Institute of Mathematical Statistics Lecture Notes - Monograph Series

Bayesian transformation hazard models

Joseph G. Ibrahim and Gousheng Yin

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196283960

Digital Object Identifier
doi:10.1214/074921706000000446

Mathematical Reviews number (MathSciNet)
MR2337834

Zentralblatt MATH identifier
1268.62034

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

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

Rights
Copyright © 2006, Institute of Mathematical Statistics

Citation

Yin, Gousheng; Ibrahim, Joseph G. Bayesian transformation hazard models. Optimality, 170--182, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000446. https://projecteuclid.org/euclid.lnms/1196283960


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