IDEAS home Printed from https://ideas.repec.org/a/sae/medema/v33y2013i6p767-779.html
   My bibliography  Save this article

A Mathematical Approach for Evaluating Markov Models in Continuous Time without Discrete-Event Simulation

Author

Listed:
  • Joost van Rosmalen
  • Mehlika Toy
  • James F. O’Mahony

Abstract

Markov models are a simple and powerful tool for analyzing the health and economic effects of health care interventions. These models are usually evaluated in discrete time using cohort analysis. The use of discrete time assumes that changes in health states occur only at the end of a cycle period. Discrete-time Markov models only approximate the process of disease progression, as clinical events typically occur in continuous time. The approximation can yield biased cost-effectiveness estimates for Markov models with long cycle periods and if no half-cycle correction is made. The purpose of this article is to present an overview of methods for evaluating Markov models in continuous time. These methods use mathematical results from stochastic process theory and control theory. The methods are illustrated using an applied example on the cost-effectiveness of antiviral therapy for chronic hepatitis B. The main result is a mathematical solution for the expected time spent in each state in a continuous-time Markov model. It is shown how this solution can account for age-dependent transition rates and discounting of costs and health effects, and how the concept of tunnel states can be used to account for transition rates that depend on the time spent in a state. The applied example shows that the continuous-time model yields more accurate results than the discrete-time model but does not require much computation time and is easily implemented. In conclusion, continuous-time Markov models are a feasible alternative to cohort analysis and can offer several theoretical and practical advantages.

Suggested Citation

  • Joost van Rosmalen & Mehlika Toy & James F. O’Mahony, 2013. "A Mathematical Approach for Evaluating Markov Models in Continuous Time without Discrete-Event Simulation," Medical Decision Making, , vol. 33(6), pages 767-779, August.
  • Handle: RePEc:sae:medema:v:33:y:2013:i:6:p:767-779
    DOI: 10.1177/0272989X13487947
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0272989X13487947
    Download Restriction: no

    File URL: https://libkey.io/10.1177/0272989X13487947?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
    ---><---

    References listed on IDEAS

    as
    1. Sita Tan & Gerrit van Oortmarssen & Nanda Piersma, 2003. "Estimating Parameters of a Microsimulation Model for Breast Cancer Screening Using the Score Function Method," Annals of Operations Research, Springer, vol. 119(1), pages 43-61, March.
    2. Bruce A. Craig & Peter P. Sendi, 2002. "Estimation of the transition matrix of a discrete‐time Markov chain," Health Economics, John Wiley & Sons, Ltd., vol. 11(1), pages 33-42, January.
    3. Glen A. Satten & Ira M. Longini, 1996. "Markov Chains with Measurement Error: Estimating the ‘True’ Course of a Marker of the Progression of Human Immunodeficiency Virus Disease," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(3), pages 275-295, September.
    4. K. Cooper & S. Brailsford & R. Davies & J. Raftery, 2006. "A review of health care models for coronary heart disease interventions," Health Care Management Science, Springer, vol. 9(4), pages 311-324, November.
    5. K Cooper & S C Brailsford & R Davies, 2007. "Choice of modelling technique for evaluating health care interventions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(2), pages 168-176, February.
    6. Jonathan Karnon, 2003. "Alternative decision modelling techniques for the evaluation of health care technologies: Markov processes versus discrete event simulation," Health Economics, John Wiley & Sons, Ltd., vol. 12(10), pages 837-848, October.
    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. Fernando Alarid-Escudero & Eline Krijkamp & Eva A. Enns & Alan Yang & M. G. Myriam Hunink & Petros Pechlivanoglou & Hawre Jalal, 2023. "An Introductory Tutorial on Cohort State-Transition Models in R Using a Cost-Effectiveness Analysis Example," Medical Decision Making, , vol. 43(1), pages 3-20, January.

