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A general piecewise multi-state survival model: application to breast cancer

Author

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  • Juan Eloy Ruiz-Castro

    (University of Granada)

  • Mariangela Zenga

    (University of Milano-Bicocca)

Abstract

Multi-state models are considered in the field of survival analysis for modelling illnesses that evolve through several stages over time. Multi-state models can be developed by applying several techniques, such as non-parametric, semi-parametric and stochastic processes, particularly Markov processes. When the development of an illness is being analysed, its progression is tracked periodically. Medical reviews take place at discrete times, and a panel data analysis can be formed. In this paper, a discrete-time piecewise non-homogeneous Markov process is constructed for modelling and analysing a multi-state illness with a general number of states. The model is built, and relevant measures, such as survival function, transition probabilities, mean total times spent in a group of states and the conditional probability of state change, are determined. A likelihood function is built to estimate the parameters and the general number of cut-points included in the model. Time-dependent covariates are introduced, the results are obtained in a matrix algebraic form and the algorithms are shown. The model is applied to analyse the behaviour of breast cancer. A study of the relapse and survival times of 300 breast cancer patients who have undergone mastectomy is developed. The results of this paper are implemented computationally with MATLAB and R.

Suggested Citation

  • Juan Eloy Ruiz-Castro & Mariangela Zenga, 2020. "A general piecewise multi-state survival model: application to breast cancer," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 813-843, December.
    • Handle: RePEc:spr:stmapp:v:29:y:2020:i:4:d:10.1007_s10260-019-00505-6
    DOI: 10.1007/s10260-019-00505-6
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    References listed on IDEAS

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    1. Jackson, Christopher, 2011. "Multi-State Models for Panel Data: The msm Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 38(i08).
    2. Bacchetti Peter & Boylan Ross D & Terrault Norah A & Monto Alexander & Berenguer Marina, 2010. "Non-Markov Multistate Modeling Using Time-Varying Covariates, with Application to Progression of Liver Fibrosis due to Hepatitis C Following Liver Transplant," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-16, February.
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