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The Slash Half-Normal Distribution Applied to a Cure Rate Model with Application to Bone Marrow Transplantation

Author

Listed:
  • Diego I. Gallardo

    (Mathematics Department, Faculty of Engineering, University of Atacama, Copiapó 1530000, Chile)

  • Yolanda M. Gómez

    (Mathematics Department, Faculty of Engineering, University of Atacama, Copiapó 1530000, Chile
    Medicine Department, Faculty of Medicine, University of Atacama, Copiapó 1530000, Chile)

  • Héctor J. Gómez

    (Department of Mathematical and Physical Sciences, Faculty of Engineering, Catholic University of Temuco, Temuco 4780000, Chile)

  • María José Gallardo-Nelson

    (Medicine Department, Faculty of Medicine, University of Atacama, Copiapó 1530000, Chile)

  • Marcelo Bourguignon

    (Statistics Department, Federal University of Rio Grande do Norte, Natal 59078-970, Brazil)

Abstract

This paper proposes, for the first time, the use of an asymmetric positive and heavy-tailed distribution in a cure rate model context. In particular, it introduces a cure-rate survival model by assuming that the time-to-event of interest follows a slash half-normal distribution and that the number of competing causes of the event of interest follows a power series distribution, which defines six new cure rate models. Several properties of the model are derived and an alternative expression for the cumulative distribution function of the model is presented, which is very useful for the computational implementation of the model. A procedure based on the expectation–maximization algorithm is proposed for the parameter estimation. Two simulation studies are performed to assess some properties of the estimators, showing the good performance of the proposed estimators in finite samples. Finally, an application to a bone marrow transplant data set is presented.

Suggested Citation

  • Diego I. Gallardo & Yolanda M. Gómez & Héctor J. Gómez & María José Gallardo-Nelson & Marcelo Bourguignon, 2023. "The Slash Half-Normal Distribution Applied to a Cure Rate Model with Application to Bone Marrow Transplantation," Mathematics, MDPI, vol. 11(3), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:518-:d:1039850
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    References listed on IDEAS

    as
    1. Balakrishnan, N. & Pal, Suvra, 2013. "Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM-Poisson family," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 41-67.
    2. Neveka Olmos & Héctor Varela & Héctor Gómez & Heleno Bolfarine, 2012. "An extension of the half-normal distribution," Statistical Papers, Springer, vol. 53(4), pages 875-886, November.
    3. Piyachart Wiangnak & Suvra Pal, 2018. "Gamma lifetimes and associated inference for interval-censored cure rate model with COM–Poisson competing cause," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(6), pages 1491-1509, March.
    4. N. Balakrishnan & Suvra Pal, 2015. "Likelihood Inference for Flexible Cure Rate Models with Gamma Lifetimes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(19), pages 4007-4048, October.
    Full references (including those not matched with items on IDEAS)

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