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

Juan Eloy Ruiz-Castro () and Mariangela Zenga ()
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Juan Eloy Ruiz-Castro: University of Granada
Mariangela Zenga: University of Milano-Bicocca

Statistical Methods & Applications, 2020, vol. 29, issue 4, No 7, 813-843

Abstract: 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.

Keywords: Survival; Breast cancer; Piecewise Markov model; Multi-state model (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10260-019-00505-6

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