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Frailty modeling via the empirical Bayes–Hastings sampler

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  • Levine, Richard A.
  • Fan, Juanjuan
  • Strickland, Pamela Ohman
  • Demirel, Shaban

Abstract

Studies of ocular disease and analyses of time to disease onset are complicated by the correlation expected between the two eyes from a single patient. We overcome these statistical modeling challenges through a nonparametric Bayesian frailty model. While this model suggests itself as a natural one for such complex data structures, model fitting routines become overwhelmingly complicated and computationally intensive given the nonparametric form assumed for the frailty distribution and baseline hazard function. We consider empirical Bayesian methods to alleviate these difficulties through a routine that iterates between frequentist, data-driven estimation of the cumulative baseline hazard and Markov chain Monte Carlo estimation of the frailty and regression coefficients. We show both in theory and through simulation that this approach yields consistent estimators of the parameters of interest. We then apply the method to the short-wave automated perimetry (SWAP) data set to study risk factors of glaucomatous visual field deficits.

Suggested Citation

  • Levine, Richard A. & Fan, Juanjuan & Strickland, Pamela Ohman & Demirel, Shaban, 2012. "Frailty modeling via the empirical Bayes–Hastings sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1303-1318.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1303-1318
    DOI: 10.1016/j.csda.2011.09.004
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    References listed on IDEAS

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    1. Stephen G. Walker & Bani K. Mallick, 1997. "Hierarchical Generalized Linear Models and Frailty Models with Bayesian Nonparametric Mixing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 845-860.
    2. Hanson, Timothy E., 2006. "Inference for Mixtures of Finite Polya Tree Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1548-1565, December.
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