Nonparametric Bayesian survival analysis using mixtures of Weibull distributions. (English) Zbl 1079.62095

Summary: Bayesian nonparametric methods have been applied to survival analysis problems since the emergence of the area of Bayesian nonparametrics. However, the use of the flexible class of Dirichlet process mixture models has been rather limited in this context. This is, arguably, to a large extent due to the standard way of fitting such models that precludes full posterior inference for many functionals of interest in survival analysis applications. To overcome this difficulty, we provide a computational approach to obtain the posterior distribution of general functionals of a Dirichlet process mixture. We model the survival distribution employing a flexible Dirichlet process mixture, with a Weibull kernel, that yields rich inference for several important functionals. In the process, a method for hazard function estimation emerges. Methods for simulation-based model fitting, in the presence of censoring, and for prior specification are provided. We illustrate the modeling approach with simulated and real data.


62N02 Estimation in survival analysis and censored data
62F15 Bayesian inference
62P10 Applications of statistics to biology and medical sciences; meta analysis
62G05 Nonparametric estimation
65C60 Computational problems in statistics (MSC2010)
Full Text: DOI


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