Vine copula based inference of multivariate event time data

In many studies multivariate event time data are generated from clusters of equal size. Flexible models are needed to capture the possibly complex association pattern in such data. 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. We develop likelihood based inference for clustered right-censored event time data using vine copulas. Due to the right-censoring single and double integrals show up in the likelihood expression and numerical integration is needed for the likelihood evaluation. A simulation study for three-dimensional data provides evidence for the good finite sample performance of the proposed method. Using a four-dimensional data set from veterinary medicine, we show how an appropriate vine copula model can be selected for the data at hand.