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A computational method for estimating a change point in the Cox hazard model

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Abstract

The hazard function describes the instantaneous rate of failure at a time t, given that the individual survives up to the instant t. The effect of the covariates produces a variation in the hazard function, hence a change point might occur. When dealing with survival analysis, it is of interest to identify where a change point has occurred. This paper proposes a new method for estimating the change point in the Cox proportional hazard model, which is based on maximum likelihood estimation combined with moments estimation (ME) and a numerical mehtod to minimize an objective function given by ME. The mean square error of the estimator is obtained by Monte Carlo simulation, considering different scenarios. For the purpose of studying the behavior of the proposed estimator in terms of its mean square error, a comparative study against a known method to estimate the change point is included. A real data application is also included.

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Acknowledgements

The authors wish to express their sincere thanks to all reviewers of the original manuscript for their comments and suggestions, which helped to improve considerably the presentation of this manuscript. The authors also thank E. González-Estrada for her support in programming.

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Authors and Affiliations

  1. Departamento de Estadística, Colegio de Postgraduados, Carretera México – Texcoco, Km. 36.5 Montecillo, C.P. 56230, Texcoco, Estado de México, Mexico

    G. Y. Arenas & J. A. Villaseñor

  2. Área de Matemáticas, Universidad Autónoma de Chapingo, Carretera México – Texcoco, Km. 38.5, C.P. 56230, Texcoco, Estado de México, Mexico

    O. Palmeros

  3. Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Avenida San Claudio y 18 Sur, Colonia San Manuel, Edificio FM1-101B, Ciudad Universitaria, C.P. 72570, Puebla, Mexico

    F. Tajonar

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  1. G. Y. Arenas
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  2. J. A. Villaseñor
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  3. O. Palmeros
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  4. F. Tajonar
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Correspondence to J. A. Villaseñor.

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Arenas, G.Y., Villaseñor, J.A., Palmeros, O. et al. A computational method for estimating a change point in the Cox hazard model. Comput Stat 36, 2491–2506 (2021). https://doi.org/10.1007/s00180-021-01087-2

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  • DOI: https://doi.org/10.1007/s00180-021-01087-2

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