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An EM algorithm for the destructive COM-Poisson regression cure rate model

Author

Listed:
  • Suvra Pal

    (University of Texas at Arlington
    University of the Witwatersrand)

  • Jacob Majakwara

    (University of the Witwatersrand)

  • N. Balakrishnan

    (McMaster University)

Abstract

In this paper, we consider a competitive scenario and assume the initial number of competing causes to undergo a destruction after an initial treatment. This brings in a more realistic and practical interpretation of the biological mechanism of the occurrence of tumor since what is recorded is only from the undamaged portion of the original number of competing causes. Instead of assuming any particular distribution for the competing cause, we assume the competing cause to follow a Conway–Maxwell Poisson distribution which brings in flexibility as it can handle both over-dispersion and under-dispersion that we usually encounter in count data. Under this setup and assuming a Weibull distribution to model the time-to-event, we develop the expectation maximization algorithm for such a flexible destructive cure rate model. An extensive simulation study is carried out to demonstrate the performance of the proposed estimation method. Finally, a melanoma data is analyzed for illustrative purpose.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:2:d:10.1007_s00184-017-0638-8
    DOI: 10.1007/s00184-017-0638-8
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    References listed on IDEAS

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    1. Peng, Yingwei & Zhang, Jiajia, 2008. "Identifiability of a mixture cure frailty model," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2604-2608, November.
    2. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
    3. Wenbin Lu, 2004. "On semiparametric transformation cure models," Biometrika, Biometrika Trust, vol. 91(2), pages 331-343, June.
    4. N. Balakrishnan & Suvra Pal, 2015. "An EM algorithm for the estimation of parameters of a flexible cure rate model with generalized gamma lifetime and model discrimination using likelihood- and information-based methods," Computational Statistics, Springer, vol. 30(1), pages 151-189, March.
    5. Vicente Cancho & Mário Castro & Josemar Rodrigues, 2012. "A Bayesian analysis of the Conway–Maxwell–Poisson cure rate model," Statistical Papers, Springer, vol. 53(1), pages 165-176, February.
    6. 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.
    7. Borges, Patrick & Rodrigues, Josemar & Balakrishnan, Narayanaswamy, 2012. "Correlated destructive generalized power series cure rate models and associated inference with an application to a cutaneous melanoma data," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1703-1713.
    8. Li, Chin-Shang & Taylor, Jeremy M. G. & Sy, Judy P., 2001. "Identifiability of cure models," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 389-395, October.
    9. 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.
    10. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
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    Cited by:

    1. 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.

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