The Bernstein-Von Mises Theorem in Semiparametric Competing Risks Models

Semiparametric Bayesian models are nowadays a popular tool in survival analysis. An important area of research concerns the investigation of frequentist properties of these models. In this paper, a Bernstein-von Mises theorem is derived for semiparametric Bayesian models of competing risks data. The cause-specific hazard is taken as the product of the conditional probability of a failure type and the overall hazard rate. We model the conditional probability as a smooth function of time and leave the cumulative overall hazard unspecified. A prior distribution is defined on the joint parameter space, which includes a beta process prior for the cumulative overall hazard. We show that the posterior distribution for any differentiable functional of interest is asymptotically equivalent to the sampling distribution derived from maximum likelihood estimation. A simulation study is provided to illustrate the coverage properties of credible intervals on cumulative incidence functions.