Weak continuity of predictive distribution for Markov survival processes

TL;DR

This paper investigates the structure of exchangeable Markov survival processes, characterizes those with weakly continuous predictive distributions, and introduces the harmonic process as a key example, with applications to censored data.

Contribution

It characterizes Markov survival processes with weakly continuous predictive distributions and introduces the harmonic process as a new family of such models.

Findings

Asymptotic growth of tied failure time blocks analyzed

Harmonic process characterized as a key family with weak continuity

Methods extended to handle censored survival data

Abstract

We explore the concept of a consistent exchangeable survival process - a joint distribution of survival times in which the risk set evolves as a continuous-time Markov process with homogeneous transition rates. We show a correspondence with the de Finetti approach of constructing an exchangeable survival process by generating iid survival times conditional on a completely independent hazard measure. We describe several specific processes, showing how the number of blocks of tied failure times grows asymptotically with the number of individuals in each case. In particular, we show that the set of Markov survival processes with weakly continuous predictive distributions can be characterized by a two-dimensional family called the harmonic process. We end by applying these methods to data, showing how they can be easily extended to handle censoring.