Some applications of phase-type distributions in recurrent events

Roufeh Asghari; Amin Hassan Zadeh

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arXiv · 2201.10093

Some applications of phase-type distributions in recurrent events

Roufeh Asghari·Amin Hassan Zadeh

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Abstract

In this paper, the recurrent events that can occur more than one over the follow-up time have been modeled by phase-type distributions. We use the finite-state continuous-time Markov process with multi states for patients with recurrent events. The number of recurrences until time $t$, the time stay for every state and the time till death are of importances. The time till death is assumed to have a phase-type distribution (which is defined in a Markov chain environment) with interpretable parameters. The underlying continuous-time Markov chain has one absorbing state (death) and transient states to reflect recovery and disease stages. A system of differential equations is obtained to calculate the probability of various number of transitions, the conditional expected time to stay in a disease stage and the probability of transition from a stage to another. The model has been calibrated via a real and simulated datasets. The bootstrap techniques have been used to construct the confidence intervals for the parameters.

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Roufeh Asghari, Amin Hassan Zadeh. 2022-01-25. Some applications of phase-type distributions in recurrent events. https://arxiv.org/abs/2201.10093

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