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Correlated destructive generalized power series cure rate models and associated inference with an application to a cutaneous melanoma data

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  • Borges, Patrick
  • Rodrigues, Josemar
  • Balakrishnan, Narayanaswamy

Abstract

In this paper, we propose a new cure rate survival model, which extends the model of Rodrigues et al. (2011) by incorporating a structure of dependence between the initiated cells. To create the structure of the correlation between the initiated cells, we use an extension of the generalized power series distribution by including an additional parameter ρ (the inflated-parameter generalized power series (IGPS) distribution, studied by Kolev and Minkova (2000)). It has a natural interpretation in terms of both a “zero-inflated” proportion and a correlation coefficient. In our approach, the number of initiated cells is assumed to follow the IGPS distribution. The IGPS distribution is a natural choice for modeling correlated count data that exhibit overdispersion. The primary advantage of this distributional assumption is that the correlation structure induced by the additional parameter ρ results in a natural characterization of the association between the initiated cells. Moreover, it provides a simple and realistic interpretation for the biological mechanism of the occurrence of the event of interest as it includes a process of destruction of tumor cells after an initial treatment or the capacity of an individual exposed to irradiation to repair initiated cells that result in cancer being induced. This means that what is recorded is only the undamaged portion of the original number of initiated cells not eliminated by the treatment or repaired by the repair system of an individual. Parameter estimation of the proposed model is then discussed through the maximum likelihood estimation procedure. Finally, we illustrate the usefulness of the proposed model by applying it to real cutaneous melanoma data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1703-1713
    DOI: 10.1016/j.csda.2011.10.013
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    References listed on IDEAS

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    1. Chen, Ming-Hui & Ibrahim, Joseph G. & Sinha, Debajyoti, 2002. "Bayesian Inference for Multivariate Survival Data with a Cure Fraction," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 101-126, January.
    2. Sudipto Banerjee & Bradley P. Carlin, 2004. "Parametric Spatial Cure Rate Models for Interval-Censored Time-to-Relapse Data," Biometrics, The International Biometric Society, vol. 60(1), pages 268-275, March.
    3. Rodrigues, Josemar & Cancho, Vicente G. & de Castro, Mrio & Louzada-Neto, Francisco, 2009. "On the unification of long-term survival models," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 753-759, March.
    4. Guosheng Yin & Joseph G. Ibrahim, 2005. "A General Class of Bayesian Survival Models with Zero and Nonzero Cure Fractions," Biometrics, The International Biometric Society, vol. 61(2), pages 403-412, June.
    5. 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.
    6. Cooner, Freda & Banerjee, Sudipto & Carlin, Bradley P. & Sinha, Debajyoti, 2007. "Flexible Cure Rate Modeling Under Latent Activation Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 560-572, June.
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    Cited by:

    1. 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.
    2. 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.
    3. Lívio Tito & Bourguignon Marcelo & Nascimento Fernando, 2020. "INAR(1) Processes with Inflated-parameter Generalized Power Series Innovations," Journal of Time Series Econometrics, De Gruyter, vol. 12(2), pages 1-27, July.
    4. Rasool Roozegar & Saralees Nadarajah & Eisa Mahmoudi, 2022. "The Power Series Exponential Power Series Distributions with Applications to Failure Data Sets," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 44-78, May.
    5. 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.
    6. Borges, Patrick & Rodrigues, Josemar & Balakrishnan, Narayanaswamy & Bazán, Jorge, 2014. "A COM–Poisson type generalization of the binomial distribution and its properties and applications," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 158-166.

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