Institute of Mathematical Statistics Lecture Notes - Monograph Series

Bayesian transformation hazard models

Joseph G. Ibrahim and Gousheng Yin

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We propose a class of transformation hazard models for rightcensored failure time data. It includes the proportional hazards model (Cox) and the additive hazards model (Lin and Ying) as special cases. Due to the requirement of a nonnegative hazard function, multidimensional parameter constraints must be imposed in the model formulation. In the Bayesian paradigm, the nonlinear parameter constraint introduces many new computational challenges. We propose a prior through a conditional-marginal specification, in which the conditional distribution is univariate, and absorbs all of the nonlinear parameter constraints. The marginal part of the prior specification is free of any constraints. This class of prior distributions allows us to easily compute the full conditionals needed for Gibbs sampling, and hence implement the Markov chain Monte Carlo algorithm in a relatively straightforward fashion. Model comparison is based on the conditional predictive ordinate and the deviance information criterion. This new class of models is illustrated with a simulation study and a real dataset from a melanoma clinical trial.

Chapter information

Javier Rojo, ed., Optimality: The Second Erich L. Lehmann Symposium (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 170-182

First available in Project Euclid: 28 November 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62N01: Censored data models
Secondary: 62N02: Estimation 62C10: Bayesian problems; characterization of Bayes procedures

additive hazards Bayesian inference constrained parameter CPO, DIC piecewise exponential distributio proportional hazards

Copyright © 2006, Institute of Mathematical Statistics


Yin, Gousheng; Ibrahim, Joseph G. Bayesian transformation hazard models. Optimality, 170--182, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000446.

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