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Mixtures of Polya trees for flexible spatial frailty survival modelling

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  • Luping Zhao
  • Timothy E. Hanson
  • Bradley P. Carlin

Abstract

Mixtures of Polya trees offer a very flexible nonparametric approach for modelling time-to-event data. Many such settings also feature spatial association that requires further sophistication, either at the point level or at the lattice level. In this paper, we combine these two aspects within three competing survival models, obtaining a data analytic approach that remains computationally feasible in a fully hierarchical Bayesian framework using Markov chain Monte Carlo methods. We illustrate our proposed methods with an analysis of spatially oriented breast cancer survival data from the Surveillance, Epidemiology and End Results program of the National Cancer Institute. Our results indicate appreciable advantages for our approach over competing methods that impose unrealistic parametric assumptions, ignore spatial association or both. Copyright 2009, Oxford University Press.

Suggested Citation

  • Luping Zhao & Timothy E. Hanson & Bradley P. Carlin, 2009. "Mixtures of Polya trees for flexible spatial frailty survival modelling," Biometrika, Biometrika Trust, vol. 96(2), pages 263-276.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:2:p:263-276
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    File URL: http://hdl.handle.net/10.1093/biomet/asp014
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    Citations

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    Cited by:

    1. Lin Zhang & Inyoung Kim, 2021. "Finite mixtures of semiparametric Bayesian survival kernel machine regressions: Application to breast cancer gene pathway subgroup analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 251-269, March.
    2. Luping Zhao & Timothy E. Hanson, 2011. "Spatially Dependent Polya Tree Modeling for Survival Data," Biometrics, The International Biometric Society, vol. 67(2), pages 391-403, June.
    3. Wolter, James Lewis, 2016. "Kernel estimation of hazard functions when observations have dependent and common covariates," Journal of Econometrics, Elsevier, vol. 193(1), pages 1-16.
    4. Angela Schörgendorfer & Adam J. Branscum & Timothy E. Hanson, 2013. "A Bayesian Goodness of Fit Test and Semiparametric Generalization of Logistic Regression with Measurement Data," Biometrics, The International Biometric Society, vol. 69(2), pages 508-519, June.
    5. Y. Hagar & M. Hayden & C. Wiedinmyer & V. Dukic, 2017. "Comparison of Models Analyzing a Small Number of Observed Meningitis Cases in Navrongo, Ghana," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(1), pages 76-104, March.
    6. Haiming Zhou & Timothy Hanson & Jiajia Zhang, 2017. "Generalized accelerated failure time spatial frailty model for arbitrarily censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(3), pages 495-515, July.

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