Bayesian Case Influence Diagnostics for Survival Models

Authors

  • Hyunsoon Cho,

    Corresponding author
    1. Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A.
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  • Joseph G. Ibrahim,

    Corresponding author
    1. Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A.
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  • Debajyoti Sinha,

    Corresponding author
    1. Department of Statistics, Florida State University, Tallahassee, Florida 32306-4330, U.S.A.
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  • Hongtu Zhu

    Corresponding author
    1. Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A.
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email:hscho@bios.unc.edu

email:ibrahim@bios.unc.edu

email:sinhad@stat.fsu.edu

email:hzhu@bios.unc.edu

Abstract

Summary We propose Bayesian case influence diagnostics for complex survival models. We develop case deletion influence diagnostics for both the joint and marginal posterior distributions based on the Kullback–Leibler divergence (K–L divergence). We present a simplified expression for computing the K–L divergence between the posterior with the full data and the posterior based on single case deletion, as well as investigate its relationships to the conditional predictive ordinate. All the computations for the proposed diagnostic measures can be easily done using Markov chain Monte Carlo samples from the full data posterior distribution. We consider the Cox model with a gamma process prior on the cumulative baseline hazard. We also present a theoretical relationship between our case-deletion diagnostics and diagnostics based on Cox's partial likelihood. A simulated data example and two real data examples are given to demonstrate the methodology.

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