My paper on exchangeable, Markov multi-state survival processes was just accepted at the Statistica Sinica. This paper builds upon prior work with my Ph.D. advisor Peter McCullagh. Here we consider temporal processes taking values over a state-space with at least one absorbing failure state that satisfy natural invariance properties of exchangeability and consistency under subsampling. The set of processes contains many well-known examples from health and epidemiology – survival, illness-death, competing risk, and comorbidity processes; an extension leads to recurrent event processes. We characterize exchangeable Markov multi-state survival processes in both discrete and continuous time. Statistical considerations impose natural constraints on the space of models appropriate for applied work. In particular, we describe constraints arising from the notion of composable systems. We end with an application of the developed models to irregularly sampled and potentially censored multi-state survival data, developing a Markov chain Monte Carlo algorithm for posterior computation.

Topics covered

The paper covers a wide range of topics:

  • Exchangeability
  • Stochastic processes
  • Uniformization-based MCMC

We provide a representation theorem for all exchangeable, Markov multi-state survival processes and highlight a particular family of probability distributions that are suitable for applied work. Inference requires extending uniformization-based MCMC methods to handle the dependency structure among units.

Of course, the theory and methods are general and should be useful to applied health scientists interested in multi-state survival data. I hope you enjoy the paper; if you have any comments or questions, please feel to reach out to me via e-mail.