Bayesian frailty models based on box-cox transformed hazards

Abstract

Due to natural or artificial clustering, multivariate failure time data often arise in biomedical research. To account for the intracluster correlation, we propose a novel class of frailty models by imposing the Box-Cox transformation on the hazard functions. This class of models generalizes the relationships between the baseline hazard and the hazard functions, which includes the proportional and the additive hazards frailty models as two special cases. Since hazards cannot be negative, complex multidimensional nonlinear parameter constraints must be imposed in the model formulation. To facilitate a tractable computational algorithm, the joint priors are constructed through a conditional-marginal specification. The conditional distribution of the prior specification is univariate and absorbs the parameter constraints, while the marginal part is free of constraints. We propose a Markov chain Monte Carlo (MCMC) computational scheme for sampling from the posterior distribution of the parameters. We derive an MCMC approximation for the conditional predictive ordinate to assess model adequacy, and illustrate the proposed method with a dataset.