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A Bayesian Cure Rate Model Based on the Power Piecewise Exponential Distribution

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  • Mário Castro

    (Universidade de São Paulo)

  • Yolanda M. Gómez

    (Universidad de Atacama)

Abstract

Cure rate models have been used in a number of fields. These models are applied to analyze survival data when the population has a proportion of subjects insusceptible to the event of interest. In this paper, we propose a new cure rate survival model formulated under a competing risks setup. The number of competing causes follows the negative binomial distribution, while for the latent times we posit the power piecewise exponential distribution. Samples from the posterior distribution are drawn through MCMC methods. Some properties of the estimators are assessed in a simulation study. A dataset on cutaneous melanoma is analyzed using the proposed model as well as some existing models for the sake of comparison.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:2:d:10.1007_s11009-019-09728-2
    DOI: 10.1007/s11009-019-09728-2
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    References listed on IDEAS

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    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. Debajyoti Sinha & Ming-Hui Chen & Sujit K. Ghosh, 1999. "Bayesian Analysis and Model Selection for Interval-Censored Survival Data," Biometrics, The International Biometric Society, vol. 55(2), pages 585-590, June.
    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. 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.
    5. 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.
    6. Ian W. McKeague & Mourad Tighiouart, 2000. "Bayesian Estimators for Conditional Hazard Functions," Biometrics, The International Biometric Society, vol. 56(4), pages 1007-1015, December.
    7. Krishna Saha & Sudhir Paul, 2005. "Bias-Corrected Maximum Likelihood Estimator of the Negative Binomial Dispersion Parameter," Biometrics, The International Biometric Society, vol. 61(1), pages 179-185, March.
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    Cited by:

    1. 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.
    2. 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.

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