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

TL;DR

This paper introduces a Bayesian extension to polyhazard survival models, utilizing Piecewise Deterministic Markov Processes for efficient sampling, enabling better inference and application to long-term survivor data.

Contribution

It develops a prior structure for joint inference in polyhazard models and employs PDMCP sampling to handle complex, transdimensional posterior distributions.

Findings

Enhanced model flexibility for long-term survival analysis

Efficient sampling scheme reduces user tuning

Applicable to stroke and kidney transplant survival data

Abstract

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.