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Bayesian nonparametric estimation of survival functions with multiple-samples information. (English) Zbl 1473.62329

Summary: 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 I. Epifani and A. Lijoi [Stat. Sin. 20, No. 4, 1455–1484 (2010; Zbl 1200.62121)] 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.

MSC:

62N02 Estimation in survival analysis and censored data
62G05 Nonparametric estimation
60G51 Processes with independent increments; Lévy processes
60G57 Random measures

Citations:

Zbl 1200.62121

Software:

invGauss
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References:

[1] Aalen, O., Borgan, O., and Gjessing, H. (2008)., Survival and event history analysis: a process point of view. Springer Science & Business Media. · Zbl 1204.62165
[2] Cont, R. and Tankov, P. (2004)., Financial modelling with jump processes. Chapman & Hall. · Zbl 1052.91043
[3] De Iorio, M., Johnson, W. O., Müller, P., & Rosner, G. L. (2009). Bayesian nonparametric nonproportional hazards survival modeling., Biometrics, 65, 762-771. · Zbl 1172.62073
[4] Doksum, K. (1974). Tailfree and neutral random probabilities and their posterior distributions., The Annals of Probability, 2, 183-201. · Zbl 1172.62073
[5] Dykstra, R. L. and Laud, P. (1981). A Bayesian nonparametric approach to reliability., The Annals of Statistics, 9, 356-367. · Zbl 0279.60097
[6] Epifani, I. and Lijoi. A. (2010). Nonparametric priors for vectors of survival functions., Statistica Sinica, 20, 1455-1484. · Zbl 0469.62077
[7] Ferguson, T. S., and Phadia, E. G. (1979). Bayesian nonparametric estimation based on censored data., The Annals of Statistics, 7, 163-186. · Zbl 1200.62121
[8] 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. · Zbl 0401.62031
[9] 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. · Zbl 1089.62520
[10] Kallsen, J. and Tankov, P. (2006). Characterization of dependence of multidimensional Lèvy processes using Lèvy copulas., Journal of Multivariate Analysis, 97, 1551-1572. · Zbl 1089.62520
[11] Kingman, J. (1967). Completely random measures., Pacific Journal of Mathematics, 21, 59-78. · Zbl 1099.62048
[12] Leisen, F., and Lijoi, A. (2011) Vectors of two-parameter Poisson-Dirichlet processes., Journal of Multivariate Analysis, 102, 482-495. · Zbl 0155.23503
[13] Leisen F., Lijoi A. and Spano D. (2013). A Vector of Dirichlet processes., Electronic Journal of Statistics, 7, 62-90. · Zbl 1207.62062
[14] 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. · Zbl 1328.60124
[15] 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. · Zbl 1367.62281
[16] MacEachern S. N. (1999). Dependent nonparametric processes. In, ASA Proceedings of the Section on Bayesian Statistical Science, Alexandria, VA: American Statistical Association. · Zbl 0716.62043
[17] Nelsen, Roger B. (2013)., An introduction to copulas. Springer Science & Business Media, 139. · Zbl 1152.62030
[18] 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. · Zbl 1152.62030
[19] 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. · Zbl 1320.62059
[20] 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. · Zbl 1320.62059
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