IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v40y2025i1d10.1007_s00180-024-01480-7.html
   My bibliography  Save this article

Likelihood inference for unified transformation cure model with interval censored data

Author

Listed:
  • Jodi Treszoks

    (University of Texas at Arlington)

  • Suvra Pal

    (University of Texas at Arlington
    University of Texas at Arlington)

Abstract

In this paper, we extend the unified class of Box–Cox transformation (BCT) cure rate models to accommodate interval-censored data. The probability of cure is modeled using a general covariate structure, whereas the survival distribution of the uncured is modeled through a proportional hazards structure. We develop likelihood inference based on the expectation maximization (EM) algorithm for the BCT cure model. Within the EM framework, both simultaneous maximization and profile likelihood are addressed with respect to estimating the BCT transformation parameter. Through Monte Carlo simulations, we demonstrate the performance of the proposed estimation method through calculated bias, root mean square error, and coverage probability of the asymptotic confidence interval. Also considered is the efficacy of the proposed EM algorithm as compared to direct maximization of the observed log-likelihood function. Finally, data from a smoking cessation study is analyzed for illustrative purpose.

Suggested Citation

  • Jodi Treszoks & Suvra Pal, 2025. "Likelihood inference for unified transformation cure model with interval censored data," Computational Statistics, Springer, vol. 40(1), pages 125-151, January.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:1:d:10.1007_s00180-024-01480-7
    DOI: 10.1007/s00180-024-01480-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-024-01480-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-024-01480-7?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. Jiang, Cuiqing & Wang, Zhao & Zhao, Huimin, 2019. "A prediction-driven mixture cure model and its application in credit scoring," European Journal of Operational Research, Elsevier, vol. 277(1), pages 20-31.
    2. Katherine Davies & Suvra Pal & Joynob A. Siddiqua, 2021. "Stochastic EM algorithm for generalized exponential cure rate model and an empirical study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(12), pages 2112-2135, September.
    3. 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.
    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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. N. Balakrishnan & M. V. Koutras & F. S. Milienos & S. Pal, 2016. "Piecewise Linear Approximations for Cure Rate Models and Associated Inferential Issues," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 937-966, December.
    10. Suvra Pal & Hongbo Yu & Zachary D. Loucks & Ian M. Harris, 2020. "Illustration of the Flexibility of Generalized Gamma Distribution in Modeling Right Censored Survival Data: Analysis of Two Cancer Datasets," Annals of Data Science, Springer, vol. 7(1), pages 77-90, March.
    11. Guoqing Diao & Guosheng Yin, 2012. "A general transformation class of semiparametric cure rate frailty models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 959-989, October.
    12. 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.
    13. 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.
    14. 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.
    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. 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.
    4. 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.
    5. 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.
    6. Li-Hsiang Lin & Li-Shan Huang, 2024. "Promotion Time Cure Model with Local Polynomial Estimation," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 16(3), pages 824-853, December.
    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. 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. Xu, Yang & Zhao, Shishun & Hu, Tao & Sun, Jianguo, 2021. "Variable selection for generalized odds rate mixture cure models with interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    11. Gunnarsson, Björn Rafn & vanden Broucke, Seppe & Baesens, Bart & Óskarsdóttir, María & Lemahieu, Wilfried, 2021. "Deep learning for credit scoring: Do or don’t?," European Journal of Operational Research, Elsevier, vol. 295(1), pages 292-305.
    12. 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.
    13. 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.
    14. 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.
    15. Suvra Pal & Hongbo Yu & Zachary D. Loucks & Ian M. Harris, 2020. "Illustration of the Flexibility of Generalized Gamma Distribution in Modeling Right Censored Survival Data: Analysis of Two Cancer Datasets," Annals of Data Science, Springer, vol. 7(1), pages 77-90, March.
    16. Yuan Mengdie & Diao Guoqing, 2014. "Semiparametric Odds Rate Model for Modeling Short-Term and Long-Term Effects with Application to a Breast Cancer Genetic Study," The International Journal of Biostatistics, De Gruyter, vol. 10(2), pages 231-249, November.
    17. Liukai Wang & Fu Jia & Lujie Chen & Qifa Xu, 2023. "Forecasting SMEs’ credit risk in supply chain finance with a sampling strategy based on machine learning techniques," Annals of Operations Research, Springer, vol. 331(1), pages 1-33, December.
    18. Lai, Xin & Yau, Kelvin K.W., 2010. "Extending the long-term survivor mixture model with random effects for clustered survival data," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2103-2112, September.
    19. Silva, Diego M.B. & Pereira, Gustavo H.A. & Magalhães, Tiago M., 2022. "A class of categorization methods for credit scoring models," European Journal of Operational Research, Elsevier, vol. 296(1), pages 323-331.
    20. 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.

    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:spr:compst:v:40:y:2025:i:1:d:10.1007_s00180-024-01480-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.