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Survival and lifetime data analysis with a flexible class of distributions

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  • Francisco J. Rubio
  • Yili Hong

Abstract

We introduce a general class of continuous univariate distributions with positive support obtained by transforming the class of two-piece distributions. We show that this class of distributions is very flexible, easy to implement, and contains members that can capture different tail behaviours and shapes, producing also a variety of hazard functions. The proposed distributions represent a flexible alternative to the classical choices such as the log-normal, Gamma, and Weibull distributions. We investigate empirically the inferential properties of the proposed models through an extensive simulation study. We present some applications using real data in the contexts of time-to-event and accelerated failure time models. In the second kind of applications, we explore the use of these models in the estimation of the distribution of the individual remaining life.

Suggested Citation

  • Francisco J. Rubio & Yili Hong, 2016. "Survival and lifetime data analysis with a flexible class of distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(10), pages 1794-1813, August.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:10:p:1794-1813
    DOI: 10.1080/02664763.2015.1120710
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    References listed on IDEAS

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    1. Catalina A. Vallejos & Mark F. J. Steel, 2015. "Objective Bayesian Survival Analysis Using Shape Mixtures of Log-Normal Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 697-710, June.
    2. M. C. Jones & Arthur Pewsey, 2009. "Sinh-arcsinh distributions," Biometrika, Biometrika Trust, vol. 96(4), pages 761-780.
    3. Zhezhen Jin, 2003. "Rank-based inference for the accelerated failure time model," Biometrika, Biometrika Trust, vol. 90(2), pages 341-353, June.
    4. Adelchi Azzalini & Marc G. Genton, 2008. "Robust Likelihood Methods Based on the Skew‐t and Related Distributions," International Statistical Review, International Statistical Institute, vol. 76(1), pages 106-129, April.
    5. Komarek, Arnost & Lesaffre, Emmanuel, 2008. "Bayesian Accelerated Failure Time Model With Multivariate Doubly Interval-Censored Data and Flexible Distributional Assumptions," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 523-533, June.
    6. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2006. "A Constructive Representation of Univariate Skewed Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 823-829, June.
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    Cited by:

    1. Naijun Sha, 2019. "A New Inference Approach for Type-II Generalized Birnbaum-Saunders Distribution," Stats, MDPI, vol. 2(1), pages 1-16, February.
    2. Worku Biyadgie Ewnetu & Irène Gijbels & Anneleen Verhasselt, 2024. "Two-piece distribution based semi-parametric quantile regression for right censored data," Statistical Papers, Springer, vol. 65(5), pages 2775-2810, July.
    3. Francisco J. Rubio & Keming Yu, 2017. "Flexible objective Bayesian linear regression with applications in survival analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 798-810, April.
    4. Worku B. Ewnetu & Irène Gijbels & Anneleen Verhasselt, 2023. "Flexible two-piece distributions for right censored survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 34-65, January.

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