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Bayesian Transformation Models for Multivariate Survival Data

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  • Mário Castro
  • Ming-Hui Chen
  • Joseph G. Ibrahim
  • John P. Klein

Abstract

type="main" xml:id="sjos12010-abs-0001"> In this paper, we propose a general class of Gamma frailty transformation models for multivariate survival data. The transformation class includes the commonly used proportional hazards and proportional odds models. The proposed class also includes a family of cure rate models. Under an improper prior for the parameters, we establish propriety of the posterior distribution. A novel Gibbs sampling algorithm is developed for sampling from the observed data posterior distribution. A simulation study is conducted to examine the properties of the proposed methodology. An application to a data set from a cord blood transplantation study is also reported.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:1:p:187-199
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    References listed on IDEAS

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    1. 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.
    2. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
    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. Donglin Zeng & Qingxia Chen & Joseph G. Ibrahim, 2009. "Gamma frailty transformation models for multivariate survival times," Biometrika, Biometrika Trust, vol. 96(2), pages 277-291.
    5. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    6. D. Zeng & D. Y. Lin, 2007. "Maximum likelihood estimation in semiparametric regression models with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 507-564, September.
    7. Chen, Qingxia & Zeng, Donglin & Ibrahim, Joseph G., 2007. "Sieve Maximum Likelihood Estimation for Regression Models With Covariates Missing at Random," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1309-1317, December.
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