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Bayesian semiparametric modeling of survival data based on mixtures of B-spline distributions


  • Cai, Bo
  • Meyer, Renate


The nonparametric part of a semiparametric regression model usually involves prior specification for an infinite-dimensional parameter F. This paper introduces a class of finite mixture models based on B-spline distributions as an approximation to priors on the set of cumulative distribution functions. This class includes the mixture of beta distributions of Diaconis and Ylvisaker (1985) and the mixtures of triangular distributions of Perron and Mengersen (2001) as special cases. We describe how this approach can be used to model the baseline hazards in a Bayesian stratified proportional hazards model. A numerical illustration is given using survival data from a multicenter clinical AIDS trial, thus generalizing the approach by Carlin and Hodges (1999). Using conditional predictive ordinates and the deviance information criterion, we compare the fit of hierarchical proportional hazards regression models based on mixtures of B-spline distributions of various degrees.

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  • Cai, Bo & Meyer, Renate, 2011. "Bayesian semiparametric modeling of survival data based on mixtures of B-spline distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1260-1272, March.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:3:p:1260-1272

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    References listed on IDEAS

    1. Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
    2. F. Perron & K. Mengersen, 2001. "Bayesian Nonparametric Modeling Using Mixtures of Triangular Distributions," Biometrics, The International Biometric Society, vol. 57(2), pages 518-528, June.
    3. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
    4. Gelfand, Alan E. & Kottas, Athanasios & MacEachern, Steven N., 2005. "Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1021-1035, September.
    5. Robert, Christian P. & Mengersen, Kerrie L., 1999. "Reparameterisation Issues in Mixture Modelling and their bearing on MCMC algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 29(3), pages 325-343, January.
    6. Bradley P. Carlin & James S. Hodges, 1999. "Hierarchical Proportional Hazards Regression Models for Highly Stratified Data," Biometrics, The International Biometric Society, vol. 55(4), pages 1162-1170, December.
    7. 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.
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, January.
    9. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, January.
    10. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
    11. Meyer, Renate & Cai, Bo & Perron, François, 2008. "Adaptive rejection Metropolis sampling using Lagrange interpolation polynomials of degree 2," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3408-3423, March.
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