Electronic Journal of Statistics

Bayesian nonparametric estimation of survival functions with multiple-samples information

Alan Riva Palacio and Fabrizio Leisen

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In many real problems, dependence structures more general than exchangeability are required. For instance, in some settings partial exchangeability is a more reasonable assumption. For this reason, vectors of dependent Bayesian nonparametric priors have recently gained popularity. They provide flexible models which are tractable from a computational and theoretical point of view. In this paper, we focus on their use for estimating multivariate survival functions. Our model extends the work of Epifani and Lijoi (2010) to an arbitrary dimension and allows to model the dependence among survival times of different groups of observations. Theoretical results about the posterior behaviour of the underlying dependent vector of completely random measures are provided. The performance of the model is tested on a simulated dataset arising from a distributional Clayton copula.

Article information

Electron. J. Statist., Volume 12, Number 1 (2018), 1330-1357.

Received: April 2017
First available in Project Euclid: 3 May 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F15: Bayesian inference 60G57: Random measures
Secondary: 60G51: Processes with independent increments; Lévy processes

Bayesian nonparametrics Survival analysis Dependent completely random measures

Creative Commons Attribution 4.0 International License.


Riva Palacio, Alan; Leisen, Fabrizio. Bayesian nonparametric estimation of survival functions with multiple-samples information. Electron. J. Statist. 12 (2018), no. 1, 1330--1357. doi:10.1214/18-EJS1420. https://projecteuclid.org/euclid.ejs/1525334453

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  • Aalen, O., Borgan, O., and Gjessing, H. (2008)., Survival and event history analysis: a process point of view. Springer Science & Business Media.
  • Cont, R. and Tankov, P. (2004)., Financial modelling with jump processes. Chapman & Hall.
  • De Finetti, B. (1938). ’Sur la condition de ”equivalence partielle”’, Colloque consacré à la théorie des probabilités, Vol. VI, Université de Genève, Hermann et C. ie, Paris.
  • De Iorio, M., Johnson, W. O., Müller, P., & Rosner, G. L. (2009). Bayesian nonparametric nonproportional hazards survival modeling., Biometrics, 65, 762–771.
  • Doksum, K. (1974). Tailfree and neutral random probabilities and their posterior distributions., The Annals of Probability, 2, 183–201.
  • Dykstra, R. L. and Laud, P. (1981). A Bayesian nonparametric approach to reliability., The Annals of Statistics, 9, 356–367.
  • Epifani, I. and Lijoi. A. (2010). Nonparametric priors for vectors of survival functions., Statistica Sinica, 20, 1455–1484.
  • Ferguson, T. S., and Phadia, E. G. (1979). Bayesian nonparametric estimation based on censored data., The Annals of Statistics, 7, 163–186.
  • Griffin, J. and Leisen, F. (2017). Compound random measures and their use in Bayesian nonparametrics., Journal of the Royal Statistical Society - Series B, 79, 525–545.
  • Ishwaran, H., and James, L. F. (2004). Computational methods for multiplicative intensity models using weighted gamma processes: proportional hazards, marked point processes, and panel count data., Journal of the American Statistical Association, 99, 175–190.
  • Kallsen, J. and Tankov, P. (2006). Characterization of dependence of multidimensional Lèvy processes using Lèvy copulas., Journal of Multivariate Analysis, 97, 1551–1572.
  • Kingman, J. (1967). Completely random measures., Pacific Journal of Mathematics, 21, 59–78.
  • Leisen, F., and Lijoi, A. (2011) Vectors of two-parameter Poisson–Dirichlet processes., Journal of Multivariate Analysis, 102, 482–495.
  • Leisen F., Lijoi A. and Spano D. (2013). A Vector of Dirichlet processes., Electronic Journal of Statistics, 7, 62–90.
  • Lijoi A., and Nipoti B. (2014). A class of hazard rate mixtures for combining survival data from different experiments, Journal of the American Statistical Association, 109, 802–814.
  • Lo, A. Y., and Weng, C. S. (1989). On a class of Bayesian nonparametric estimates: II. Hazard rate estimates., Annals of the Institute of Statistical Mathematics, 41, 227–245.
  • MacEachern S. N. (1999). Dependent nonparametric processes. In, ASA Proceedings of the Section on Bayesian Statistical Science, Alexandria, VA: American Statistical Association.
  • Nelsen, Roger B. (2013)., An introduction to copulas. Springer Science & Business Media, 139.
  • Nieto-Barajas, L. E. (2014). Bayesian semiparametric analysis of short-and long-term hazard ratios with covariates., Computational Statistics and Data Analysis, 71, 477–490.
  • Zhu, W., and Leisen, F. (2015). “A multivariate extension of a vector of two-parameter Poisson–Dirichlet processes.”, Journal of Nonparametric Statistics, 27, 89–105.