Bayesian Nonparametric Modeling of Heterogeneous Groups of Censored Data

TL;DR

This paper compares three Bayesian nonparametric methods for modeling survival functions across heterogeneous groups with censored data, highlighting their accuracy and applicability to real-world datasets.

Contribution

It provides a comparative analysis of Dirichlet, hierarchical Dirichlet, and nested Dirichlet processes for survival analysis of heterogeneous groups.

Findings

Hierarchical Dirichlet process outperforms others in certain scenarios.

Models effectively share information across small groups.

Application to real-world injury data demonstrates practical utility.

Abstract

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.