  In many studies multivariate event time data are generated from clusters
having a possibly complex association pattern. Flexible models are needed to
capture this dependence. Vine copulas serve this purpose. Inference methods for
vine copulas are available for complete data. Event time data, however, are
often subject to right-censoring. As a consequence, the existing inferential
tools, e.g. likelihood estimation, need to be adapted. A two-stage estimation
approach is proposed. First, the marginal distributions are modeled. Second,
the dependence structure modeled by a vine copula is estimated via likelihood
maximization. Due to the right-censoring single and double integrals show up in
the copula likelihood expression such that numerical integration is needed for
its evaluation. For the dependence modeling a sequential estimation approach
that facilitates the computational challenges of the likelihood optimization is
provided. A three-dimensional simulation study provides evidence for the good
finite sample performance of the proposed method. Using four-dimensional
mastitis data, it is shown how an appropriate vine copula model can be selected
for data at hand.
