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A class of Bayesian shared gamma frailty models with multivariate failure time data.

Guosheng Yin1, Joseph G Ibrahim

  • 1Department of Biostatistics, M. D. Anderson Cancer Center, The University of Texas, Houston, Texas 77030, USA. gsyin@mdanderson.org

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We introduce flexible shared gamma frailty models for multivariate failure time data using Box-Cox transformations. These models offer broad applicability and include existing models as special cases, simplifying Bayesian analysis.

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Area of Science:

  • Statistics
  • Biostatistics
  • Survival Analysis

Background:

  • Multivariate failure time data analysis is crucial in many fields.
  • Existing shared gamma frailty models have limitations in flexibility.
  • Bayesian computation for these models can be challenging due to constraints.

Purpose of the Study:

  • To propose a novel, flexible class of shared gamma frailty models for multivariate failure time data.
  • To incorporate Box-Cox transformations to generalize hazard function relationships.
  • To develop a computationally feasible Bayesian approach for these models.

Main Methods:

  • A new class of shared gamma frailty models is proposed using Box-Cox transformation on the hazard function.
  • Joint priors are constructed via conditional-marginal specification to handle nonlinear constraints.
  • Gibbs sampling is employed for Bayesian inference, facilitated by the prior structure.

Main Results:

  • The proposed models encompass Cox and additive gamma frailty models as special cases.
  • The conditional-marginal prior specification simplifies constrained Bayesian computation.
  • The methodology is demonstrated effectively using a real-world dataset.

Conclusions:

  • The novel shared gamma frailty models offer enhanced flexibility for multivariate survival data.
  • The proposed Bayesian computational strategy effectively addresses the challenges posed by constraints.
  • This approach provides a valuable tool for analyzing complex failure time data.