  Datasets containing large samples of time-to-event data arising from several
small heterogeneous groups are commonly encountered in statistics. This
presents problems as they cannot be pooled directly due to their heterogeneity
or analyzed individually because of their small sample size. 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 modelling 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 a real-world injury dataset.
