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Bayesian bivariate survival analysis using the power variance function copula.

Jose S Romeo1,2, Renate Meyer3, Diego I Gallardo4

  • 1Department of Mathematics, University of Santiago, Santiago, Chile. jose.romeo@usach.cl.

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Summary
This summary is machine-generated.

This study introduces a one-stage Bayesian approach for analyzing multivariate survival data, offering a unified method for Power Variance Function (PVF) copulas. The new Bayesian technique simultaneously estimates marginal and PVF copula parameters, improving upon existing two-stage frequentist methods.

Keywords:
Archimedean copulasBayesian analysisDependenceMultivariate survival analysis

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Area of Science:

  • Statistics
  • Biostatistics
  • Survival Analysis

Background:

  • Copula models are vital for understanding dependence in multivariate survival data.
  • Power Variance Function (PVF) copulas offer a flexible framework, encompassing common copulas like Clayton and Gumbel.
  • Existing frequentist methods use a two-stage estimation process for marginal and copula parameters.

Purpose of the Study:

  • To develop and evaluate a one-stage Bayesian approach for simultaneously estimating marginal distributions and PVF copula parameters.
  • To provide a unified and efficient method for modeling complex dependence structures in survival data.
  • To explore both parametric and semiparametric models for marginal distributions within the Bayesian framework.

Main Methods:

  • A novel one-stage Bayesian methodology is proposed for simultaneous estimation.
  • The approach incorporates both parametric (e.g., Weibull) and semiparametric (e.g., piecewise exponential) models for marginal distributions.
  • A new simulation method using conditional sampling and numerical approximation is introduced for generating data with PVF dependence.

Main Results:

  • The Bayesian approach demonstrates favorable small sample properties in simulation studies.
  • Simultaneous estimation of marginal and PVF copula parameters is achieved effectively.
  • The methodology is successfully applied to real-world twin data, showcasing its practical utility.

Conclusions:

  • The one-stage Bayesian method offers an effective alternative to traditional two-stage frequentist procedures for PVF copula modeling.
  • This unified approach enhances the analysis of multivariate survival data, particularly in complex scenarios.
  • The flexibility in modeling marginal distributions (parametric/semiparametric) adds to the method's applicability.