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

Bo Henry Lindqvist1

  • 1Norwegian University of Science and Technology, Trondheim, Norway. bo.lindqvist@ntnu.no.

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Summary
This summary is machine-generated.

This study extends phase-type distributions to model competing risks using Markov chains. It addresses parameter identifiability issues in Coxian competing risks models, offering a new statistical inference approach.

Keywords:
Competing risksCoxian distributionIdentifiabilityPhase-type distribution

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Area of Science:

  • Probability Theory
  • Stochastic Processes
  • Survival Analysis

Background:

  • Phase-type distributions are a flexible class of distributions for modeling.
  • Coxian distributions are a specific type of phase-type distribution with canonical representations.
  • Modeling competing risks is crucial in various fields, including reliability and medicine.

Purpose of the Study:

  • To extend phase-type modeling to effectively handle competing risks.
  • To investigate and address the non-uniqueness of Markov chain representations in competing risks scenarios.
  • To develop identifiable parameterizations for Coxian competing risks models.

Main Methods:

  • Review of main results for phase-type distributions and Coxian distributions.
  • Extension of phase-type modeling to competing risks using finite state Markov chains with multiple absorbing states.
  • Analysis of non-uniqueness issues in Markov chain representations for competing risks.
  • Development of identifiable parameterizations for the Coxian competing risks model.

Main Results:

  • Established a framework for phase-type competing risks modeling using multi-absorbing state Markov chains.
  • Identified and addressed challenges related to the non-uniqueness of Markov chain representations in this context.
  • Proposed identifiable parameterizations for the Coxian competing risks model.
  • Demonstrated the practical application through statistical inference and real data analysis.

Conclusions:

  • The proposed extension provides a robust method for phase-type competing risks analysis.
  • The focus on identifiable parameterizations enhances the reliability of model fitting and interpretation.
  • The study contributes to the advancement of statistical modeling for complex risk scenarios.