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Bayesian Inference for Multivariate Survival Data with a Cure Fraction

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  • Chen, Ming-Hui
  • Ibrahim, Joseph G.
  • Sinha, Debajyoti
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    Abstract

    We develop Bayesian methods for right censored multivariate failure time data for populations with a cure fraction. We propose a new model, called the multivariate cure rate model, and provide a natural motivation and interpretation of it. To create the correlation structure between the failure times, we introduce a frailty term, which is assumed to have a positive stable distribution. The resulting correlation structure induced by the frailty term is quite appealing and leads to a nice characterization of the association between the failure times. Several novel properties of the model are derived. First, conditional on the frailty term, it is shown that the model has a proportional hazards structure with the covariates depending naturally on the cure rate. Second, we establish mathematical relationships between the marginal survivor functions of the multivariate cure rate model and the more standard mixture model for modelling cure rates. With the introduction of latent variables, we show that the new model is computationally appealing, and novel computational Markov chain Monte Carlo (MCMC) methods are developed to sample from the posterior distribution of the parameters. Specifically, we propose a modified version of the collapsed Gibbs technique (J. S. Liu, 1994, J. Amer. Statist. Assoc.89, 958-966) to sample from the posterior distribution. This development will lead to an efficient Gibbs sampling procedure, which would otherwise be extremely difficult. We characterize the propriety of the joint posterior distribution of the parameters using a class of noninformative improper priors. A real dataset from a melanoma clinical trial is presented to illustrate the methodology.

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    File URL: http://www.sciencedirect.com/science/article/B6WK9-45V27TX-7/2/11f3d14ef9059c30ab5406d7eef79404
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 80 (2002)
    Issue (Month): 1 (January)
    Pages: 101-126

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    Handle: RePEc:eee:jmvana:v:80:y:2002:i:1:p:101-126

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    Related research

    Keywords: cure rate frailty model Gibbs sampling latent variables posterior distribution stable law;

    References

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    1. Asselain, B. & Fourquet, A. & Hoang, T. & Tsodikov, A. D. & Yakovlev, A. Yu., 1996. "A parametric regression model of tumor recurrence: An application to the analysis of clinical data on breast cancer," Statistics & Probability Letters, Elsevier, vol. 29(3), pages 271-278, September.
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    Cited by:
    1. Guoqing Diao & Guosheng Yin, 2012. "A general transformation class of semiparametric cure rate frailty models," Annals of the Institute of Statistical Mathematics, Springer, vol. 64(5), pages 959-989, October.
    2. Yu, Binbing & Peng, Yingwei, 2008. "Mixture cure models for multivariate survival data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1524-1532, January.
    3. Carvalho Lopes, Celia Mendes & Bolfarine, Heleno, 2012. "Random effects in promotion time cure rate models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 75-87, January.
    4. Niu, Yi & Peng, Yingwei, 2014. "Marginal regression analysis of clustered failure time data with a cure fraction," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 129-142.
    5. Borges, Patrick & Rodrigues, Josemar & Balakrishnan, Narayanaswamy, 2012. "Correlated destructive generalized power series cure rate models and associated inference with an application to a cutaneous melanoma data," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1703-1713.
    6. Chen, Chyong-Mei & Lu, Tai-Fang C., 2012. "Marginal analysis of multivariate failure time data with a surviving fraction based on semiparametric transformation cure models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 645-655.

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