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Non‐homogeneous Markov models in the analysis of survival after breast cancer

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  • Rafael Pérez‐Ocón
  • Juan Eloy Ruiz‐Castro
  • M. Luz Gámiz‐Pérez

Abstract

A cohort of 300 women with breast cancer who were submitted for surgery is analysed by using a non‐homogeneous Markov process. Three states are onsidered: no relapse, relapse and death. As relapse times change over time, we have extended previous approaches for a time homogeneous model to a non omogeneous multistate process. The trends of the hazard rate functions of transitions between states increase and then decrease, showing that a changepoint can be considered. Piecewise Weibull distributions are introduced as transition intensity functions. Covariates corresponding to treatments are incorporated in the model multiplicatively via these functions. The likelihood function is built for a general model with k changepoints and applied to the data set, the parameters are estimated and life‐table and transition probabilities for treatments in different periods of time are given. The survival probability functions for different treatments are plotted and compared with the corresponding function for the homogeneous model. The survival functions for the various cohorts submitted for treatment are fitted to the mpirical survival functions.

Suggested Citation

  • Rafael Pérez‐Ocón & Juan Eloy Ruiz‐Castro & M. Luz Gámiz‐Pérez, 2001. "Non‐homogeneous Markov models in the analysis of survival after breast cancer," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(1), pages 111-124.
    • Handle: RePEc:bla:jorssc:v:50:y:2001:i:1:p:111-124
    DOI: 10.1111/1467-9876.00223
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    Cited by:

    1. Gustavo Soutinho & Luís Meira-Machado, 2022. "Methods for checking the Markov condition in multi-state survival data," Computational Statistics, Springer, vol. 37(2), pages 751-780, April.
    2. Jeffrey Kharoufeh & Steven Cox & Mark Oxley, 2013. "Reliability of manufacturing equipment in complex environments," Annals of Operations Research, Springer, vol. 209(1), pages 231-254, October.
    3. Chen, Baojiang & Zhou, Xiao-Hua, 2013. "A correlated random effects model for non-homogeneous Markov processes with nonignorable missingness," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 1-13.
    4. R. A. Hubbard & L. Y. T. Inoue & J. R. Fann, 2008. "Modeling Nonhomogeneous Markov Processes via Time Transformation," Biometrics, The International Biometric Society, vol. 64(3), pages 843-850, September.

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