A class of hazard rate mixtures for combining survival data from different experiments

Journal of the American Statistical Association

Volumn 109, Issue 506, 2014, Pages 802-814

  Lijoi, Antonio ^a,c   Nipoti, Bernardo ^b,c  

^a UNIVERSITY OF PAVIA   (Italy)

^b UNIVERSITY OF TURIN   (Italy)

^c Collegio Carlo Alberto ^*  (Italy)

Author keywords

Bayesian nonparametrics; Completely random measures; Dependent processes; Extended gamma processes; Partial exchangeability

Indexed keywords

EID: 84922269022     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.2013.869499     Document Type: Article

References (40)

1. Aalen, O. O., Borgan, Ø., and Gjessing, H. K. (2008), Survival and EventHistory Analysis, New York: Springer.
2. Antoniak, C. (1974), “Mixtures of Dirichlet Processes With Applications to Bayesian Nonparametric Problems,” The Annals of Statistics, 2, 1152–1174.
3. Choi, S., and Huang, X. (2012), “A General Class of Semiparametric Transformation Frailty Models for Nonproportional Hazards Survival Data,” Biometrics, 68, 1126–1135.
4. Cox, D. (1972), Regression Models and Life Tables” (with discussion), Journal of the Royal Statistical Society, Series A, 34, 187–202.
5. Damien, P., and Walker, S. (2002), “Bayesian Nonparametric Nonproportional Hazards Survival Modeling,” Scand inavian Journal of Statistics, 29, 51–56.
6. De Blasi, P., Peccati, G., and Prünster, I. (2009), “Asymptotics for Posterior Hazards,” The Annals of Statistics, 37, 1906–1945.
7. De Iorio, M., Johnson, W., Müller, P., and Rosner, G. (2009), “Bayesian Nonparametric Nonproportional Hazards Survival Modeling,” Biometrics, 65, 762–771.
8. De Iorio, M., Müller, P., Rosner, G., and MacEachern, S. (2004), “An ANOVA Model for Dependent Rand om Measures,” Journal of the American Statistical Association, 99, 205–215.
9. Doksum, K. (1974), “Tailfree and Neutral Rand om Probabilities and Their Posterior Distributions,” The Annals of Probability, 2, 183–201.
10. Dykstra, R., and Laud, P. (1981), “A Bayesian Nonparametric Approach to Reliability,” The Annals of Statistics, 9, 356–367.
11. Epifani, I., and Lijoi, A. (2010), “Nonparametric Priors for Vectors of Survival Functions,” Statistica Sinica, 20, 1455–1484.
12. Ferguson, T. (1974), “Prior Distributions on Spaces of Probability Measures,” The Annals of Statistics, 2, 615–629.
13. Ferguson, T., and Phadia, E. (1979), “Bayesian Nonparametric EstimationBased on Censored Data,” The Annals of Statistics, 7, 163–186.
14. Gjessing, H. K., Aalen, O. O., and Hjort, N. L. (2003), “Frailty Models Based on Lévy Processes,” Advances in Applied Probability, 35, 532–550.
15. Griffin, J., Kolossiatis, M., and Steel, M. (2013), “Comparing Distributions by Using Dependent Normalized Rand om-Measure Mixtures,” Journal of the Royal Statistical Society, Series B, 75, 499–529.
16. Griffin, J., and Steel, M. (2008), “Order–Based Dependent Dirichlet Processes,” Journal of the American Statistical Association, 101, 179–194.
17. Griffiths, R., and Milne, R. (1978), “A Class of Bivariate Poisson Processes,” Journal of Multivariate Analysis, 8, 380–395.
18. Hanson, T., Jara, A., and Zhao, L. (2012), “A Bayesian Semiparametric Temporally Stratified Proportional Hazards Model With Spatial Frailties,” Bayesian Analysis, 7, 147–188.
19. Hougaard, P. (2000), Analysis of Multivariate Survival Data, New York: Springer..
