Lifetime Data Analysis

, Volume 17, Issue 1, pp 43–70

Bayesian local influence for survival models

Article

DOI: 10.1007/s10985-010-9170-0

Cite this article as:
Ibrahim, J.G., Zhu, H. & Tang, N. Lifetime Data Anal (2011) 17: 43. doi:10.1007/s10985-010-9170-0
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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.

Keywords

Bayesian local influenceBayesian perturbation manifoldPerturbed modelPosterior distributionPriorSurvival model

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Joseph G. Ibrahim
    • 1
  • Hongtu Zhu
    • 1
  • Niansheng Tang
    • 2
  1. 1.Department of Biostatistics, School of Public HealthUniversity of North Carolina at Chapel HillChapel HillUSA
  2. 2.Department of StatisticsYunnan UniversityKunmingPeople’s Republic of China