Bayesian local influence for survival models |
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Authors: | Email author" target="_blank">Joseph?G?IbrahimEmail author Hongtu?Zhu Niansheng?Tang |
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Institution: | (1) Division of Biostatistics, University of Minnesota, Minneapolis, MN 55455, USA;(2) Departments of Biostatistics, Statistics, and Epidemiology, University of Kentucky, Lexington, KY 40536, USA;(3) Department of Statistics, University of California, Irvine, Irvine, CA 92697, USA |
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Abstract: | The aim of this paper is to develop a Bayesian local influence method (Zhu et al. 2009, submitted) for assessing minor perturbations
to the prior, the sampling distribution, and individual observations in survival analysis. We introduce a perturbation model
to characterize simultaneous (or individual) perturbations to the data, the prior distribution, and the sampling distribution.
We construct a Bayesian perturbation manifold to the perturbation model and calculate its associated geometric quantities
including the metric tensor to characterize the intrinsic structure of the perturbation model (or perturbation scheme). We
develop local influence measures based on several objective functions to quantify the degree of various perturbations to statistical
models. We carry out several simulation studies and analyze two real data sets to illustrate our Bayesian local influence
method in detecting influential observations, and for characterizing the sensitivity to the prior distribution and hazard
function. |
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Keywords: | |
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