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A New Cure Rate Model Based on Flory–Schulz Distribution: Application to the Cancer Data

Author

Listed:
  • Reza Azimi

    (Department of Statistics And Computer Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran)

  • Mahdy Esmailian

    (Department of Statistics And Computer Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran)

  • Diego I. Gallardo

    (Departamento de Matematica, Facultad de Ingenieria, Universidad de Atacama, Copiapo 1530000, Chile)

  • Héctor J. Gómez

    (Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile)

Abstract

In this article a new flexible survival cure rate model is introduced by assuming that the number of competing causes of the event of interest follows the Flory–Schulz distribution and the competing causes follow the generalized truncated Nadarajah–Haghighi distribution. Parameter estimation for the proposed model is derived based on the maximum likelihood estimation method. A simulation study is performed to show the performance of the ML estimators. We discuss three real data applications related to real cancer data sets to assess the usefulness of the proposed model compared with some existing cure rate models for the sake of comparison.

Suggested Citation

  • Reza Azimi & Mahdy Esmailian & Diego I. Gallardo & Héctor J. Gómez, 2022. "A New Cure Rate Model Based on Flory–Schulz Distribution: Application to the Cancer Data," Mathematics, MDPI, vol. 10(24), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4643-:d:996950
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    References listed on IDEAS

    as
    1. Vicente Cancho & Josemar Rodrigues & Mario de Castro, 2011. "A flexible model for survival data with a cure rate: a Bayesian approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(1), pages 57-70.
    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. 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.
    4. 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.
    5. 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.
    6. Tsodikov A.D. & Ibrahim J.G. & Yakovlev A.Y., 2003. "Estimating Cure Rates From Survival Data: An Alternative to Two-Component Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1063-1078, January.
    7. Hanin, Leonid & Huang, Li-Shan, 2014. "Identifiability of cure models revisited," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 261-274.
    8. Durga H. Kutal & Lianfen Qian, 2018. "A Non-Mixture Cure Model for Right-Censored Data with Fréchet Distribution," Stats, MDPI, vol. 1(1), pages 1-13, November.
    9. 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.
    10. Joseph G. Ibrahim & Ming-Hui Chen & Debajyoti Sinha, 2001. "Bayesian Semiparametric Models for Survival Data with a Cure Fraction," Biometrics, The International Biometric Society, vol. 57(2), pages 383-388, June.
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