Bayesian Nonparametric Erlang Mixture Modeling for Survival Analysis

TL;DR

This paper introduces a Bayesian nonparametric Erlang mixture model for survival analysis, providing flexible hazard estimation and accommodating multiple groups with dependent priors, demonstrated through synthetic and real data.

Contribution

It presents a novel Erlang mixture model with Dirichlet process priors for flexible survival and hazard analysis, including extensions for multiple groups.

Findings

Effective hazard function estimation demonstrated

Model flexibility balances complexity and computational efficiency

Successful application to synthetic and real datasets

Abstract

We develop a flexible Erlang mixture model for survival analysis. The model for the survival density is built from a structured mixture of Erlang densities, mixing on the integer shape parameter with a common scale parameter. The mixture weights are constructed through increments of a distribution function on the positive real line, which is assigned a Dirichlet process prior. The model has a relatively simple structure, balancing flexibility with efficient posterior computation. Moreover, it implies a mixture representation for the hazard function that involves time-dependent mixture weights, thus offering a general approach to hazard estimation. We extend the model to handle survival responses corresponding to multiple experimental groups, using a dependent Dirichlet process prior for the group-specific distributions that define the mixture weights. Model properties, prior specification, and posterior simulation are discussed, and the methodology is illustrated with synthetic and real data examples.