IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i3p518-d1039850.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/3/518/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/3/518/
    Download Restriction: no
    ---><---

    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. 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.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Suvra Pal & Yingwei Peng & Wisdom Aselisewine, 2024. "A new approach to modeling the cure rate in the presence of interval censored data," Computational Statistics, Springer, vol. 39(5), pages 2743-2769, July.
    2. Suvra Pal & Souvik Roy, 2021. "On the estimation of destructive cure rate model: A new study with exponentially weighted Poisson competing risks," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 324-342, August.
    3. Neveka M. Olmos & Emilio Gómez-Déniz & Osvaldo Venegas, 2022. "The Heavy-Tailed Gleser Model: Properties, Estimation, and Applications," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    4. Héctor J. Gómez & Karol I. Santoro & Inmaculada Barranco-Chamorro & Osvaldo Venegas & Diego I. Gallardo & Héctor W. Gómez, 2023. "A Family of Truncated Positive Distributions," Mathematics, MDPI, vol. 11(21), pages 1-15, October.
    5. Talha Arslan, 2021. "An α -Monotone Generalized Log-Moyal Distribution with Applications to Environmental Data," Mathematics, MDPI, vol. 9(12), pages 1-18, June.
    6. Jimmy Reyes & Yuri A. Iriarte & Pedro Jodrá & Héctor W. Gómez, 2019. "The Slash Lindley-Weibull Distribution," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 235-251, March.
    7. Rocha, Ricardo & Nadarajah, Saralees & Tomazella, Vera & Louzada, Francisco, 2017. "A new class of defective models based on the Marshall–Olkin family of distributions for cure rate modeling," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 48-63.
    8. Suvra Pal & Jacob Majakwara & N. Balakrishnan, 2018. "An EM algorithm for the destructive COM-Poisson regression cure rate model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(2), pages 143-171, February.
    9. Emura, Takeshi & Shiu, Shau-Kai, 2014. "Estimation and model selection for left-truncated and right-censored lifetime data with application to electric power transformers analysis," MPRA Paper 57528, University Library of Munich, Germany.
    10. Neveka Olmos & Héctor Varela & Heleno Bolfarine & Héctor Gómez, 2014. "An extension of the generalized half-normal distribution," Statistical Papers, Springer, vol. 55(4), pages 967-981, November.
    11. Sellers, Kimberly F. & Morris, Darcy Steeg & Balakrishnan, Narayanaswamy, 2016. "Bivariate Conway–Maxwell–Poisson distribution: Formulation, properties, and inference," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 152-168.
    12. Kimberly F. Sellers & Tong Li & Yixuan Wu & Narayanaswamy Balakrishnan, 2021. "A Flexible Multivariate Distribution for Correlated Count Data," Stats, MDPI, vol. 4(2), pages 1-19, April.
    13. Juan M. Astorga & Jimmy Reyes & Karol I. Santoro & Osvaldo Venegas & Héctor W. Gómez, 2020. "A Reliability Model Based on the Incomplete Generalized Integro-Exponential Function," Mathematics, MDPI, vol. 8(9), pages 1-12, September.
    14. Gómez, Yolanda M. & Bolfarine, Heleno & Gómez, Héctor W., 2019. "Gumbel distribution with heavy tails and applications to environmental data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 115-129.
    15. Leonardo Barrios & Yolanda M. Gómez & Osvaldo Venegas & Inmaculada Barranco-Chamorro & Héctor W. Gómez, 2022. "The Slashed Power Half-Normal Distribution with Applications," Mathematics, MDPI, vol. 10(9), pages 1-21, May.
    16. Neveka M. Olmos & Emilio Gómez-Déniz & Osvaldo Venegas & Héctor W. Gómez, 2024. "A Composite Half-Normal-Pareto Distribution with Applications to Income and Expenditure Data," Mathematics, MDPI, vol. 12(11), pages 1-17, May.
    17. Pal, Suvra & Balakrishnan, N., 2016. "Destructive negative binomial cure rate model and EM-based likelihood inference under Weibull lifetime," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 9-20.
    18. Mastrantonio, Gianluca, 2018. "The joint projected normal and skew-normal: A distribution for poly-cylindrical data," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 14-26.
    19. Karol I. Santoro & Diego I. Gallardo & Osvaldo Venegas & Isaac E. Cortés & Héctor W. Gómez, 2023. "A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical Data," Mathematics, MDPI, vol. 11(22), pages 1-15, November.
    20. Cleanderson R. Fidelis & Edwin M. M. Ortega & Gauss M. Cordeiro, 2024. "Residual Analysis for Poisson-Exponentiated Weibull Regression Models with Cure Fraction," Stats, MDPI, vol. 7(2), pages 1-16, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:518-:d:1039850. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.