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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
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    References listed on IDEAS

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    1. 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.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
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