of Heterogeneous Groups of Censored Data

Applied statisticians often encounter large samples of time-to-event data arising from a number of different groups with only a small number of observations per group. Bayesian nonparametric modelling approaches can be used to model such datasets given their ability to flexibly share information across groups. In this paper, we will compare three popular Bayesian nonparametric methods for modelling the survival functions of heterogeneous groups. Specifically, we will first compare the modelilng accuracy of the Dirichlet process, the hierarchical Dirichlet process, and the nested Dirichlet process on simulated datasets of different sizes, where group survival curves differ in shape or in expectation. We then will compare the models on two real world injury datasets.