IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v14y2012i3d10.1007_s11009-011-9260-9.html
   My bibliography  Save this article

On the Moments and the Distribution of the Cost of a Semi Markov Model for Healthcare Systems

Author

Listed:
  • Aleka A. Papadopoulou

    (Aristotle University of Thessaloniki)

  • George Tsaklidis

    (Aristotle University of Thessaloniki)

  • Sally McClean

    (University of Ulster)

  • Lalit Garg

    (University of Ulster)

Abstract

In this paper we extend our previous semi-Markov reward model which attached costs to duration in states, by including costs of making a transition from one state to another. Theoretical results concerning the moments and consequently the distribution of interval costs for every member and of the total cost per unit period at any time and also through time intervals are obtained and provided in analytic form for the semi Markov reward model with discounting. The results are applied to an open healthcare system. In the healthcare domain such transition costs allow us to evaluate the overall costs of therapy or clinical intervention where an operation or other treatment may be an option. This model can be used for strategic approaches to planning and evaluating long-term patient care. The results demonstrate the potential of the model to demonstrate differential costs of different therapeutic strategies and explore optimal solutions.

Suggested Citation

  • Aleka A. Papadopoulou & George Tsaklidis & Sally McClean & Lalit Garg, 2012. "On the Moments and the Distribution of the Cost of a Semi Markov Model for Healthcare Systems," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 717-737, September.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-011-9260-9
    DOI: 10.1007/s11009-011-9260-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-011-9260-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-011-9260-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. L. Jianyong & Z. Xiaobo, 2004. "On Average Reward Semi-Markov Decision Processes with a General Multichain Structure," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 339-352, May.
    2. Fredrik Stenberg & Raimondo Manca & Dmitrii Silvestrov, 2007. "An Algorithmic Approach to Discrete Time Non-homogeneous Backward Semi-Markov Reward Processes with an Application to Disability Insurance," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 497-519, December.
    3. Aleka Papadopoulou & George Tsaklidis, 2007. "Some Reward Paths in Semi-Markov Models with Stochastic Selection of the Transition Probabilities," Methodology and Computing in Applied Probability, Springer, vol. 9(3), pages 399-411, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guglielmo D’Amico & Filippo Petroni & Flavio Prattico, 2015. "Performance Analysis of Second Order Semi-Markov Chains: An Application to Wind Energy Production," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 781-794, September.
    2. Zacharias Kyritsis & Aleka Papadopoulou, 2017. "The Quality of Life Via Semi Markov Reward Modelling," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1029-1045, December.
    3. Guglielmo D'Amico & Ada Lika & Filippo Petroni, 2019. "Risk Management of Pension Fund: A Model for Salary Evolution," IJFS, MDPI, vol. 7(3), pages 1-17, August.
    4. Dmitrii Silvestrov & Raimondo Manca, 2017. "Reward Algorithms for Semi-Markov Processes," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1191-1209, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zacharias Kyritsis & Aleka Papadopoulou, 2017. "The Quality of Life Via Semi Markov Reward Modelling," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1029-1045, December.
    2. Guglielmo D’Amico & Filippo Petroni & Flavio Prattico, 2015. "Performance Analysis of Second Order Semi-Markov Chains: An Application to Wind Energy Production," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 781-794, September.
    3. Guglielmo D'Amico & Ada Lika & Filippo Petroni, 2019. "Risk Management of Pension Fund: A Model for Salary Evolution," IJFS, MDPI, vol. 7(3), pages 1-17, August.
    4. Aleka Papadopoulou & George Tsaklidis, 2007. "Some Reward Paths in Semi-Markov Models with Stochastic Selection of the Transition Probabilities," Methodology and Computing in Applied Probability, Springer, vol. 9(3), pages 399-411, September.
    5. D’Amico, Guglielmo & Manca, Raimondo & Salvi, Giovanni, 2013. "A semi-Markov modulated interest rate model," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2094-2102.
    6. Maegebier, Alexander, 2013. "Valuation and risk assessment of disability insurance using a discrete time trivariate Markov renewal reward process," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 802-811.
    7. Guglielmo D’Amico & Fulvio Gismondi & Filippo Petroni, 2020. "Insurance Contracts for Hedging Wind Power Uncertainty," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    8. D'Amico, Guglielmo & Guillen, Montserrat & Manca, Raimondo, 2009. "Full backward non-homogeneous semi-Markov processes for disability insurance models: A Catalunya real data application," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 173-179, October.
    9. Prasenjit Mondal, 2016. "On undiscounted semi-Markov decision processes with absorbing states," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(2), pages 161-177, April.
    10. Guglielmo D'Amico & Raimondo Manca & Giovanni Salvi, 2012. "A Semi-Markov Modulated Interest Rate Model," Papers 1210.3164, arXiv.org.
    11. D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2017. "Insuring wind energy production," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 542-553.
    12. Guglielmo D'Amico & Montserrat Guillen & Raimondo Manca & Filippo Petroni, 2017. "Multi-state models for evaluating conversion options in life insurance," Papers 1707.01028, arXiv.org.
    13. Prasenjit Mondal, 2020. "Computing semi-stationary optimal policies for multichain semi-Markov decision processes," Annals of Operations Research, Springer, vol. 287(2), pages 843-865, April.
    14. Thomas Sloan, 2008. "Simultaneous determination of production and maintenance schedules using in‐line equipment condition and yield information," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(2), pages 116-129, March.
    15. Dmitrii Silvestrov & Raimondo Manca, 2017. "Reward Algorithms for Semi-Markov Processes," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1191-1209, December.
    16. F. Castella & G. Dujardin & B. Sericola, 2009. "Moments’ Analysis in Homogeneous Markov Reward Models," Methodology and Computing in Applied Probability, Springer, vol. 11(4), pages 583-601, December.
    17. Prasenjit Mondal, 2015. "Linear Programming and Zero-Sum Two-Person Undiscounted Semi-Markov Games," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-20, December.
    18. Guglielmo D’Amico & Filippo Petroni & Salvatore Vergine, 2021. "An Analysis of a Storage System for a Wind Farm with Ramp-Rate Limitation," Energies, MDPI, vol. 14(13), pages 1-25, July.
    19. Tim De Feyter & Marie-Anne Guerry & Komarudin, 2017. "Optimizing cost-effectiveness in a stochastic Markov manpower planning system under control by recruitment," Annals of Operations Research, Springer, vol. 253(1), pages 117-131, June.
    20. Guglielmo D’Amico & Giuseppe Di Biase & Raimondo Manca, 2011. "A customer’s utility measure based on the reliability of multi-state systems," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 34(1), pages 1-20, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-011-9260-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.