Diffusion piecewise exponential models for survival extrapolation using Piecewise Deterministic Monte Carlo

TL;DR

This paper introduces a diffusion-based prior framework for piecewise exponential survival models, improving long-term hazard extrapolation by integrating prior information with observed data, and employs advanced sampling techniques for efficient inference.

Contribution

It proposes the diffusion piecewise exponential model with a Poisson process prior for knot locations, enabling more realistic hazard extrapolations beyond observed data.

Findings

Enhanced hazard extrapolation accuracy in health data

Efficient posterior sampling with Piecewise Deterministic Markov Processes

Improved survival estimates for cancer datasets

Abstract

The piecewise exponential model is a flexible non-parametric approach for time-to-event data, but extrapolation beyond final observation times typically relies on random walk priors and deterministic knot locations, resulting in unrealistic long-term hazards. We introduce the diffusion piecewise exponential model, a prior framework consisting of a discretised diffusion for the hazard, that can encode a wide variety of information about the long-term behaviour of the hazard, time changed by a Poisson process prior for knot locations. This allows the behaviour of the hazard in the observation period to be combined with prior information to inform extrapolations. Efficient posterior sampling is achieved using Piecewise Deterministic Markov Processes, whereby we extend existing approaches using sticky dynamics from sampling spike-and-slab distributions to more general transdimensional posteriors. We focus on applications in Health Technology Assessment, where the need to compute mean survival requires hazard functions to be extrapolated beyond the observation period, showcasing performance on datasets for Colon cancer and Leukaemia patients.