Bayesian non-parametric frailty model for dependent competing risks in a repairable systems framework

The aim of this article is to analyze multiple repairable systems data under the presence of dependent competing risks. It is known that the dependence effect in this scenario influences the estimates of the model parameters. Hence, under the assumption that the cause-specific intensities follow a power law process (PLP), we propose a frailty-induced dependence approach to incorporate the dependence among the cause-specific recurrent processes. Moreover, the misspecification of the frailty distribution may lead to errors when estimating the parameters of interest. Because of this, we considered a nonparametric approach to model the frailty density using a Dirichlet process mixture prior, which offers more flexibility to provide consistent estimates for the PLP model, as well as insights about heterogeneity among the systems. We proposed an orthogonal parametrization for the PLP model parameters that allowed us to specify a joint prior distribution for the parameters that returned closed-form estimators for the posterior mean. Additionally, a hybrid MCMC sampler algorithm composed by Hamiltonian Monte Carlo and Gibbs sampling was built for computing the posterior estimates with respect to the frailty distribution. A simulation study was conducted to evaluate the efficiency of our estimates. This method was used to analyze a real dataset. Algorithms, code, and data are provided in supplementary material available online.