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Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM-Poisson family

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  • Balakrishnan, N.
  • Pal, Suvra

Abstract

Recently, a new cure rate survival model has been proposed by considering the Conway–Maxwell Poisson distribution as the distribution of the competing cause variable. This model includes some of the well-known cure rate models discussed in the literature as special cases. Cancer clinical trials often lead to right censored data and so the EM algorithm can be used as an efficient tool for the estimation of the model parameters based on right censored data. By considering this Conway–Maxwell Poisson-based cure rate model and by assuming the lognormal distribution for the time-to-event variable, the steps of the EM algorithm are developed here for the estimation of the parameters of different cure rate survival models. The standard errors of the MLEs are obtained by inverting the observed information matrix. An extensive Monte Carlo simulation study is performed to illustrate the method of inference developed. Model discrimination between different cure rate models is addressed by the likelihood ratio test as well as by Akaike and Bayesian information criteria. Finally, the proposed methodology is illustrated with a real data on cutaneous melanoma.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:67:y:2013:i:c:p:41-67
    DOI: 10.1016/j.csda.2013.04.018
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    1. Sellers, Kimberly F. & Morris, Darcy Steeg & Balakrishnan, Narayanaswamy, 2016. "Bivariate Conway–Maxwell–Poisson distribution: Formulation, properties, and inference," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 152-168.
    2. 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.
    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 & 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.
    5. 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.
    6. Kimberly F. Sellers & Tong Li & Yixuan Wu & Narayanaswamy Balakrishnan, 2021. "A Flexible Multivariate Distribution for Correlated Count Data," Stats, MDPI, vol. 4(2), pages 1-19, April.
    7. Emura, Takeshi & Shiu, Shau-Kai, 2014. "Estimation and model selection for left-truncated and right-censored lifetime data with application to electric power transformers analysis," MPRA Paper 57528, University Library of Munich, Germany.
    8. 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.
    9. Man-Ho Ling & Narayanaswamy Balakrishnan & Chenxi Yu & Hon Yiu So, 2021. "Inference for One-Shot Devices with Dependent k -Out-of- M Structured Components under Gamma Frailty," Mathematics, MDPI, vol. 9(23), pages 1-24, November.
    10. Cleanderson R. Fidelis & Edwin M. M. Ortega & Gauss M. Cordeiro, 2024. "Residual Analysis for Poisson-Exponentiated Weibull Regression Models with Cure Fraction," Stats, MDPI, vol. 7(2), pages 1-16, May.
    11. 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.
    12. 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.

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