    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. K Cooper & R Davies & J Raftery & P Roderick, 2008. "Use of a coronary heart disease simulation model to evaluate the costs and effectiveness of drugs for the prevention of heart disease," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1173-1181, September.
    2. Olivier Ethgen & Baudouin Standaert, 2012. "Population–versus Cohort–Based Modelling Approaches," PharmacoEconomics, Springer, vol. 30(3), pages 171-181, March.
    3. K Cooper & S C Brailsford & R Davies, 2007. "Choice of modelling technique for evaluating health care interventions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(2), pages 168-176, February.
    4. Jesús Isaac Vázquez-Serrano & Rodrigo E. Peimbert-García & Leopoldo Eduardo Cárdenas-Barrón, 2021. "Discrete-Event Simulation Modeling in Healthcare: A Comprehensive Review," IJERPH, MDPI, vol. 18(22), pages 1-20, November.
    5. Lih-Wen Mau & Jaime M. Preussler & Linda J. Burns & Susan Leppke & Navneet S. Majhail & Christa L. Meyer & Tatenda Mupfudze & Wael Saber & Patricia Steinert & David J. Vanness, 2020. "Healthcare Costs of Treating Privately Insured Patients with Acute Myeloid Leukemia in the United States from 2004 to 2014: A Generalized Additive Modeling Approach," PharmacoEconomics, Springer, vol. 38(5), pages 515-526, May.
    6. Risha Gidwani & Louise B. Russell, 2020. "Estimating Transition Probabilities from Published Evidence: A Tutorial for Decision Modelers," PharmacoEconomics, Springer, vol. 38(11), pages 1153-1164, November.
    7. Vernon T. Farewell & Li Su & Christopher Jackson, 2019. "Partially hidden multi-state modelling of a prolonged disease state defined by a composite outcome," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(4), pages 696-711, October.
    8. Annemieke Leunis & W. Redekop & Kees van Montfort & Bob Löwenberg & Carin Uyl-de Groot, 2013. "The Development and Validation of a Decision-Analytic Model Representing the Full Disease Course of Acute Myeloid Leukemia," PharmacoEconomics, Springer, vol. 31(7), pages 605-621, July.
    9. repec:jss:jstsof:38:i08 is not listed on IDEAS
    10. Villacorta, Pablo J. & Verdegay, José L., 2016. "FuzzyStatProb: An R Package for the Estimation of Fuzzy Stationary Probabilities from a Sequence of Observations of an Unknown Markov Chain," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 71(i08).
    11. Topuz, Kazim & Urban, Timothy L. & Yildirim, Mehmet B., 2024. "A Markovian score model for evaluating provider performance for continuity of care—An explainable analytics approach," European Journal of Operational Research, Elsevier, vol. 317(2), pages 341-351.
    12. Hossein Haji Ali Afzali & Jonathan Karnon & Jodi Gray, 2012. "A proposed model for economic evaluations of major depressive disorder," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 13(4), pages 501-510, August.
    13. Mattias Ekman & Peter Lindgren & Carolin Miltenburger & Genevieve Meier & Julie Locklear & Mary Chatterton, 2012. "Cost Effectiveness of Quetiapine in Patients with Acute Bipolar Depression and in Maintenance Treatment after an Acute Depressive Episode," PharmacoEconomics, Springer, vol. 30(6), pages 513-530, June.
    14. Leslie Anne Campbell & John T. Blake & George Kephart & Eva Grunfeld & Donald MacIntosh, 2017. "Understanding the Effects of Competition for Constrained Colonoscopy Services with the Introduction of Population-level Colorectal Cancer Screening," Medical Decision Making, , vol. 37(2), pages 253-263, February.
    15. Paul S. Albert, 1999. "A Mover–Stayer Model for Longitudinal Marker Data," Biometrics, The International Biometric Society, vol. 55(4), pages 1252-1257, December.
    16. Paul Yip & Mehdi Soleymani & Kam Pui Wat & Edward Pinkney & Kwok Fai Lam, 2020. "Modeling Internal Movement of Children Born in Hong Kong to Nonlocal Mothers," IJERPH, MDPI, vol. 17(15), pages 1-12, July.
    17. Linda Möstel & Marius Pfeuffer & Matthias Fischer, 2020. "Statistical inference for Markov chains with applications to credit risk," Computational Statistics, Springer, vol. 35(4), pages 1659-1684, December.
    18. James A. Hall & Kika Konstantinou & Martyn Lewis & Raymond Oppong & Reuben Ogollah & Sue Jowett, 2019. "Systematic Review of Decision Analytic Modelling in Economic Evaluations of Low Back Pain and Sciatica," Applied Health Economics and Health Policy, Springer, vol. 17(4), pages 467-491, August.
    19. Barsotti, Flavia & De Castro, Yohann & Espinasse, Thibault & Rochet, Paul, 2014. "Estimating the transition matrix of a Markov chain observed at random times," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 98-105.
    20. An Tran-Duy & Annelies Boonen & Wietske Kievit & Piet Riel & Mart Laar & Johan Severens, 2014. "Modelling Outcomes of Complex Treatment Strategies Following a Clinical Guideline for Treatment Decisions in Patients with Rheumatoid Arthritis," PharmacoEconomics, Springer, vol. 32(10), pages 1015-1028, October.
    21. Beate Jahn & Christina Kurzthaler & Jagpreet Chhatwal & Elamin H. Elbasha & Annette Conrads-Frank & Ursula Rochau & Gaby Sroczynski & Christoph Urach & Marvin Bundo & Niki Popper & Uwe Siebert, 2019. "Alternative Conversion Methods for Transition Probabilities in State-Transition Models: Validity and Impact on Comparative Effectiveness and Cost-Effectiveness," Medical Decision Making, , vol. 39(5), pages 509-522, July.

    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:sae:medema:v:33:y:2013:i:6:p:767-779. 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: SAGE Publications (email available below). General contact details of provider: .

    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.