Skip to main content

2018 | OriginalPaper | Buchkapitel

Phase-Type Models and Their Extension to Competing Risks

verfasst von : Bo Henry Lindqvist, Susanne Hodneland Kjølen

Erschienen in: Recent Advances in Multi-state Systems Reliability

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We present an extension of the phase-type methodology for modeling of lifetime distributions to include the case of competing risks. This is done by considering finite state Markov chains in continuous time with more than one absorbing state, letting each absorbing state correspond to a particular risk. The special structure of Coxian phase-type models is considered in particular. The chapter emphasizes the use of phase-type models in statistical modeling and inference for survival and competing risks data.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Aalen OO (1995) Phase type distributions in survival analysis. Scandinavian J Statistics 22(4):447–463MATH Aalen OO (1995) Phase type distributions in survival analysis. Scandinavian J Statistics 22(4):447–463MATH
2.
Zurück zum Zitat Aslett, LJM, Wilson SP (2011) Markov chain Monte Carlo for inference on phasetype models. ISI Aslett, LJM, Wilson SP (2011) Markov chain Monte Carlo for inference on phasetype models. ISI
3.
Zurück zum Zitat Asmussen S, Nerman O, Olsson M (1996) Fitting phase-type distributions via the EM algorithm. Scandinavian J Statistics 23(4):419–441 Asmussen S, Nerman O, Olsson M (1996) Fitting phase-type distributions via the EM algorithm. Scandinavian J Statistics 23(4):419–441
4.
Zurück zum Zitat Beyersmann J, Allignol A, Schumacher M (2011) Competing risks and multistate models with R. Springer Science & Business Media Beyersmann J, Allignol A, Schumacher M (2011) Competing risks and multistate models with R. Springer Science & Business Media
5.
Zurück zum Zitat Bladt M, Gonzalez A, Lauritzen SL (2003) The estimation of phase-type related functionals using Markov chain Monte Carlo methods. Scandinavian Actuarial J 2003(4):280–300MathSciNetCrossRefMATH Bladt M, Gonzalez A, Lauritzen SL (2003) The estimation of phase-type related functionals using Markov chain Monte Carlo methods. Scandinavian Actuarial J 2003(4):280–300MathSciNetCrossRefMATH
6.
Zurück zum Zitat Borgan O (1998) Three contributions to the encyclopedia of biostatistics: The Nelson-Aalen. Kaplan-Meier and Aalen-Johansen estimators, Encyclopedia of Biostatistics Borgan O (1998) Three contributions to the encyclopedia of biostatistics: The Nelson-Aalen. Kaplan-Meier and Aalen-Johansen estimators, Encyclopedia of Biostatistics
7.
Zurück zum Zitat Braarud IH (2012) Phase type and competing risk models in survival analysis. Department of Mathematical Sciences, Norwegian University of Science and Technology, Project work Braarud IH (2012) Phase type and competing risk models in survival analysis. Department of Mathematical Sciences, Norwegian University of Science and Technology, Project work
8.
Zurück zum Zitat Cox DR (1955) A use of complex probabilities in the theory of stochastic processes. In: Mathematical proceedings of the Cambridge philosophical society vol 51, No 02. Cambridge University Press, pp 313–319 Cox DR (1955) A use of complex probabilities in the theory of stochastic processes. In: Mathematical proceedings of the Cambridge philosophical society vol 51, No 02. Cambridge University Press, pp 313–319
9.
Zurück zum Zitat Cox DR (1959) The analysis of exponentially distributed life-times with two types of failure. J Royal Stat Soc Series B (Methodological) 21:411–421MathSciNetMATH Cox DR (1959) The analysis of exponentially distributed life-times with two types of failure. J Royal Stat Soc Series B (Methodological) 21:411–421MathSciNetMATH
