We consider exchangeable Markov multi-state survival processes, which are temporal processes taking values over a state-space , with at least one absorbing failure state that satisfy the natural invariance properties of exchangeability and consistency under subsampling. The set of processes contains many well-known examples from health and epidemiology including survival, illness-death, competing risk, and comorbidity processes. Here, 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 to irregularly sampled and potentially censored multi-state survival data, developing a Markov chain Monte Carlo algorithm for inference.
Keywords: Markov chain Monte Carlo; Markov process; composable systems; exchangeability; multi-state survival process.