Bayesian mixed model for survival data with semicompeting risks based on the Clayton copula

Motivated by a chronic kidney disease dataset, we propose a Bayesian model for clustered semicompeting risks data based on Archimedean copulas, allowing for treatment switching. We consider the modeling of both independent and clustered observations. For clustered data, random effects are included to consider the dependence among observations in the same group. For the Clayton copula, we provide theoretical results for the posterior distribution when improper priors are used. A simulation study was conducted to evaluate the performance of the proposed model. Finally, the results of the analysis of chronic kidney disease data are discussed.