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