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Exchangeable Markov multi-state survival processes.

Walter Dempsey1

  • 1University of Michigan.

Statistica Sinica
|October 28, 2021
PubMed
Summary
This summary is machine-generated.

We introduce exchangeable Markov multi-state survival processes, unifying models in health and epidemiology. This framework enables robust inference for complex survival data, including recurrent events and censored observations.

Keywords:
Markov chain Monte CarloMarkov processcomposable systemsexchangeabilitymulti-state survival process

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Stochastic Processes

Background:

  • Multi-state survival models are crucial in health and epidemiology for analyzing transitions between health states.
  • Existing models often lack the flexibility to handle complex dependencies and data structures inherent in real-world health data.
  • Exchangeability and consistency under subsampling are desirable properties for robust statistical modeling.

Purpose of the Study:

  • To characterize exchangeable Markov multi-state survival processes in both discrete and continuous time.
  • To develop a theoretical framework that unifies various survival process models used in applied health research.
  • To address statistical constraints and introduce the concept of composable systems for model development.

Main Methods:

  • Mathematical characterization of exchangeable Markov multi-state survival processes.
  • Development of statistical constraints for applied modeling, including the notion of composable systems.
  • Application to irregularly sampled and potentially censored multi-state survival data using Markov chain Monte Carlo (MCMC) methods.

Main Results:

  • A unified characterization of exchangeable Markov multi-state survival processes is provided.
  • Constraints for applied statistical modeling, particularly composable systems, are described.
  • An MCMC algorithm is developed for inference on complex, real-world survival data.

Conclusions:

  • Exchangeable Markov multi-state survival processes offer a flexible and unified framework for health and epidemiological research.
  • The developed methods allow for robust inference even with irregularly sampled and censored data.
  • This work provides a foundation for advanced modeling of complex health trajectories.