A general piecewise multi-state survival model: Application to breast cancer
Identificadores
URI: http://hdl.handle.net/10481/69357Metadatos
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Springer
Materia
Survival Breast Cancer Piecewise Markov model Multi-state model
Date
2019-12-17Referencia bibliográfica
Ruiz-Castro, J.E., Zenga, M. A general piecewise multi-state survival model: application to breast cancer. Stat Methods Appl 29, 813–843 (2020). https://doi.org/10.1007/s10260-019-00505-6
Patrocinador
Ministerio de Economía y Competitividad FQM-307; European Regional Development Fund (ERDF) MTM2017-88708-P; University of Milano-Bicocca 2014-ATE-0228Résumé
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.