Competing Risks Modeling by Extended Phase-Type Semi-Markov Distributions

Abstract

We present competing risks models within a semi-Markov process framework via the semi-Markov phase-type distribution. We consider semi-Markov processes in continuous and discrete time with a finite number of transient states and a finite number of absorbing states. Each absorbing state represents a failure mode (in system reliability) or a cause of death of an individual (in survival analysis). This is an extension of the continuous-time Markov competing risks model presented in Lindqvist and Kjølen [2018]. We derive the joint distribution of the lifetime and the failure cause via the transition function of semi-Markov processes in continuous and discrete-time. Some examples are given for illustration.

Phase-type models for competing risks, with emphasis on identifiability issues

“…The new applications have also motivated new theoretical developments and extensions of the classical models. For example, while the present study has been limited to phase-type modeling via homogeneous Markov chains, there have recently been published papers which involve nonhomogenous Markov chains (Bladt and Yslas 2020), semi-Markov models (Garcia-Maya et al 2021), and models including unobserved heterogeneity (Surya 2016). Guihenneuc-Jouyaux et al (2000) considered a Markov model of disease progression with a single absorbing state, where noisy biomarker measurements, depending on the state of the Markov chain, were available.…”

Phase‐type models involving restarting and instantaneous transitions, with applications to degradation and maintenance

“…In a similar way, Slud et al 6 studied phase‐type models for survival data, introducing a second absorbing state for direct transition to the state of death or cure. Other applications in survival analysis involving competing risks and Markov chains, are given in, for example, Llorca et al, 20 Abner et al 21 and Garcia‐Maya et al 22 The latter authors considered phase‐type modeling of competing risks in a semi‐Markov process framework. In a recent paper, Wu and Cui 23 studied periodically inspected reliability systems involving competing risks, under environment processes modeled by absorbing Markov chains.…”