Nonparametric Bayesian survival analysis using mixtures of Weibull distributions |
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| Institution: | 1. School of Management, Shandong University, Jinan, China;2. College of Mathematics and Statistics, Shenzhen University, Shenzhen, China;3. Institute of Economics and Finance, Nanjing Audit University, Nanjing, China;4. Department of Statistics, Chinese University of Hong Kong, Hong Kong, China;1. Department of Statistics, University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA;2. Department of Statistics, University of Wisconsin–Madison, 1300 University Avenue, Madison, WI 53706, USA;3. Department of Entomology, University of Wisconsin–Madison, 1300 University Avenue, Madison, WI 53706, USA;1. Department of Community Health Sciences, Cumming School of Medicine, University of Calgary, 3280 Hospital Drive NW, Calgary, Alberta T2N 4Z6, Canada;2. O''Brien Institute for Public Health, University of Calgary, 3280 Hospital Drive NW, Calgary, Alberta T2N 4Z6, Canada;3. Department of Surgery, Cumming School of Medicine, University of Calgary, Foothills Medical Centre, 3280 Hospital Drive NW, Calgary, Alberta T2N 4Z6, Canada;4. Alberta Health Services, Foothills Medical Centre, 1403-29 Street NW, Calgary, Alberta T2N 2T9, Canada;5. Alberta Bone and Joint Health Institute, 3280 Hospital Drive NW, Calgary, Alberta T2N 4Z6, Canada;6. Department of Medicine, Cumming School of Medicine, University of Calgary, 3280 Hospital Drive NW, Calgary, Alberta T2N 4Z6, Canada;7. McCaig Institute for Bone and Joint Health, 3280 Hospital Drive NW, Calgary, Alberta T2N 4Z6, Canada;1. Université catholique de Louvain, Institut de Statistique, Biostatistique et Sciences Actuarielles, Voie du Roman Pays 20, B-1348 Louvain-la-Neuve, Belgium;2. Institut des sciences humaines et sociales, Méthodes quantitatives en sciences sociales, Université de Liège, boulevard du Rectorat 7, 4000 Liège, Belgium |
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| Abstract: | 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. |
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