Jospeph Ibrahim
Department of Biostatistics
University of North Carolina at Chapel Hill
A Class of Bayesian Box-Cox Transformation Hazard Regression Models
We propose a class of Box-Cox transformation hazard models for
right-censored failure time data. It includes the proportional hazards
model and the additive hazards model as two special cases. Due to the
requirement of a nonnegative hazard function, complex multidimensional
parameter constraints must be imposed in the model formulation. In the
Bayesian paradigm, the nonlinear parameter constraint poses many new
computational challenges. We propose a prior specification scheme which
facilitates a tractable computational algorithm. The joint priors are
constructed 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 fitting adequacy is evaluated using the Conditional
Predictive Ordinate and the Deviance Information Criterion. This new class
of models is illustrated with a real dataset involving a melanoma clinical
trial. Extensions to frailty models and cure rate models are also
discussed.
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