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Bayesian local influence for survival models

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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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Authors and Affiliations

  1. Department of Biostatistics, School of Public Health, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599-7420, USA

    Joseph G. Ibrahim & Hongtu Zhu

  2. Department of Statistics, Yunnan University, Kunming, People’s Republic of China

    Niansheng Tang

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  1. Joseph G. Ibrahim
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  2. Hongtu Zhu
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  3. Niansheng Tang
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Correspondence to Joseph G. Ibrahim.

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Ibrahim, J.G., Zhu, H. & Tang, N. Bayesian local influence for survival models. Lifetime Data Anal 17, 43–70 (2011). https://doi.org/10.1007/s10985-010-9170-0

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