10.
Zurück zum Zitat Faddy MJ, Graves N, Pettitt AN (2009) Modeling length of stay in hospital and other right skewed data: Comparison of phase-type, gamma and lognormal distributions. Value Health 12:309–314CrossRef Faddy MJ, Graves N, Pettitt AN (2009) Modeling length of stay in hospital and other right skewed data: Comparison of phase-type, gamma and lognormal distributions. Value Health 12:309–314CrossRef
11.
Zurück zum Zitat Gillespie J, McClean S, Scotney B, Garg L, Barton M, Fullerton K (2011) Costing hospital resources for stroke patients using phase-type models. Health Care Manag Sci 14(3):279–291CrossRef Gillespie J, McClean S, Scotney B, Garg L, Barton M, Fullerton K (2011) Costing hospital resources for stroke patients using phase-type models. Health Care Manag Sci 14(3):279–291CrossRef
12.
Zurück zum Zitat Laache CH (2014) Phase-type inference on competing risks models with covariates, using MCMC methods. Master’s thesis, Department of Mathematical Sciences, Norwegian University of Science and Technology Laache CH (2014) Phase-type inference on competing risks models with covariates, using MCMC methods. Master’s thesis, Department of Mathematical Sciences, Norwegian University of Science and Technology
13.
Zurück zum Zitat Lawless JF (2003) Statistical models and methods for lifetime data. Wiley-Interscience, Hoboken, NJMATH Lawless JF (2003) Statistical models and methods for lifetime data. Wiley-Interscience, Hoboken, NJMATH
14.
Zurück zum Zitat Lindqvist, B. (2016). Phase-type models for competing risks. In: Frenkel I, Lisnianski A (eds) Proceedings of the second international symposium on stochastic models in reliability engineering, life science and operations management (SMRLO16). Beer Sheva, Israel, pp 37–40, 15–18 February 2016, IEEE CPS, 978-1-4673-9941-8/16. doi:10.1109/SMRLO.2016.17 Lindqvist, B. (2016). Phase-type models for competing risks. In: Frenkel I, Lisnianski A (eds) Proceedings of the second international symposium on stochastic models in reliability engineering, life science and operations management (SMRLO16). Beer Sheva, Israel, pp 37–40, 15–18 February 2016, IEEE CPS, 978-1-4673-9941-8/16. doi:10.​1109/​SMRLO.​2016.​17
15.
Zurück zum Zitat McGrory CA, Pettitt AN, Faddy MJ (2009) A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean. Comput Stat Data Anal 53(12):4311–4321MathSciNetCrossRefMATH McGrory CA, Pettitt AN, Faddy MJ (2009) A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean. Comput Stat Data Anal 53(12):4311–4321MathSciNetCrossRefMATH
16.
Zurück zum Zitat Neuts MF (1981) Matrix-geometric solutions in stochastic models. Johns Hopkins University Press, Baltimore/LondonMATH Neuts MF (1981) Matrix-geometric solutions in stochastic models. Johns Hopkins University Press, Baltimore/LondonMATH
17.
Zurück zum Zitat O’Cinneide CA (1989) On non-uniqueness of representations of phase type distributions. Commun Stat—Stoch Models 5:247–259 O’Cinneide CA (1989) On non-uniqueness of representations of phase type distributions. Commun Stat—Stoch Models 5:247–259
18.
Zurück zum Zitat Payne K, Marshall AH, Cairns KJ (2011) Investigating the efficiency of fitting Coxian phase-type distributions to health care data. IMA J Manag Math. doi:10.1093/imaman/dpr008 Payne K, Marshall AH, Cairns KJ (2011) Investigating the efficiency of fitting Coxian phase-type distributions to health care data. IMA J Manag Math. doi:10.​1093/​imaman/​dpr008
19.
20.
Metadaten
Titel
Phase-Type Models and Their Extension to Competing Risks
verfasst von
Bo Henry Lindqvist
Susanne Hodneland Kjølen
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-63423-4_6

Neuer Inhalt