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

2025-05-09

AI Summary

In survival analysis, conventional piecewise exponential models rely on fixed changepoints and random-walk priors for long-term extrapolation, leading to distorted hazard estimates and failing to meet health technology assessment (HTA) requirements for reliable mean survival time estimation. We propose a diffusion-based piecewise exponential model: it employs a discretized diffusion process to construct a hazard function prior and couples a Poisson process to dynamically locate changepoints, enabling robust, data- and prior-informed extrapolation. We further extend sticky dynamics to support variable-dimensional posterior sampling. This work is the first to unify diffusion priors with stochastic changepoint mechanisms within a single framework, enabling efficient sampling via piecewise deterministic Markov processes (PDMPs). Evaluated on colon cancer and leukemia datasets, our method significantly improves long-term survival prediction accuracy and satisfies HTA’s stringent requirements for mean survival time extrapolation.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Extrapolating long-term hazards beyond observed data
• Combining hazard behavior with prior information
• Efficient posterior sampling for survival analysis

Innovation

• Diffusion piecewise exponential model for hazard encoding
• Poisson process prior for flexible knot locations
• Piecewise Deterministic Markov Processes for efficient sampling