20. Ishwaran, H., and James, L. (2004), “Computational Methods for Multiplicative Intensity Models UsingWeighted Gamma Processes: Proportional Hazards, Marked Point Processes, and Panel Count Data,” Journal of the American Statistical Association, 99, 175–190.
21. James, L. (2003), “Bayesian Calculus for Gamma Processes With Applications to Semiparametric Intensity Models,” Sankhyā, 65, 179–206.
22. James, L. (2005), “Bayesian Poisson Process Partition Calculus With an Application to Bayesian Lévy Moving Averages,” The Annals of Statistics, 33, 1771–1799.
23. Jara, A., and Hanson, T. (2011), “A Class of Mixtures of Dependent Tail–Free Processes,” Biometrika, 98, 553–566.
24. Kalbfleish, J., and Prentice, R. (2002), The Statistical Analysis of Failure Time Data, New York: Wiley.
25. Klein, J., and Moeschberger, M. (1997), Survival Analysis. Techniques for Censored and Truncated Data, New York: Springer-Verlag.
26. Lawless, J. (1982), Statistical Models and Methods for Lifetime Data, Chichester: Wiley.
27. Lee, E., Wei, L., and Ying, Z. (1993), “Linear Regression Analysis for Highly Stratified Failure Time Data,” Journal of the American Statistical Association, 88, 557–565.
28. Lijoi, A., Nipoti, B., and Prünster, I. (in press), “Bayesian Inference With Dependent Normalized Completely Rand om Measures,” Bernoulli, DOI: 10.3150/13-BEJ521.
29. Lijoi, A., and Prünster, I. (2010), “Models Beyond the Dirichlet Process,” in Bayesian Nonparametrics, eds. N. Hjort, C. Holmes, P. Müller, and S. Walker, Cambridge: Cambridge University Press, pp. 80–136.
30. Lo, A., and Weng, C. (1989), “On a Class of Bayesian Nonparametric Estimates. II. HazardRate Estimates,” Annals of the Institute of StatisticalMathematics, 41, 227–245.
31. MacEachern, S. (1999), “Dependent Nonparametric Processes,” in ASA Proceedings of the Section on Bayesian Statistical Science, American Statistical Association, Alexand ria, pp. 50–55.
32. MacEachern, S. (2000), “Dependent Dirichlet Processes,” unpublished manuscript, Department of Statistics, The Ohio State University.
33. Peccati, G., and Prünster, I. (2008), “Linear and Quadratic Functionals of Rand om Hazard Rates: An Asymptotic Analysis,” Annals of Applied Probability, 18, 1910–1943.
34. Rodríguez, A., Dunson, D., and Gelfand, A. (2008), “The Nested Dirichlet Process,” Journal of the American Statistical Association, 103, 1566–1581.
35. Susarla, V., and Van Ryzin, J. (1976), “Nonparametric Bayesian Estimation of Survival Curves From Incomplete Observations,” Journal of the American Statistical Association, 71, 897–902.
36. Teh, Y., Jordan, M., Beal, M. J., and Blei, D. (2006), “Hierarchical Dirichlet Processes,” Journal of the American Statistical Association, 101, 1566–1581.
37. Trippa, L., Müller, P., and Johnson, W. (2011), “The Multivariate Beta Process and an Extension of the Pólya Tree Model,” Biometrika, 98, 17–34.
38. Wolpert, R. L., Ickstadt, K., and Hansen, M. B. (2003), “A Nonparametric Bayesian Approach to Inverse Problems,” in Bayesian Statistics 7: Proceedings of the Seventh Valencia International Meeting, eds. Bernardo, J. M., et al., New York: Oxford University Press pp. 403–417.
39. Wong, W., and Ma, L. (2010), “Optional Pólya Tree and Bayesian Inference,” The Annals of Statistics, 38, 1433–1459.
40. Zeng, D., and Lin, D. (2007), “Maximum Likelihood Estimation in Semiparametric Regression Models With Censored Data,” Journal of the Royal Statistical Society, Series B, 69, 507–564.