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Bayesian Semiparametric Cure Rate Model with an Unknown Threshold

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  • LUIS E. NIETO‐BARAJAS
  • GUOSHENG YIN

Abstract

. We propose a Bayesian semiparametric model for survival data with a cure fraction. We explicitly consider a finite cure time in the model, which allows us to separate the cured and the uncured populations. We take a mixture prior of a Markov gamma process and a point mass at zero to model the baseline hazard rate function of the entire population. We focus on estimating the cure threshold after which subjects are considered cured. We can incorporate covariates through a structure similar to the proportional hazards model and allow the cure threshold also to depend on the covariates. For illustration, we undertake simulation studies and a full Bayesian analysis of a bone marrow transplant data set.

Suggested Citation

  • Luis E. Nieto‐Barajas & Guosheng Yin, 2008. "Bayesian Semiparametric Cure Rate Model with an Unknown Threshold," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 540-556, September.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:3:p:540-556
    DOI: 10.1111/j.1467-9469.2007.00589.x
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    References listed on IDEAS

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    1. Judy P. Sy & Jeremy M. G. Taylor, 2000. "Estimation in a Cox Proportional Hazards Cure Model," Biometrics, The International Biometric Society, vol. 56(1), pages 227-236, March.
    2. K. F. Lam & Hongqi Xue, 2005. "A semiparametric regression cure model with current status data," Biometrika, Biometrika Trust, vol. 92(3), pages 573-586, September.
    3. 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.
    4. Wenbin Lu, 2004. "On semiparametric transformation cure models," Biometrika, Biometrika Trust, vol. 91(2), pages 331-343, June.
    5. Rebecca A. Betensky & David A. Schoenfeld, 2001. "Nonparametric Estimation in a Cure Model with Random Cure Times," Biometrics, The International Biometric Society, vol. 57(1), pages 282-286, March.
    6. Yingwei Peng & Keith B. G. Dear, 2000. "A Nonparametric Mixture Model for Cure Rate Estimation," Biometrics, The International Biometric Society, vol. 56(1), pages 237-243, March.
    7. Luis E. Nieto‐Barajas & Stephen G. Walker, 2002. "Markov Beta and Gamma Processes for Modelling Hazard Rates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 413-424, September.
    8. 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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    Cited by:

    1. Sandip Barui & Grace Y. Yi, 2020. "Semiparametric methods for survival data with measurement error under additive hazards cure rate models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 421-450, July.
    2. Wende Clarence Safari & Ignacio López-de-Ullibarri & María Amalia Jácome, 2023. "Latency function estimation under the mixture cure model when the cure status is available," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 608-627, July.
    3. Bertrand, A. & Legrand, C. & Léonard, D. & Van Keilegom, I., 2017. "Robustness of estimation methods in a survival cure model with mismeasured covariates," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 3-18.
    4. Mário Castro & Ming-Hui Chen & Joseph G. Ibrahim & John P. Klein, 2014. "Bayesian Transformation Models for Multivariate Survival Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 187-199, March.
    5. 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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