Averaging polyhazard models using Piecewise deterministic Monte Carlo with applications to data with long-term survivors

Polyhazard models are a class of flexible parametric models for modelling survival over extended time horizons. Their additive hazard structure allows for flexible, non-proportional hazards whose characteristics can change over time while retaining a parametric form, which allows for survival to be extrapolated beyond the observation period of a study. Significant user input is required, however, in selecting the number of latent hazards to model, their distributions and the choice of which variables to associate with each hazard. The resulting set of models is too large to explore manually, limiting their practical usefulness. Motivated by applications to stroke survivor and kidney transplant patient survival times we extend the standard polyhazard model through a prior structure allowing for joint inference of parameters and structural quantities, and develop a sampling scheme that utilises state-of-the-art Piecewise Deterministic Markov Processes to sample from the resulting transdimensional posterior with minimal user tuning.