IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i6p1703-1713.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311003707
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2011.10.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    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. Yu, Binbing & Peng, Yingwei, 2008. "Mixture cure models for multivariate survival data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1524-1532, January.
    2. Yolanda M. Gómez & Diego I. Gallardo & Marcelo Bourguignon & Eduardo Bertolli & Vinicius F. Calsavara, 2023. "A general class of promotion time cure rate models with a new biological interpretation," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 66-86, January.
    3. Diego I. Gallardo & Heleno Bolfarine & Atonio Carlos Pedroso-de-Lima, 2017. "A clustering cure rate model with application to a sealant study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 2949-2962, December.
    4. Vicente G. Cancho & Dipak K. Dey & Francisco Louzada, 2016. "Unified multivariate survival model with a surviving fraction: an application to a Brazilian customer churn data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(3), pages 572-584, March.
    5. Carvalho Lopes, Celia Mendes & Bolfarine, Heleno, 2012. "Random effects in promotion time cure rate models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 75-87, January.
    6. Suvra Pal & N. Balakrishnan, 2017. "Likelihood inference for the destructive exponentially weighted Poisson cure rate model with Weibull lifetime and an application to melanoma data," Computational Statistics, Springer, vol. 32(2), pages 429-449, June.
    7. Chen, Chyong-Mei & Lu, Tai-Fang C., 2012. "Marginal analysis of multivariate failure time data with a surviving fraction based on semiparametric transformation cure models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 645-655.
    8. Vicente G. Cancho & Márcia A. C. Macera & Adriano K. Suzuki & Francisco Louzada & Katherine E. C. Zavaleta, 2020. "A new long-term survival model with dispersion induced by discrete frailty," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 221-244, April.
    9. Amanda D’Andrea & Ricardo Rocha & Vera Tomazella & Francisco Louzada, 2018. "Negative Binomial Kumaraswamy-G Cure Rate Regression Model," JRFM, MDPI, vol. 11(1), pages 1-14, January.
    10. Hu, Tao & Xiang, Liming, 2016. "Partially linear transformation cure models for interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 257-269.
    11. 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.
    12. Xiaoguang Wang & Ziwen Wang, 2021. "EM algorithm for the additive risk mixture cure model with interval-censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 91-130, January.
    13. Bao Yiqi & Cibele Maria Russo & Vicente G. Cancho & Francisco Louzada, 2016. "Influence diagnostics for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(6), pages 1027-1060, May.
    14. Janette Larney & James Samuel Allison & Gerrit Lodewicus Grobler & Marius Smuts, 2023. "Modelling the Time to Write-Off of Non-Performing Loans Using a Promotion Time Cure Model with Parametric Frailty," Mathematics, MDPI, vol. 11(10), pages 1-17, May.
    15. Hu, Tao & Xiang, Liming, 2013. "Efficient estimation for semiparametric cure models with interval-censored data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 139-151.
    16. Shuangge Ma, 2011. "Additive risk model for current status data with a cured subgroup," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 117-134, February.
    17. Lu Wang & Pang Du & Hua Liang, 2012. "Two-Component Mixture Cure Rate Model with Spline Estimated Nonparametric Components," Biometrics, The International Biometric Society, vol. 68(3), pages 726-735, September.
    18. Francisco Louzada & M�rio de Castro & Vera Tomazella & Jhon F.B. Gonzales, 2014. "Modeling categorical covariates for lifetime data in the presence of cure fraction by Bayesian partition structures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(3), pages 622-634, March.
    19. Olayidé Boussari & Laurent Bordes & Gaëlle Romain & Marc Colonna & Nadine Bossard & Laurent Remontet & Valérie Jooste, 2021. "Modeling excess hazard with time‐to‐cure as a parameter," Biometrics, The International Biometric Society, vol. 77(4), pages 1289-1302, December.
    20. 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.

    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:eee:csdana:v:56:y:2012:i:6:p:1703-1713. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.