  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.

Methodology