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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
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    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.
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