We propose a novel and general class of Box-Cox transformation models on the hazard functions for right censored survival data. This new class of models allows a very broad range of shapes and relationships between the baseline hazard as well as the hazard function. It includes the Cox proportional hazards model and the additive hazards model as two special cases. Several properties of the model are derived, and interpretations as well as illustrations of the behavior of the Box-Cox transformation parameter are provided. A novel class of joint prior distributions is proposed for the model parameters. Due to the requirement of a positive hazard function in the survival model, complex multidimensional nonlinear parameter constraints must be imposed in the model formulation. As a result, computations for this new Bayesian model pose many new challenges. We propose an efficient Markov chain Monte Carlo (MCMC) computational scheme for sampling from the posterior distribution of the parameters. The proposed prior distributions facilitate a tractable computational algorithm. The joint priors are constructed through a conditional-marginal specification, in which the conditional distribution is univariate, and one which absorbs all of the non-linear parameter constraints. The marginal part of the prior specification is free of any constraints. This novel class of prior distributions allows us to easily compute the full conditionals needed for Gibbs sampling, incorporating the constraints, and hence implement the Markov chain Monte Carlo algorithm in a relatively straightforward fashion. This new class of models is illustrated with a detailed simulation study as well as a real dataset involving a melanoma clinical trial.
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