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An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data

Author

Listed:
  • Diego I. Gallardo

    (Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile)

  • Mário de Castro

    (Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos 13560-095, Brazil)

  • Héctor W. Gómez

    (Departamento de Matemática, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile)

Abstract

A cure rate model under the competing risks setup is proposed. For the number of competing causes related to the occurrence of the event of interest, we posit the one-parameter Bell distribution, which accommodates overdispersed counts. The model is parameterized in the cure rate, which is linked to covariates. Parameter estimation is based on the maximum likelihood method. Estimates are computed via the EM algorithm. In order to compare different models, a selection criterion for non-nested models is implemented. Results from simulation studies indicate that the estimation method and the model selection criterion have a good performance. A dataset on melanoma is analyzed using the proposed model as well as some models from the literature.

Suggested Citation

  • Diego I. Gallardo & Mário de Castro & Héctor W. Gómez, 2021. "An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1815-:d:605828
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    References listed on IDEAS

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    1. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    2. Vicente G. Cancho & Márcia A. C. Macera & Adriano K. Suzuki & Francisco Louzada & Katherine E. C. Zavaleta, 2020. "A new long-term survival model with dispersion induced by discrete frailty," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 221-244, April.
    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. 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.
    5. Scheike, Thomas H. & Zhang, Mei-Jie, 2011. "Analyzing Competing Risk Data Using the R timereg Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 38(i02).
    Full references (including those not matched with items on IDEAS)

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