UCSC-SOE-22-11: Bayesian Nonparametric Erlang Mixture Modeling for Survival Analysis

Yunzhe Li, Juhee Lee and Athanasios Kottas
07/26/2022 10:26 AM
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.

UPDATED: November 14, 2022