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A Modified Cure Rate Model Based on a Piecewise Distribution with Application to Lobular Carcinoma Data

Author

Listed:
  • Yolanda M. Gómez

    (Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile)

  • John L. Santibañez

    (Departamento de Matemática, Universidad de Atacama, Copiapó 7500015, Chile)

  • Vinicius F. Calsavara

    (Cedars-Sinai Medical Center, 8700 Beverly Boulevard, Los Angeles, CA 90048, USA)

  • Héctor W. Gómez

    (Departamento de Estadística y Ciencia de Datos, Universidad de Antofagasta, Antofagasta 1240000, Chile)

  • Diego I. Gallardo

    (Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile)

Abstract

A novel cure rate model is introduced by considering, for the number of concurrent causes, the modified power series distribution and, for the time to event, the recently proposed power piecewise exponential distribution. This model includes a wide variety of cure rate models, such as binomial, Poisson, negative binomial, Haight, Borel, logarithmic, and restricted generalized Poisson. Some characteristics of the model are examined, and the estimation of parameters is performed using the Expectation–Maximization algorithm. A simulation study is presented to evaluate the performance of the estimators in finite samples. Finally, an application in a real medical dataset from a population-based study of incident cases of lobular carcinoma diagnosed in the state of São Paulo, Brazil, illustrates the advantages of the proposed model compared to other common cure rate models in the literature, particularly regarding the underestimation of the cure rate in other proposals and the improved precision in estimating the cure rate of our proposal.

Suggested Citation

  • Yolanda M. Gómez & John L. Santibañez & Vinicius F. Calsavara & Héctor W. Gómez & Diego I. Gallardo, 2024. "A Modified Cure Rate Model Based on a Piecewise Distribution with Application to Lobular Carcinoma Data," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:883-:d:1358568
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    References listed on IDEAS

    as
    1. 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.
    2. N. Balakrishnan & M. V. Koutras & F. S. Milienos, 2018. "A weighted Poisson distribution and its application to cure rate models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(17), pages 4297-4310, September.
    3. Mário Castro & Yolanda M. Gómez, 2020. "A Bayesian Cure Rate Model Based on the Power Piecewise Exponential Distribution," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 677-692, June.
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