IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i4p363-d497534.html
   My bibliography  Save this article

A Longitudinal Study of the Bladder Cancer Applying a State-Space Model with Non-Exponential Staying Time in States

Author

Listed:
  • Delia Montoro-Cazorla

    (Department of Statistics and Operational Research, University of Jaén, 23071 Jaén, Spain)

  • Rafael Pérez-Ocón

    (Department of Statistics and Operational Research, University of Granada, 18071 Granada, Spain)

  • Alicia Pereira das Neves-Yedig

    (Department of Statistics and Operational Research, University of Granada, 18071 Granada, Spain)

Abstract

A longitudinal study for 847 bladder cancer patients for a period of fifteen years is presented. After the first surgery, the patients undergo successive ones (recurrences). A state-model is selected for analyzing the evolution of the cancer, based on the distribution of the times between recurrences. These times do not follow exponential distributions, and are approximated by phase-type distributions. Under these conditions, a multidimensional Markov process governs the evolution of the disease. The survival probability and mean times in the different states (levels) of the disease are calculated empirically and also by applying the Markov model, the comparison of the results indicate that the model is well-fitted to the data to an acceptable significance level of 0.05. Two sub-cohorts are well-differenced: those reaching progression (the bladder is removed) and those that do not. These two cases are separately studied and performance measures calculated, and the comparison reveals details about the characteristics of the patients in these groups.

Suggested Citation

  • Delia Montoro-Cazorla & Rafael Pérez-Ocón & Alicia Pereira das Neves-Yedig, 2021. "A Longitudinal Study of the Bladder Cancer Applying a State-Space Model with Non-Exponential Staying Time in States," Mathematics, MDPI, vol. 9(4), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:363-:d:497534
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/4/363/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/4/363/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xikui Wang & Jeffrey S. Pai & Kevin J. Shand, 2007. "A semi‐Markov model of disease recurrence in insured dogs," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(5), pages 429-437, September.
    2. Søren Asmussen, 2000. "Matrix‐analytic Models and their Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 193-226, June.
    3. Nikolaos Limnios, 2012. "Reliability Measures of Semi-Markov Systems with General State Space," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 895-917, December.
    Full references (including those not matched with items on IDEAS)

    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. María Luz Gámiz & Nikolaos Limnios & Mari Carmen Segovia-García, 2023. "The continuous-time hidden Markov model based on discretization. Properties of estimators and applications," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 525-550, October.
    2. Yonit Barron, 2018. "Group maintenance policies for an R-out-of-N system with phase-type distribution," Annals of Operations Research, Springer, vol. 261(1), pages 79-105, February.
    3. Mathieu Bargès & Hélène Cossette & Etienne Marceau, 2009. "TVaR-based capital allocation with copulas," Working Papers hal-00431265, HAL.
    4. Lirong Cui & Quan Zhang & Dejing Kong, 2016. "Some New Concepts and Their Computational Formulae in Aggregated Stochastic Processes with Classifications Based on Sojourn Times," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 999-1019, December.
    5. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2014. "A reliability system under different types of shock governed by a Markovian arrival process and maintenance policy K," European Journal of Operational Research, Elsevier, vol. 235(3), pages 636-642.
    6. Albrecher, Hansjorg & Boxma, Onno J., 2004. "A ruin model with dependence between claim sizes and claim intervals," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 245-254, October.
    7. Yonit Barron & Chananel Benshimol, 2024. "Emergency Supply Alternatives for a Storage Facility of a Repairable Multi-Component System," Mathematics, MDPI, vol. 12(17), pages 1-33, August.
    8. Yi, He & Cui, Lirong, 2017. "Distribution and availability for aggregated second-order semi-Markov ternary system with working time omission," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 50-60.
    9. Alexander Herbertsson, 2011. "Modelling default contagion using multivariate phase-type distributions," Review of Derivatives Research, Springer, vol. 14(1), pages 1-36, April.
    10. Yi, He & Cui, Lirong & Shen, Jingyuan & Li, Yan, 2018. "Stochastic properties and reliability measures of discrete-time semi-Markovian systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 162-173.
    11. N. C. Caballé & I. T. Castro, 2019. "Assessment of the maintenance cost and analysis of availability measures in a finite life cycle for a system subject to competing failures," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 255-290, March.
    12. He Yi & Lirong Cui & Narayanaswamy Balakrishnan & Jingyuan Shen, 2022. "Multi-Point and Multi-Interval Bounded-Covering Availability Measures for Aggregated Markovian Repairable Systems," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2427-2453, December.
    13. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2011. "Two shock and wear systems under repair standing a finite number of shocks," European Journal of Operational Research, Elsevier, vol. 214(2), pages 298-307, October.
    14. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2014. "Matrix stochastic analysis of the maintainability of a machine under shocks," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 11-17.
    15. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2016. "A warmstandby system under shocks and repair governed by MAPs," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 331-338.
    16. Brenda Garcia-Maya & Nikolaos Limnios & Bo Henry Lindqvist, 2022. "Competing Risks Modeling by Extended Phase-Type Semi-Markov Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 309-319, March.
    17. Herbertsson, Alexander, 2007. "Modelling Default Contagion Using Multivariate Phase-Type Distributions," Working Papers in Economics 271, University of Gothenburg, Department of Economics.
    18. Lijun Shang & Baoliang Liu & Kaiye Gao & Li Yang, 2023. "Random Warranty and Replacement Models Customizing from the Perspective of Heterogeneity," Mathematics, MDPI, vol. 11(15), pages 1-22, July.
    19. Guglielmo D'Amico, 2016. "Generalized semi-Markovian dividend discount model: risk and return," Papers 1605.02472, arXiv.org.
    20. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.

    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:gam:jmathe:v:9:y:2021:i:4:p:363-:d:497534. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.